Indefinite Causal Order

Speculative If the order in which two operations act on a system can itself be placed in superposition — not the operations, not their inputs, but the order — then causal order is a resource a circuit can spend, the way it spends entanglement. That conditional is the whole subject. Every laboratory realisation so far controls the order with a single photon’s own polarisation or path, on a bench whose spacetime is flat and classical, and whether that counts is a live published argument, set out in section 4.

Established The magnitude is best stated as gate calls saved and channel capacity created, because those are the only two quantities anyone has measured. On the smallest instance of the gate-commutation problem — decide whether two unknown unitaries commute or anticommute — the best causally ordered quantum circuit must call one of the gates twice, and its maximum average success probability is 0.9288. The 2015 Vienna switch called each gate once and measured 0.973 ± 0.016 on Pauli pairs and 0.976 ± 0.015 averaged over 100 random gate pairs, at an interferometer visibility of 99.4 ± 0.2. Established That is a factor of two in gate calls and about 4.4 percentage points of success probability, on a problem with two gates in it. It is a real advantage and it is a small one, and eleven years later no larger instance has been run.

Frontier The prize that would justify the field is a separation that grows with problem size, and one has been claimed: a 2019 photonic experiment reported an exponential advantage in communication complexity from switching gate order. The 2024 Nature Reviews Physics survey lists it alongside super-Heisenberg metrological scaling, quantum battery charging, and channel activation in which two individually zero-capacity depolarising channels combined in a switch transmit a nonzero amount of quantum information. Speculative Each is a benchtop result with a few photons in it, and none has been reproduced on a platform that could scale.

Handwave The condition, stated plainly: this upside is real only if the advantage is attributable to indefinite causal order rather than to coherent control of channels, and two published results say it is not. A 2020 Grenoble analysis showed the advantage survives when the order is definite and only the channel choice is coherently controlled, so “causal indefiniteness plays no role”; a 2023 Toronto experiment superposed two zero-capacity channels and concluded that the expanded qutrit channel description “in itself is sufficient to explain the capacity enhancement without any use of superposition”. Speculative The gains are not in dispute. Their attribution is, and section 5 is about the fact that no experiment has yet been designed to separate the two explanations.

Established The formalism came first and the experiment came afterwards, which is unusual for a pre-paradigmatic subject and shapes everything about it. In 2012 Oreshkov, Costa and Brukner asked what correlations two parties can produce if each acts once inside a sealed laboratory and nothing whatever is assumed about a global order between them. The answer is the process matrix: an object that reduces to an ordinary quantum channel whenever an order exists, and does not reduce to one when it does not.

Established The formalism supplies two very different certificates, and confusing them is the single commonest error made about this field. A causal inequality is a bound obeyed by every probability distribution that can be written as a mixture of “A acted before B” and “B acted before A”. It is the causal analogue of a Bell inequality and it carries the same device-independent force: violate it and no account in terms of a definite order survives, whatever is inside the boxes. Established A causal witness is the analogue of an entanglement witness: an observable whose expectation value is bounded on all causally separable processes, computed from a tomographic model of the apparatus. A causal witness tells you what your process is, given that you already trust your description of your devices. A causal inequality tells you what nature is, given nothing.

Established The process that violates a causal inequality has no known physical realisation, and the process everyone can build cannot violate one. The Oreshkov–Costa–Brukner process is a mathematical object; nobody has proposed a physical system that implements it. The quantum switch, written down by Chiribella, D’Ariano, Perinotti and Valiron in 2013, is the one causally nonseparable process with a laboratory recipe: a control qubit in a superposition of two states routes a target through gate A then gate B on one branch and B then A on the other, and the branches are recombined coherently. Established It is causally nonseparable, and it is strictly weaker than the OCB process: it cannot produce correlations that violate any causal inequality.

Established That weakness was turned into a theorem in 2021. Purves and Short proved in Physical Review Letters that quantum experiments in which superpositions of temporal orders produce observable interference “can be simulated by a classical causal model, and therefore cannot violate a causal inequality”. Frontier A companion structural result by Wechs, Dourdent, Abbott and Branciard in 2021 identifies the quantum switch as a quantum-controlled circuit — a QC-QC — and shows that processes arising from quantum control of causal order “can only generate ‘causal’ correlations, compatible with a well-defined causal order”. The switch is not a machine for breaking causal order. It is a machine for making the order of two operations a quantum degree of freedom.

Frontier Whether that is the same thing is the disagreement the field is actually having. Oreshkov argued in 2019 that the switch genuinely realises indefinite causal structure, because the input and output systems of the two operations are time-delocalised subsystems — nontrivial subsystems of Hilbert spaces that are tensor products of spaces belonging to systems at different times — and that once those are recognised, the process is a circuit with a causal cycle rather than a simulation of one. Frontier Paunković and Vojinovic argued in 2020 that current optical implementations “do not feature superpositions of causal orders between spacetime events” at all, because the bench’s spacetime geometry is classical and definite; on their reading only superposed gravitational fields would do it. Speculative Both papers are in the same journal, neither has been withdrawn, and the dispute is about what a physical event is, not about any number either side expects to measure differently.

Established The measured record is a nine-year sequence of photonic experiments in which the certificate got progressively stronger and the platform did not change at all. Every result below is a table-top interferometer with single photons in it, run by one of about six groups.

Established 2015, first implementation. Procopio and ten co-authors at Vienna built a two-switch in a Mach–Zehnder interferometer, with the spatial mode as control and polarisation as target, and solved the commute-or-anticommute problem with one call to each gate: 0.973 ± 0.016 for Pauli gates, 0.976 ± 0.015 averaged over 100 random pairs, against a causally ordered ceiling of 0.9288. Frontier The authors were careful in a way later coverage was not, writing that the result “can be interpreted as a superposition of causal orders” and is “consistent with a causally non-separable process”.

Established 2017, first causal witness. Rubino and colleagues at Vienna reported the first experimental measurement of a causal witness, in Science Advances. The publisher’s page would not serve to this session, so the result is carried here on the authority of the 2024 Nature Reviews Physics survey, which describes it as the first such measurement and as the demonstration of causal non-separability.

Established 2018, the anchor: eighteen standard deviations. Goswami, Giarmatzi, Kewming, Costa, Branciard, Romero and White, at Brisbane, built a switch in which polarisation controls the order of two operations acting on the photon’s spatial modes — the inverse of the 2015 encoding, chosen to avoid that experiment’s limitations — and measured a causal witness 18 standard deviations beyond the definite-order bound, in Physical Review Letters 121, 090503. Frontier This is the result the commission for this brief named as its anchor, and it holds exactly as stated, with one correction recorded in section 15: the query-complexity advantage the commission attaches to it belongs to the 2015 Vienna experiment, three years earlier and on a different apparatus.

Established 2023, a stable platform. Strömberg, Schiansky, Peterson, Quintino and Walther demonstrated a quantum switch in a Sagnac configuration, whose common-path geometry is intrinsically stable against the path-length drift that limits Mach–Zehnder switches, and reported near-unity success probability on the channel-discrimination task. Frontier Nine years in, the engineering news is that the interferometer stopped drifting; that is an accurate measure of how fast the experimental side of this field moves.

Established 2023, the theoretical move that changed what an experiment could claim. Van der Lugt, Barrett and Chiribella derived, in Nature Communications 14, 5811, an inequality satisfied by every correlation obeying three assumptions: a hidden variable fixing a definite partial order on the agents; relativistic causality, in which spacelike-separated parties cannot influence one another and there is no retrocausation, which they stress is strictly weaker than Bell locality, requiring only parameter independence; and free interventions. Established The bound is 7/4, and the quantum switch reaches approximately 1.8536. This is the first certificate in the subject that does not require trusting the apparatus, and it is not a causal inequality in the 2012 sense — it buys device-independence with an extra relativistic assumption.

Established 2025–2026, the certificate measured, twice. A Beijing group — Qu, Lin, Xiao, Zhan and Xue — measured the van der Lugt–Barrett–Chiribella inequality at 1.8090 ± 0.0024 against the 1.75 bound, a violation of 24 standard deviations, with terms 0.4846 ± 0.0022, 0.4895 ± 0.0022 and 0.8348 ± 0.0023. Established They closed the locality loophole by putting 20 m of spacelike separation between two of the parties and the freedom-of-choice loophole with random number generators, and they state plainly that the fair-sampling assumption is retained. Established Independently, Richter, Antesberger, Cao, Walther and Rozema published in PRX Quantum 7, 010354 on 17 March 2026 a measurement of 1.8328 ± 0.0045, 18 standard deviations over the same bound, and describe their own experiment as retaining loopholes and as a step toward rather than an instance of a loophole-free test.

Frontier Two independent violations of the same inequality, at 18 and 24 standard deviations, on two continents, within a year. By the standards of experimental quantum foundations that is a replicated result, and it is the strongest thing this subject has. Speculative What it certifies is that the correlations cannot be explained by a definite causal order plus relativistic causality plus free choice. What it does not certify is that any causal inequality in the original sense has been violated, and the Qu group say so explicitly: standard causal inequalities “have been shown not to be violated by the quantum switch”.

Frontier 2024, the certificate strengthened logically. Van der Lugt and Ormrod showed that the device-independent argument can be run possibilistically — using the Greenberger–Horne–Zeilinger and Mermin nonlocality proofs in place of a Bell inequality — so that it “does not rely on the validity of probability theory at the hidden variable level”, and that the switch’s correlations are incompatible with a definite causal order holding even on a small fraction of runs. Speculative That closes an escape route nobody had yet tried to use, which is the most reliable sign that a field is arguing with itself rather than with data.

Frontier 2026, the control system addressed for the first time. Valibouse, Cladera-Rosselló, Antesberger, Lima, Walther and Rozema attacked the standing complaint that no photonic switch has ever produced a locally readable measurement outcome inside the superposition of orders. Their protocol couples the system to a time-delocalised ancilla that interacts at two distinct times but yields a single result, implemented with post-selected linear-optical logic and quantum-eraser measurements; they certify indefinite causal order with a causal witness of about −0.305. Speculative This is the first experiment addressed at the objection rather than at the witness value, and it is post-selected, which is precisely the assumption the objection is about.

Frontier Against all of that stands a body of work arguing that the advantages are misattributed. Abbott, Wechs, Horsman, Mhalla and Branciard showed in Quantum 4, 333 (2020) that information can be transmitted through channels that are coherently controlled with a definite causal order, and that in that scenario “causal indefiniteness plays no role”; the deeper point is that two implementations of nominally identical channels become distinguishable under coherent control, so the standard channel description is incomplete. Established Pang, Lupu-Gladstein, Ferretti, Yilmaz, Brodutch and Steinberg then measured it: superposing two zero-capacity depolarising channels, they concluded that “the expanded qutrit channel description in itself is sufficient to explain the capacity enhancement without any use of superposition”. Frontier A measured advantage with a contested cause is a weaker asset than a measured advantage, and this field has the former.

Frontier 2026, the simulation argument sharpened from the other side. Steffinlongo and Dourdent showed in Physical Review Research 8, 013127 that the SHIFT measurement — the structure associated with the non-causal Lugano process — can be implemented using a quantum switch of classical communications, so that discriminating it “witnesses causal nonseparability rather than noncausality”. Speculative They identify a broad class of superpositions of classical communications, built from ordinary classical processes, that generate causally indefinite-looking measurements. The gap between what a witness detects and what a causal inequality would detect is now populated with explicit classical-ish constructions, and that is bad news for witness-based claims.

Frontier 2025, the simulation argument answered. De la Hamette, Kabel, Christodoulou and Brukner published in Physical Review Letters 135, 141402 a relativistic definition of causal order between operationally defined events that is a well-defined observable in both general relativity and quantum theory, and showed that this observable does not distinguish the indefinite causal order implemented on an optical bench from a gravitational quantum switch. Speculative If that framework is the right one, the optical-versus-gravitational distinction that the 2020 objection rests on is not an observable distinction at all — and the dispute becomes a question about which definition of an event to adopt, which no experiment settles.

Frontier Question one, and the one that would change every other answer: is the photonic quantum switch a realisation of indefinite causal order or a simulation of it? Three positions are in print and none has conceded. Frontier Oreshkov (2019): a realisation, because the operations act on time-delocalised subsystems and the resulting structure is a circuit with a causal cycle. Frontier Paunković and Vojinović (2020): not a realisation, because the events sit in a classical, definite spacetime and only a superposed gravitational field could put spacetime events in superposed order. Frontier De la Hamette and colleagues (2025): the question is malformed as posed, because the relativistic observable that defines causal order between operational events gives the same answer on the bench and in the gravitational case. Speculative This is a dispute about the reference of the word ‘event’, and the field has not agreed a protocol that would decide it.

Frontier Question two: which degree of freedom is the control, and does it matter? In the 2015 experiment the spatial mode controlled operations on polarisation; in 2018 polarisation controlled operations on spatial modes. Speculative The objection that has real force is not that the control is a photonic degree of freedom but that the control is never measured in a basis that would destroy the order information while preserving the interference, so no experiment has demonstrated that the order was genuinely undetermined rather than merely unrecorded. Speculative The 2026 time-delocalised-ancilla experiment is the first to attack this directly, and it is post-selected; a loss-tolerant version is the decisive measurement named in section 7.

Frontier Question three: is there a task whose advantage cannot be reproduced by coherent control with definite order? Every advantage measured to date — the query saving, the channel activation, the communication-complexity separation — has a coherent-control account in the literature or an explicit reduction. Speculative A 2026 study of six configurations combining quantum switches with coherent superposition of channels reports that certain hybrid architectures beat either mechanism alone, which sharpens the taxonomy without settling the attribution. Handwave Nobody has published a task with a proof that no definite-order coherently controlled circuit can match it, and until somebody does, the applied case for this subject rests on an unproved exclusivity claim.

Speculative Question four: can a gravitational quantum switch be specified concretely enough to cost? Zych, Costa, Pikovski and Brukner showed in 2019 that a massive body in spatial superposition entangles the temporal order of events for two agents, giving a Bell inequality on temporal order that a classical causal structure cannot violate; the construction is semi-classical and non-perturbative and does not require quantising gravity. Speculative Móller, Sahdo and Yokomizo gave in 2024 a concrete geometry — an agent in free fall crossing the interior of massive spherical shells in a superposition of radii, with a definite exterior geometry supplying a classical reference frame. Handwave Neither paper states a mass, a radius or a decoherence budget. The most-cited proposal in the field for the experiment that would settle its central dispute has never been costed, which is section 5’s subject.

Speculative Question five: is the Oreshkov–Costa–Brukner process physical? It violates a causal inequality on paper, and fourteen years after it was written down no physical system has been proposed that implements it. Handwave Two readings are available and both are held: that the process is an artefact of a formalism that is more permissive than nature, or that it describes a regime — quantum gravity — that no laboratory can reach. No result distinguishes them, and the 2021 Purves–Short theorem makes the first reading considerably more comfortable.

Speculative Question six: what exactly does the device-independent certificate rule out? The assumption set is definite causal order, relativistic causality and free interventions, and the violation kills the conjunction. Speculative An advocate of definite order can keep it by giving up relativistic causality — admitting superluminal influence or retrocausation between the sealed laboratories — exactly as a local realist can keep locality by giving up measurement independence in a Bell test. Frontier The certificate is genuine and its logical shape is the familiar one: it converts a metaphysical preference into a cost, rather than refuting it.

Frontier Bottleneck one, and the one that gates every device-independent claim: post-selection and loss. Photonic switches are built from interferometers, beam splitters and heralded single photons, and they run at detection efficiencies far below the threshold at which the fair-sampling assumption can be dropped. Established The 2025–2026 Beijing experiment closed locality with 20 m of spacelike separation and freedom-of-choice with random number generators, and retained fair sampling; the 2026 Vienna experiment retains loopholes its authors do not enumerate as closed. Speculative Every loophole-free Bell test since 2015 has needed superconducting nanowire detectors above roughly 90% system efficiency and an optical path short enough to keep transmission high; a switch adds two full gate stages and a recombination to that path, and nobody has published a loss budget showing it can be done.

Frontier Bottleneck two: there is no non-photonic implementation worth the name. Every result in section 3 is optical. Speculative The reason is structural rather than a matter of engineering taste: the switch needs a control degree of freedom that can be coherently superposed while two physical operations act at different times, and photons supply that for free because their polarisation and path are naturally independent and their coherence survives metres of propagation. Speculative In a superconducting processor the natural encoding makes the two orders into two gate sequences on the same qubits, which is a circuit identity rather than an interferometer, and the causal-order interpretation becomes harder to defend rather than easier. Handwave A platform-independent demonstration would be the strongest available answer to the simulation objection, and the absence of even a proposal for one after thirteen years is itself evidence about the objection.

Speculative Bottleneck three: the gravitational switch has no number attached to any of its parameters. The two best-developed proposals — the 2019 temporal-order Bell test and the 2024 superposed spherical shells — specify a geometry and an entangling mechanism and stop there. Speculative Neighbouring proposals for gravitationally induced entanglement, which need a far weaker effect, call for masses around 10⁻¹⁴ kg held in superposition for seconds at separations of tens of micrometres, and are themselves decades from demonstration. Handwave A gravitational quantum switch needs a mass whose own gravitational field measurably reorders events for a second system, which is a strictly harder requirement, and no published estimate says by how much.

Frontier Bottleneck four: the control is never read out. In every implementation the control degree of freedom is prepared, used and then either discarded or measured in a basis that reveals the interference, and the causal witness is reconstructed from tomography of the whole apparatus. Speculative The commission for this brief names the decisive experiment as device-independent certification with the control system measured, on a genuinely time-delocalised implementation, and that is the right target: it is the one measurement that separates ‘the order was in superposition’ from ‘the order was definite on each run and we did not record which’. Speculative The 2026 time-delocalised ancilla protocol is the first instrument built to do it and it works only with post-selection, so the two bottlenecks that matter most are the same bottleneck.

Frontier Bottleneck five, non-technical and possibly decisive: there is no agreed operational definition of an event. Oreshkov’s time-delocalised subsystems, Paunković and Vojinović’s spacetime events, and de la Hamette and colleagues’ relativistic operational events are three different referents for the same word, and the three yield different verdicts on the same apparatus. Handwave A field whose central claim changes truth value with the definition of its central noun cannot be settled by improving its error bars, and improving error bars is what it has been doing.

Frontier This subject depends on photon-source and detector technology built for other purposes, and on nothing else it could plausibly fund itself. Heralded single-photon sources, superconducting nanowire single-photon detectors and phase-stable integrated interferometers all arrive from quantum communication and photonic computing programmes, and the switch community consumes them. Established The 2023 Sagnac demonstration is the clearest case: its contribution is a common-path geometry borrowed from classical interferometry, and its result is stability rather than a new certificate.

Frontier The dependency that actually blocks progress is theoretical and has a name: a task with a proved separation. Until someone proves that a particular problem cannot be solved as well by any coherently controlled definite-order circuit, every measured advantage will be met with a reduction, and the field will keep arguing about attribution. Speculative That proof is a question in quantum query and communication complexity rather than in foundations, and the people who could produce it mostly do not work on causal order.

Speculative A second theoretical dependency: a physical model for any causal-inequality-violating process. The Purves–Short theorem says quantum theory will not supply one, so the candidate source is a post-quantum theory or a quantum theory of gravity; Speculative that puts the deepest question in this brief downstream of Quantum Gravity, which is the one page on this map that could in principle deliver it and which reports that every quantum-gravity experiment returning a number has returned a null.

Speculative A third: levitated-optomechanics mass records. Any gravitational switch inherits the whole macroscopic-superposition problem, which Objective Collapse Models tracks in detail: the interference record is around 10⁻²² kg and the collapse-test target is 10⁻¹⁷ kg, five orders below what a measurable gravitational reordering would need. Handwave The dependency runs one way and it is long.

Frontier Finally, an institutional dependency that is cheap and missing: a preregistered convention on what a causal-order claim asserts. Nothing prevents the field agreeing, before the next result, which definition of an event a paper is using and which of the three certificates — witness, Bell-like inequality under relativistic causality, or causal inequality — it claims. Speculative Its absence is why press coverage of every result in section 3 has said ‘cause and effect reversed’ and why none of the papers said that.

Frontier The tests below rank by what a result would settle, not by how hard they are, and the ordering is not the field’s own: the field ranks by achievable sigma.

Speculative Tier one, and the decisive experiment for this brief: a device-independent certification in which the control system is itself measured, on an implementation whose operations act on time-delocalised subsystems, without post-selection. Frontier Each of the three components exists separately. The van der Lugt–Barrett–Chiribella inequality supplies a device-independent certificate with a bound of 7/4 and a quantum maximum near 1.8536, and it has been violated twice, at 1.8090 ± 0.0024 and 1.8328 ± 0.0045. Frontier The 2026 Vienna protocol supplies a time-delocalised ancilla that interacts at two distinct times and returns one outcome, certified at a causal witness of about −0.305. Speculative No experiment has combined them, and the obstacle is loss: the ancilla protocol uses post-selected linear-optical logic and quantum-eraser measurement, and post-selection is exactly the assumption a device-independent claim must not make. Speculative A version with system detection efficiency above the fair-sampling threshold, reporting the control outcome run by run alongside a violated inequality, would answer the ‘which degree of freedom is the control’ objection with a measurement instead of an argument. Nothing else on this list would.

Speculative Tier two: a task with a proved exclusivity, then measured. Frontier The attribution problem is not empirical — the advantages are real and reproduced — it is that a definite-order coherently controlled circuit reproduces each one. Speculative The experiment that would matter is a demonstration of a task accompanied by a theorem that no coherently controlled definite-order circuit achieves it, run head-to-head against the best such circuit on the same bench. Handwave The theorem does not exist and the head-to-head has never been run, which means the field has never performed its own control experiment.

Frontier Tier three: close fair sampling on the Bell-like causal inequality. Established The Beijing measurement already closes locality, with 20 m of spacelike separation, and freedom of choice, with random number generators; only fair sampling remains. Speculative A loophole-free version would put this subject on the same evidential footing as the 2015 loophole-free Bell tests, and would be the first foundational claim about causal order that survives an adversarial reading of the apparatus. Speculative It is engineering rather than physics, it has a known recipe from the Bell-test literature, and no group has announced it.

Speculative Tier four: a non-photonic switch. Speculative Implementing the switch on superconducting circuits, trapped ions or a nuclear-spin register, with a causal witness measured on that platform, would test whether the effect is a property of processes or an artefact of photonic encodings where path and polarisation are conveniently independent. Handwave It is the cheapest experiment on this list and nobody has done it, which either means it is uninteresting or means the community expects the answer to be awkward.

Speculative Tier five: the gravitational switch, which is the only test that all three positions in section 4 agree would be decisive. Speculative The 2019 temporal-order Bell test and the 2024 superposed spherical shells both give a protocol; neither gives a mass or a coherence time. Handwave Before it is an experiment it needs to be a budget, and the first useful output would be a single published number: the mass and superposition lifetime at which the gravitational reordering exceeds the decoherence rate.

Speculative A null on tier one is as informative as a violation and is the outcome this brief expects more of. Frontier If a loss-free control readout shows a definite order on each run with the interference intact, the switch is a quantum-controlled circuit and nothing more, and the 2021 Wechs result was the whole story. Speculative That would not make the query saving or the channel activation go away; it would relocate them to coherent control, where two published analyses already put them.

Frontier The hardware requirement for the decisive experiment is unusually specific and unusually modest, which is the strongest practical argument for doing it. A switch that closes fair sampling needs heralded single photons, two programmable gate stages, a recombination, and system detection efficiency high enough that no fair-sampling assumption is required — the standard set by loophole-free Bell tests, which reached it with superconducting nanowire detectors and short, low-loss optical paths. Speculative The switch geometry adds two gate stages and a recombination to that path, so the engineering problem is loss budgeting rather than invention, and the components are the ones Quantum Networks and Precision Quantum Sensing already buy.

Frontier Phase stability is the requirement the field has actually solved. The Sagnac common-path configuration removed the differential path-length drift that limited Mach–Zehnder switches, and integrated photonic implementations push in the same direction. Speculative Integration also makes the simulation objection sharper rather than weaker: an on-chip switch is visibly a routing circuit, and the further the apparatus gets from two physically separated laboratories, the harder it is to argue that two parties acted in an indefinite order.

Speculative For the control readout, the requirement is a detector that registers the control outcome without absorbing the interference, which is what the 2026 time-delocalised ancilla protocol approximates with post-selection and a quantum eraser. Speculative A deterministic version needs a nonlinearity strong enough for a controlled-NOT between the control mode and an ancilla at the single-photon level, which is the same requirement that has blocked deterministic linear-optical quantum computing for twenty-five years and is tracked by Fault-Tolerant Quantum Computing. Handwave That is the honest engineering statement: the decisive experiment for this brief is gated by the same missing component as the largest photonics programme in the world.

Handwave For the gravitational switch there is no engineering specification to state. The requirement is a mass in spatial superposition whose own gravitational field reorders events for a second system faster than the superposition decoheres, and no published proposal gives either rate. Speculative The nearest measured anchor is matter-wave interference at around 10⁻²² kg, and the collapse-test community’s next target, 10⁻¹⁷ kg, is itself five orders of magnitude away; gravitational entanglement proposals need roughly 10⁻¹⁴ kg. A gravitational switch needs more than any of them and nobody has said how much more.

Frontier The nearest page on this map is Quantum Gravity, and the relationship is a supply relationship rather than an overlap. That brief owns the experimental programme — can gravity mediate entanglement, and what the nulls have eliminated — and reports that every quantum-gravity experiment returning a number has returned a null. Speculative This page inherits one thing from it: the only physical mechanism anyone has proposed for a genuine superposition of causal order between spacetime events is a superposed gravitational field, so the gravitational switch is a downstream application of exactly the capability that page says does not exist yet. Neither page restates the other, and the seam is the mass scale.

Frontier The sibling page is Wigner’s Friend Experiments, and the two subjects have the same evidential shape to a degree that is worth naming. Both derive an inequality from a small set of assumptions about agents in sealed laboratories; both have violated that inequality in a photonic experiment; Speculative and in both the live objection is not about the statistics but about whether the physical system playing the role in the theorem — a control degree of freedom here, a friend there — is the kind of thing the theorem is about. The van der Lugt inequality and the local-friendliness inequality are the same move made twice, and a reader who follows one will follow the other.

Speculative Objective Collapse Models supplies the mass-scale constraint and a cautionary parallel. The constraint is direct: any gravitational switch needs a superposition far beyond what collapse experiments are chasing, and if a collapse mechanism is real it caps the switch’s mass before gravity does. Speculative The parallel is that both fields spent a decade improving a number while the theory that gave the number meaning kept acquiring parameters — there, noise colour and dissipation; here, the definition of an event.

Frontier The applied adjacency is quantum communication, and it is where the attribution dispute bites. Channel activation, communication-complexity separations and metrological scaling are all claimed as switch applications, and all sit inside the remit of Quantum Networks. Speculative If the coherent-control account is correct, those capabilities survive and the causal-order framing does not, which would be a good outcome for the engineering and a bad one for the foundations.

Speculative The instrument adjacency is Precision Quantum Sensing, which builds the detectors any loophole-free version needs, and Fault-Tolerant Quantum Computing, which owns the missing photon-photon nonlinearity. Handwave Neither programme is waiting on causal order and neither would notice if this subject stopped.

Frontier This is a field of roughly six groups, no named programme, and no budget line anyone publishes. The experimental work in section 3 comes from Vienna, Brisbane, Beijing, Hefei and Toronto; the theory from Vienna, Oxford, Grenoble, Brussels, Barcelona and Belgrade. Established The Vienna group’s own research page describes the quantum switch as its primary experimental platform and lists outputs from 2015 to 2024, and names no funding programme (the group’s own page).

Speculative The institutional requirement that would help most costs nothing: a stated convention on what is being claimed. Three certificates are in circulation with three different strengths, and papers, press offices and review articles move between them without marking the transition. Speculative A one-page convention — this experiment measured a causal witness, which assumes a tomographic model of the apparatus; this one violated a Bell-like inequality under relativistic causality; no experiment has violated a causal inequality and a theorem says none will — would remove most of the confusion in the secondary literature at a cost of a single community meeting.

Speculative The second requirement is a registered adversarial collaboration on the simulation question. Oreshkov’s position and Paunković and Vojinović’s position have coexisted for six years without either side proposing a measurement that would distinguish them. Speculative The 2025 relativistic observable is the first proposal that could, and it argues the distinction is not observable at all — which is a result the other two positions should either accept or answer in print.

Frontier The third is mundane and is the only one with money in it: a fair-sampling-free photonic switch needs a detector budget of the kind that funds a Bell-test group, not a foundations postdoc. Speculative The experiment that would settle the subject’s strongest claim costs about what one loophole-free Bell test cost a decade ago, and nobody has asked for it.

Frontier The ethical exposure here is almost entirely about communication, because there is no deployed technology to regulate. No indefinite-causal-order device processes anyone’s data, and none is on a roadmap. Speculative What does exist is a nine-year record of press coverage describing these experiments as reversing cause and effect, or as demonstrating that an effect can precede its cause, which is not what any of the papers claim and is flatly inconsistent with the 2021 theorem that quantum theory cannot violate a causal inequality.

Speculative That gap has a cost and the cost is borne by adjacent fields. Foundational quantum results are the raw material for a large volume of quantum-adjacent marketing, and ‘causality is optional’ is a more saleable line than ‘the order of two gates can be a quantum degree of freedom’. Speculative The correction is available and cheap: papers in this field are unusually careful, and it is the summaries that overclaim.

Speculative A second consideration is the one this brief has been making structurally: a field whose central term has three incompatible definitions in print is vulnerable to being read as unfalsifiable. Handwave That is a reputational risk to quantum foundations as a whole, and it is the reason the definitional convention in section 10 is listed as an institutional requirement rather than as housekeeping.

Speculative There is no dual-use question here that is specific to causal order. The communication advantages, if they survive attribution, are advantages in channel capacity and communication complexity, and inherit the security questions that Quantum Networks and Post-Quantum Migration already own. Handwave Nothing in this subject creates a new one.

Speculative The civilizational question for this subject is not what a switch would do but what it would mean if causal order were genuinely a quantum variable. Every physical theory since Newton has treated the order of events as the stage rather than as a state, and the process-matrix formalism is the first serious framework in which the stage has a density matrix. Handwave If that turns out to describe nature rather than a permissive formalism, the consequence is not a device; it is that a category everyone has reasoned with for three centuries becomes contingent.

Speculative The sober version is much smaller and is the one the evidence supports. The quantum switch is a quantum-controlled circuit whose correlations are compatible with a well-defined causal order, and its measured advantages have a coherent-control account. Frontier On that reading the durable contribution of thirteen years of work is a formalism — higher-order quantum maps, process matrices, quantum-controlled circuits — that has already been useful for channel-discrimination, metrology and circuit-design questions with nothing indefinite about them. That is a real contribution and it is a mathematics contribution.

Speculative The asymmetry of outcomes is worth naming because it is unusual. A positive result on the gravitational switch would be evidence about the quantum nature of spacetime, which is the largest open question in physics; a null on the tier-one control readout would reclassify a decade of experiments as elegant demonstrations of coherent control. Handwave Almost no intermediate outcome is available, and neither outcome changes anyone’s Tuesday.

Handwave Any claim beyond that — that indefinite causal order enables computation outside the quantum circuit model, or communication outside relativistic causality — runs against a published theorem, and this page does not make one.

These horizons track certificates and loopholes, because there is no engineering programme here to track and the platform has not changed in nine years:

• 10 yr: Frontier Expect the Bell-like causal inequality to be violated again, on integrated photonics, with the fair-sampling loophole closed by a group that already owns loophole-free Bell-test hardware; that is engineering with a known recipe. Speculative Expect the first loss-tolerant control readout on a time-delocalised implementation, which is the decisive experiment named in section 7, and expect it to be reported as a confirmation whichever way it comes out. Speculative Expect at least one non-photonic implementation, and expect the argument about whether it counts to be identical to the current one.
• 25 yr: Speculative This is the window in which the attribution question is either settled by a proved exclusivity theorem or abandoned; the mathematics is the bottleneck and mathematics does not schedule. Speculative If the exclusivity theorem arrives and the head-to-head is run, causal order becomes a resource with a measured exchange rate against coherent control; if it does not, the applied literature migrates to coherent control and the foundational literature continues without it. Handwave The modal outcome on this horizon is the second.
• 50 yr: Handwave A gravitational quantum switch requires a mass in superposition far beyond any published roadmap, and the first milestone is not an experiment but a number: the mass and coherence time at which gravitational reordering beats decoherence. Speculative If that number is ever published and is within twenty orders of magnitude of laboratory reach, this subject acquires a programme; if it is not, it stays a benchtop discipline indefinitely.
• 100 / 250+ yr: Handwave Beyond useful forecasting. The defensible statement is structural: a claim that cannot be settled by improving error bars is settled by a definition or not at all, and this one has had three definitions for six years. Handwave Any specific claim about what a confirmed indefinite causal order would be used for is an assertion, and this page does not make one.

• Depends on One typed dependency on this map and it is a soft one. Quantum Gravity is upstream of the only mechanism anyone has proposed for a genuine superposition of causal order between spacetime events, and reports that every experiment in that programme returning a number has returned a null; this page inherits that null rather than restating it. Objective Collapse Models supplies the mass ceiling any gravitational implementation must respect. Precision Quantum Sensing supplies the detectors, and is not blocking, because those detectors are being built for metrology regardless.
• Requires (not on this map) Six conditions, in the order of the tokens above. The separation. A task with a theorem showing no coherently controlled definite-order circuit matches it; without one, every measured advantage has a published reduction and the applied case does not close. The control readout. A measurement of the control degree of freedom, run by run, that does not destroy the interference and does not rely on post-selection; the 2026 time-delocalised ancilla protocol is the first attempt and is post-selected. The detectors. System detection efficiency high enough to drop the fair-sampling assumption across two gate stages and a recombination, which is the loophole-free Bell-test standard applied to a longer optical path. The budget. A single published number giving the mass and superposition lifetime at which a gravitational quantum switch works; the two leading proposals give a geometry and no parameters. The definition. An agreed operational referent for ‘event’, since the same apparatus is a realisation under one definition and a simulation under another. The process. A physical model of any process that violates a causal inequality, which quantum theory has been proved not to supply.
• Enables If the exclusivity theorem and the control readout both land, the enabled things are channel activation, communication-complexity savings and metrological scaling inside Quantum Networks, at magnitudes measured on two-gate instances and never extrapolated. No typed enabling edge is claimed: a resource whose advantages currently have a competing explanation enables nothing on a schedule.
• Adjacent Wigner’s Friend Experiments runs the identical argumentative structure on observers rather than on operation order, and the two pages should be read together. Fault-Tolerant Quantum Computing owns the missing photon-photon nonlinearity; Quantum Gravity owns the mass scale; Objective Collapse Models owns the competing account of what limits macroscopic superposition.

Established “Experiments have shown that cause and effect can be reversed.” They have not, and a theorem says they cannot. Established Purves and Short proved in 2021 that quantum experiments with superposed temporal orders can be simulated by a classical causal model and therefore cannot violate a causal inequality; Wechs and colleagues showed the same year that quantum-controlled circuits, the class the switch belongs to, generate only correlations compatible with a well-defined causal order. No experiment has ever sent a signal backwards in time or produced a correlation requiring it.

Established “A causal inequality has now been violated.” A Bell-like causal inequality has been violated, twice, and the distinction is the whole content of the result. Established The van der Lugt–Barrett–Chiribella inequality assumes definite causal order, relativistic causality and free interventions, and is bounded at 7/4; measurements of 1.8090 ± 0.0024 and 1.8328 ± 0.0045 exceed it by 24 and 18 standard deviations. Frontier A causal inequality in the 2012 sense assumes only definite causal order, and the experimental group that produced the 24-sigma result states that standard causal inequalities have been shown not to be violated by the quantum switch.

Frontier “The 18-sigma quantum switch measured a query-complexity advantage.” Two different experiments, three years apart. Established The 18-standard-deviation causal witness is Goswami and colleagues, Physical Review Letters 121, 090503 (2018), a Brisbane apparatus using polarisation to control operations on spatial modes; it reports a witness value and no complexity result. Established The measured advantage — one call to each gate instead of two, at 0.973 ± 0.016 against a causally ordered ceiling of 0.9288 — is Procopio and colleagues, Nature Communications 6, 7913 (2015), a Vienna apparatus with the encodings the other way round. This brief’s commission named them as one result; they are two, and the correction is recorded here rather than smoothed over.

Frontier “The quantum switch is the process Oreshkov, Costa and Brukner found.” It is not, and the difference is a strict hierarchy. Established The OCB process violates a causal inequality and has no known physical realisation. Established The quantum switch is physically realisable, is causally nonseparable, and provably cannot violate a causal inequality. Speculative Most popular accounts of this field describe the first and cite an experiment on the second.

Frontier “Indefinite causal order gives an exponential speed-up.” An exponential advantage in communication complexity was reported photonically in 2019 and is listed as such in the 2024 Nature Reviews Physics survey. Speculative It is not a computational speed-up, it has not been reproduced on a scalable platform, and it is subject to the same attribution question as every other advantage here: a coherently controlled definite-order circuit has not been excluded. Speculative Two published results — a 2020 Grenoble analysis and a 2023 Toronto measurement — find that the channel-capacity version of the advantage needs no indefinite order at all.

Frontier “The photonic switch only simulates indefinite causal order.” This is a serious published position and it is not the settled one. Frontier Paunković and Vojinović argue the optical implementations “do not feature superpositions of causal orders between spacetime events” because the bench’s geometry is classical; Frontier Oreshkov argues they genuinely realise indefinite causal structure, because the operations act on time-delocalised subsystems and the structure is a circuit with a causal cycle; Frontier de la Hamette, Kabel, Christodoulou and Brukner argue the relativistic observable that defines causal order between operational events does not distinguish the bench from the gravitational case at all. Speculative Anyone who tells you this is settled in either direction is reporting one of three papers.

Speculative “A causal witness is a device-independent certificate.” It is not; it is the causal analogue of an entanglement witness and requires a trusted tomographic model of the apparatus. Frontier That is why the 2023 device-independent inequality was a notable theoretical advance despite certifying a weaker-sounding thing, and why a 2026 result reporting a causal witness of −0.305 is a different kind of claim from a 24-sigma inequality violation.

Speculative “Nothing here is testable, so it is philosophy.” Established Three distinct certificates have been measured, two of them device-independent under stated assumptions, and the loopholes remaining are enumerated: fair sampling in both violations, and post-selection in the control-readout protocol. Speculative The part that is not testable is the definition of an event, and the useful criticism of this field is not that it is untestable but that its most-quoted claim and its most-testable claim are different claims.

Speculative “A gravitational quantum switch is decades away.” Handwave Nobody knows, because no proposal states a mass, a separation or a coherence time. Speculative The honest statement is that the nearest measured anchor — matter-wave interference around 10⁻²² kg — is many orders of magnitude below even gravitational-entanglement proposals near 10⁻¹⁴ kg, and a switch needs more than those. A distance nobody has measured is not a schedule.