Pith. sign in

REVIEW 6 minor 137 references

A map of indefinite causal order

T0 review · 0 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper maps indefinite causal order through three frameworks — the quantum switch, the process matrices framework, and the superposition of causal structures — and identifies the quantum switch as a causally nonseparable process that…

desk verdict A careful, useful map of the ICO literature, but the anchor example's contested physicality could mislead newcomers if they skip Section 5. read the letter →

arxiv 2506.04607 v1 pith:Q4OFTAIH submitted 2025-06-05 quant-ph

Jorge Escandón-Monardes This is my paper
classification quant-ph
keywords indefinitecausalorderquantumswitchprocessmatricesnonseparabilityinequalitiessuperpositionofstructuresgravityinformation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper is a map of indefinite causal order (ICO), the idea that physical events can fail to have a fixed cause-and-effect order. It claims the field is organised by three complementary frameworks: the quantum switch, which superposes the order of two quantum operations under the control of an ancilla; process matrices, which describe correlations between labs without assuming any global causal order; and superpositions of causal structures, where spacetime geometries themselves are quantised. On the map, the quantum switch is the paradigmatic ICO process: it is causally nonseparable, cannot be built from a fixed-order circuit using one copy of each gate, and yet it violates no causal inequality. The point of the map is to let a newcomer navigate these frameworks and their applications without getting lost in the literature, while making the open debates explicit.

What carries the argument

The load-bearing objects are the quantum switch, a higher-order quantum operation (a supermap) that applies two channels $\mathcal{A}$ and $\mathcal{B}$ in an order controlled by a qubit, so the target undergoes either $\mathcal{B}\circ\mathcal{A}$ or $\mathcal{A}\circ\mathcal{B}$ coherently; the process matrix $W$, a positive semidefinite operator satisfying a completeness relation that connects inputs and outputs of isolated labs, with causal nonseparability defined as the impossibility of writing $W = qW^{A\nprec B} + (1-q)W^{B\nprec A}$ as a mixture of definite-order processes; and the superposition of causal structures, in which each manifold $\mathcal{M}$ is assigned a quantum state $|\mathcal{M}\rangle$, so a superposition of geometries yields an indefinite order of events. The machinery's work is to give each framework a precise definition of indefinite causal order and to connect those definitions to experiments and applications.

What would settle it

An explicit construction of a fixed-order quantum circuit that uses exactly one copy of each input gate and reproduces the quantum switch's action on all unitary inputs would refute the central framing, since cited work proves no such circuit exists.

Watch

Extended reading notes

Core claim

The central claim is that indefinite causal order is not one phenomenon but a territory with three main landmarks. The quantum switch applies two channels in a coherent superposition of orders, giving computational, communication, thermodynamic, and metrological advantages over fixed-order circuits; the process matrices framework formalises causal nonseparability — a process that cannot be written as a mixture of definite-order processes — and contains processes, such as the OCB process, that violate causal inequalities but cannot be realised by quantum theory alone; and the superposition of causal structures assigns quantum states to classical manifolds, producing a gravitational quantum switch in which time dilation makes the order of events indefinite. The paper asserts, on the authority of the cited results, that the quantum switch is causally nonseparable yet satisfies every causal inequality, and that the gravitational version is the only one some critics accept as genuine, with the photonic implementations disputed as simulations.

Load-bearing premise

The map's reliability rests on the cited claim that the quantum switch cannot be reproduced by a fixed-order quantum circuit using each gate only once, and on the contested status of the photonic experiments as genuine indefinite causal order; the paper reports the dispute without settling it.

Editorial extensions

If this is right

  • If the map is right, the quantum switch is a genuine resource: it distinguishes commuting from anticommuting unitaries deterministically, activates the capacity of completely depolarizing channels, and improves metrological precision, all while violating no causal inequality.
  • The process matrices framework goes beyond quantum mechanics: some causally nonseparable processes such as the OCB process violate causal inequalities, but standard quantum theory cannot realise them, so the boundary of physical implementability is a live open question.
  • The superposition of causal structures turns spacetime itself into the control system, so gravitational time dilation can realise a quantum switch without any interferometric routing of the target.
  • The unresolved debate over whether photonic implementations are genuine or simulations shifts the question onto the definition of an event, and the paper's map keeps that question open.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extension: if the resource behind the switch's communication advantages is really the coherence of the control system rather than indefinite order, then a fixed-order interferometric coherent-control setup should reproduce the same capacity activation; the cited evidence already hints this is partially true.
  • Extension: a systematic measure of causal nonseparability strength would let the field sort processes like the quantum switch, the OCB process, and the Grenoble process into a hierarchy; no such measure is currently proposed, though the map's causal-witness structure suggests one can be built.
  • Extension: if the event-definition debate resolves toward the operational 'coincidence of worldlines' view, then photonic and gravitational quantum switches become equally genuine, which would retroactively validate all photonic applications as ICO demonstrations.
  • Extension: the map implies that multipartite ICO is strictly richer than bipartite: dynamical control of causal order and locally-classical-but-globally-noncausal correlations appear only with three or more parties, so future experimental effort could target tripartite processes rather than two-party switches.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

0 major / 6 minor

Summary. This paper is a conceptual review or "map" of indefinite causal order (ICO), written as an excerpt from the author's PhD thesis. It motivates ICO through Hardy's quantum-gravity program and then surveys three frameworks: the quantum switch, process matrices, and superposition of causal structures. It summarizes applications in quantum computing, communication, thermodynamics, and metrology, reviews certification methods for causal nonseparability, and closes with a list of ongoing debates. No new technical results or derivations are claimed; the contribution is organizational and bibliographic, with 137 references.

Significance. If accurate, the map is a useful entry point for newcomers and a quick reference for researchers. The paper is generally careful in attribution and explicitly presents both sides of the main contested issues, particularly the debate over whether photonic and NMR realizations of the quantum switch are genuine ICO instances or fine-grained simulations (Refs. [98,99] versus [132]). It also lists open questions in Section 6 rather than presenting the field as settled. The main value is the broad, organized bibliography and the explicit acknowledgment of unresolved questions. Because there are no derivations or predictions, the correctness burden is fidelity to the cited literature, and the paper is, in the main, faithful to the sources it cites. The main risk is that a newcomer could read the applications section as settled experimental evidence for physical ICO, but the later debate sections go some way toward mitigating this risk.

minor comments (6)
  1. [Section 3.1 and Section 3.2] The quantum switch is introduced and its applications are surveyed without an explicit cross-reference to the physicality debate acknowledged in Section 4.1 and Section 5. In particular, Ref. [7] is described as the "first experimental implementation" and Section 3.2 lists many experiments, while Section 5 reports Refs. [98,99] claiming that these are fine-grained fixed-order simulations. Because the switch is the map's anchor example, a sentence at the first mention of experimental implementations and at the start of Section 3.2 should state that the physicality of these realizations is contested and direct the reader to Sections 5 and 6.3.
  2. [Section 5] The sentence "According to this operational view, the photonic implementation of the quantum switch is as genuine as its gravitational version, provided a superposition of causal structures is involved" is confusing, because photonic experiments do not involve a superposition of causal structures. Please clarify whether this is intended as a rebuttal of Refs. [98,99] or as a separate conditional statement about the operational notion of event.
  3. [Throughout] The manuscript contains numerous typos and grammatical errors, including "succesful", "indefintie", "squemes", "teeths" in the Figure 1 caption, "separtates" in the Figure 7 caption, "highligthed", "certifiyng", and "worldine". A careful proofreading pass is needed before publication.
  4. [Prologue] The sentence "a map never replace the terrain" should read "a map never replaces the terrain", and the phrase "while full of references" would be clearer as "while being full of references".
  5. [Section 3.2] The sentence "He showed that the quantum switch can deterministically discriminates between a pair of commuting and a pair of anticommuting unitaries" has a subject-verb agreement error and should read "can deterministically discriminate".
  6. [References] Some entries are preprints or unpublished items (e.g., Ref. [24] is a Research Square preprint and Refs. [75,79,128] are arXiv preprints); if published versions now exist, they should be updated, and the reference list should be checked for consistency of formatting.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is a literature map with no derived predictions; load-bearing claims are attributed to external sources and the sole self-citation is terminological.

full rationale

The paper explicitly disclaims derivation: 'The map is written at a conceptual level, without mathematical technicalities while full of references.' It contains no equations, fits, or original predictions whose outputs could reduce to their inputs. The central classifications—the quantum switch as a causally nonseparable process, the process-matrix definition of causal separability, and the gravitational quantum switch—are each attributed to external references ([5], [91], [97], [125]) rather than derived in the text. The only self-citation, Ref. [33], is used solely for terminology ('Following Ref. [33], we refer to this generalised quantum switch as (N, p)-switch') and to point to a family of promise problems; it is not load-bearing. The paper also flags the unresolved dispute about whether photonic implementations are genuine instances of ICO (Section 5, citing Refs. [98,99]), which is a physicality or correctness concern, not a circularity. Since every substantive claim is traceable to independent external work, there is no reduction of any claim to its own inputs.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

This is a review, so the ledger contains only meta-assumptions about the correctness of the cited literature and the adequacy of the standard quantum formalism. No new parameters, axioms, or entities are introduced.

assumptions (3)
  • domain assumption Correctness of the cited primary literature (e.g., causal non-separability of the quantum switch [97], impossibility of fixed-order simulation [5]).
    The map's usefulness depends on the reliability of the results it summarizes; the paper does not verify them independently.
  • domain assumption Standard quantum mechanics framework: quantum operations, channels, and supermaps are well-defined.
    The quantum switch and process matrix sections presuppose the formalism of quantum theory.
  • domain assumption The definition of causal non-separability is a meaningful criterion for indefinite causal order.
    Section 4.1 adopts the process matrices framework's definition; the review inherits this without critical examination.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A map of indefinite causal order." pith.science (2026). https://pith.science/paper/Q4OFTAIH

@misc{pith2026250604607,
  author       = {Pith},
  title        = {Pith review of: A map of indefinite causal order},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q4OFTAIH}},
  note         = {Machine review of arXiv:2506.04607}
}
read the original abstract

In this "map" we are going to present the concept of indefinite causal order and make a quick journey through its different flavours. We will start with a broad conceptual motivation for studying indefinite causal order, based on the approach of Lucien Hardy to quantum gravity. Then, we will introduce the quantum switch, which is a particular instance of indefinite causal order, followed by the process matrices framework and the superposition of causal structures. Finally, we will comment on some ongoing debates within the field. This document started as an excerpt of the author's PhD Thesis and is intended as a map of indefinite causal order, which can be used to guide the trip of any explorer in the field.

Figures

Figures reproduced from arXiv: 2506.04607 by the authors.

Figure 1
Figure 1. Quantum supermaps and quantum combs. A box represents a quantum operation or 1-comb (upper left); a diagram with two teeth represents a 2-comb, i.e., a supermap where a quantum box can be plugged (upper center); a diagram with three teeths represents a 3-comb where up to two boxes or one 2-comb can be plugged (upper right). When two combs are combined, the result is a new comb. For example, a 4-comb can take a 3-com… view at source ↗
Figure 2
Figure 2. Quantum switch. The simplest quantum switch applies two gates in two different orders, which is coherently controlled by a control qubit. In photonic realizations, the order of the operations can be controlled by the path degree of freedom of photons, which we illustrate by colour wires. When the control is in a superposition of states, the order of the gates becomes indefinite. |+⟩ √ 1 2 [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 3
Figure 3. Fixed order circuit equivalent to the quantum switch. In order to implement the same transformation than the quantum switch in a fixed order circuit with unitary inputs A and B, at least one extra copy of one of the gates is required. Controlled-SWAP gates are used as a router to ensure the coherent control of the order of the operations. can be fixed in a later time by measuring the control system in the computatio… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Photonic quantum switch by Procopio et al. (2015). (a) Source of entangled photons. One photon is used as a herald while the other is routed into a quantum switch. (b) Quantum switch. Unitaries U1 and U2, which act on the polarization degree of freedom, are applied on …
Figure 5
Figure 5. Figure 5: Coherent control of operations versus coherent control of orders. In the coherent control of operations (left), also called “superposition of quantum channels”, two quantum channels are applied on a target system, each one in a different arm of an interferometer. Inste…
Figure 6
Figure 6. Figure 6: Bipartite process matrix. Alice and Bob perform quantum operations acting on some input systems and obtain outcomes a and b. Their labs are connected by an unknown causal structure represented by a process matrix W, which may be causally non-separable. The joint probab…
Figure 7
Figure 7. Figure 7: Causal Witness. The inner ellipse represents the set of causally separable processes and the bigger ellipse represents the set of all process matrices. For every causally non-separable process Wns, it can be defined a hyperplane S (a causal witness) that separtates Wns…
Figure 8
Figure 8. Figure 8: Gravitational quantum switch. A massive body is in a superposition of two different locations, while two clocks are in fixed locations. Due to gravitational time dilation, an event defined in one clock can be in the causal past of an event defined in the other clock. T…
Figure 9
Figure 9. Figure 9: Photonic quantum switch embedded in spacetime. The implementation of the photonic quantum switch comprises four points in spacetime. A genuine quantum switch should comprise only two events. Figure from Ref. [98] [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: Superposition of causal structures. In the superposition of classical manifolds, an event is a crossing of worldlines. For each branch, the corresponding events are identified via a quantum controlled diffeomorphism. Figure from Ref. [132]. relativistic causality), th…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

137 extracted references · 72 canonical work pages

  1. [33]

    Practical computational advantage from the quantum switch on a generalized family of promise problems

    J. Escand´ on-Monardes, A. Delgado, and S. P. Walborn, “Practical computational advantage from the quantum switch on a generalized family of promise problems”, Quantum7, 945 (2023)

    2023

  2. [132]

    de la Hamette, V

    A.-C. de la Hamette, V. Kabel, M. Christodoulou, and ˇC. Brukner, Quantum diffeomorphisms cannot make indefinite causal order definite , arXiv:2211.15685., 2022

    arXiv 2022

  3. [1]

    Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure

    L. Hardy, “Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure”, Journal of Physics A: Mathematical and Theoretical 40, 3081 (2007)

    2007

  4. [2]

    Quantum gravity computers: on the theory of computation with indefinite causal structure

    L. Hardy, “Quantum gravity computers: on the theory of computation with indefinite causal structure”, in Quantum reality, relativistic causality, and closing the epistemic circle: essays in honour of abner shimony (Springer Netherlands, Dordrecht, 2009), pp. 379–401

    2009

  5. [3]

    Transforming quantum operations: quantum supermaps

    G. Chiribella, G. M. D’Ariano, and P. Perinotti, “Transforming quantum operations: quantum supermaps”, Europhysics Letters 83, 30004 (2008)

    2008

  6. [4]

    Theoretical framework for quantum networks

    G. Chiribella, G. M. D’Ariano, and P. Perinotti, “Theoretical framework for quantum networks”, Phys. Rev. A 80, 022339 (2009)

    2009

  7. [5]

    Quantum computations without definite causal structure

    G. Chiribella, G. M. D’Ariano, P. Perinotti, and B. Valiron, “Quantum computations without definite causal structure”, Phys. Rev. A 88, 022318 (2013)

    2013

  8. [6]

    Bavaresco, S

    J. Bavaresco, S. Yoshida, T. Odake, H. Kristj´ ansson, P. Taranto, M. Murao, and M. T. Quintino, Can the quantum switch be deterministically simulated? , arXiv:2409.18202., 2024

    work page arXiv 2024

Show all 137 references
  1. [7]

    Experimental superposition of orders of quantum gates

    L. M. Procopio, A. Moqanaki, M. Ara´ ujo, F. Costa, I. A. Calafell, E. G. Dowd, D. R. Hamel, L. A. Rozema, ˇC. Brukner, and P. Walther, “Experimental superposition of orders of quantum gates”, Nature Communications 6, 7913 (2015)

    2015

  2. [8]

    Experimental verification of an indefinite causal order

    G. Rubino, L. A. Rozema, A. Feix, M. Ara´ ujo, J. M. Zeuner, L. M. Procopio, ˇC. Brukner, and P. Walther, “Experimental verification of an indefinite causal order”, Science Advances 3, e1602589 (2017)

    2017

  3. [9]

    Indefinite causal order in a quantum switch

    K. Goswami, C. Giarmatzi, M. Kewming, F. Costa, C. Branciard, J. Romero, and A. G. White, “Indefinite causal order in a quantum switch”, Phys. Rev. Lett. 121, 090503 (2018)

    2018

  4. [10]

    Experimental quantum switching for exponentially superior quantum communication complexity

    K. Wei, N. Tischler, S.-R. Zhao, Y.-H. Li, J. M. Arrazola, Y. Liu, W. Zhang, H. Li, L. You, Z. Wang, Y.-A. Chen, B. C. Sanders, Q. Zhang, G. J. Pryde, F. Xu, and J.-W. Pan, “Experimental quantum switching for exponentially superior quantum communication complexity”, Phys. Rev....

    2019

  5. [11]

    Increasing communication capacity via superposition of order

    K. Goswami, Y. Cao, G. A. Paz-Silva, J. Romero, and A. G. White, “Increasing communication capacity via superposition of order”, Phys. Rev. Research 2, 033292 (2020)

    2020

  6. [12]

    Experimental transmission of quantum information using a superposition of causal orders

    Y. Guo, X.-M. Hu, Z.-B. Hou, H. Cao, J.-M. Cui, B.-H. Liu, Y.-F. Huang, C.-F. Li, G.-C. Guo, and G. Chiribella, “Experimental transmission of quantum information using a superposition of causal orders”, Phys. Rev. Lett. 124, 030502 (2020)

    2020

  7. [13]

    Experimental quantum communication enhancement by superposing trajectories

    G. Rubino, L. A. Rozema, D. Ebler, H. Kristj´ ansson, S. Salek, P. Allard Gu´ erin, A. A. Abbott, C. Branciard, ˇC. Brukner, G. Chiribella, and P. Walther, “Experimental quantum communication enhancement by superposing trajectories”, Phys. Rev. Res. 3, 013093 (2021)

    2021

  8. [14]

    Quantum simulation of indefinite causal order induced quantum refrigeration

    H. Cao, N.-N. Wang, Z. Jia, C. Zhang, Y. Guo, B.-H. Liu, Y.-F. Huang, C.-F. Li, and G.-C. Guo, “Quantum simulation of indefinite causal order induced quantum refrigeration”, Phys. Rev. Res. 4, L032029 (2022)

    2022

  9. [15]

    Experimental entanglement of temporal order

    G. Rubino, L. A. Rozema, F. Massa, M. Ara´ ujo, M. Zych, ˇC. Brukner, and P. Walther, “Experimental entanglement of temporal order”, Quantum 6, 621 (2022)

    2022

  10. [16]

    Semi-device-independent certification of indefinite causal order in a photonic quantum switch

    H. Cao, J. Bavaresco, N.-N. Wang, L. A. Rozema, C. Zhang, Y.-F. Huang, B.-H. Liu, C.-F. Li, G.-C. Guo, and P. Walther, “Semi-device-independent certification of indefinite causal order in a photonic quantum switch”, Optica 10, 561–568 (2023)

    2023

  11. [17]

    W.-Q. Liu, Z. Meng, B.-W. Song, J. Li, Q.-Y. Wu, X.-X. Chen, J.-Y. Hong, A.-N. Zhang, and Z.-q. Yin, Experimentally demonstrating indefinite causal order algorithms to solve the generalized deutsch’s problem, arXiv:2305.05416, 2023

    2023 arXiv

  12. [18]

    Demonstration of universal time-reversal for qubit processes

    P. Schiansky, T. Str¨ omberg, D. Trillo, V. Saggio, B. Dive, M. Navascu´ es, and P. Walther, “Demonstration of universal time-reversal for qubit processes”, Optica 10, 200–205 (2023)

    2023

  13. [19]

    Demonstration of a quantum switch in a sagnac configuration

    T. Str¨ omberg, P. Schiansky, R. W. Peterson, M. T. Quintino, and P. Walther, “Demonstration of a quantum switch in a sagnac configuration”, Phys. Rev. Lett. 131, 060803 (2023)

    2023

  14. [20]

    Experimental super-heisenberg quantum metrology with indefinite gate order

    P. Yin, X. Zhao, Y. Yang, Y. Guo, W.-H. Zhang, G.-C. Li, Y.-J. Han, B.-H. Liu, J.-S. Xu, G. Chiribella, G. Chen, C.-F. Li, and G.-C. Guo, “Experimental super-heisenberg quantum metrology with indefinite gate order”, Nature Physics 19, 1122–1127 (2023)

    2023

  15. [21]

    Charging quantum batteries via indefinite causal order: theory and experiment

    G. Zhu, Y. Chen, Y. Hasegawa, and P. Xue, “Charging quantum batteries via indefinite causal order: theory and experiment”, Phys. Rev. Lett. 131, 240401 (2023). 15

    2023

  16. [22]

    Noisy quantum parameter estimation with indefinite causal order

    M. An, S. Ru, Y. Wang, Y. Yang, F. Wang, P. Zhang, and F. Li, “Noisy quantum parameter estimation with indefinite causal order”, Phys. Rev. A 109, 012603 (2024)

    2024

  17. [23]

    Higher-order process matrix tomography of a passively-stable quantum switch

    M. Antesberger, M. T. Quintino, P. Walther, and L. A. Rozema, “Higher-order process matrix tomography of a passively-stable quantum switch”, PRX Quantum 5, 010325 (2024)

    2024

  18. [24]

    C.-F. Li, L. Chen, Y.-X. Yang, G.-C. Li, X.-S. Hong, S.-Q. Zhang, H.-Q. Xu, Y.-C. Liu, G. Chiribella, G. Chen, and G. Guo, Nonlinear enhancement of measurement precision via a hybrid quantum switch , Preprint available at Research Square., 2024

    2024

  19. [25]

    Demonstration of superior communication through thermodynamically free channels in an optical quantum switch

    H. Tang, Y. Guo, X.-M. Hu, Y.-F. Huang, B.-H. Liu, C.-F. Li, and G.-C. Guo, “Demonstration of superior communication through thermodynamically free channels in an optical quantum switch”, Phys. Rev. A 110, 032422 (2024)

    2024

  20. [26]

    Experimental realization of a quantum refrigerator driven by indefinite causal orders

    X. Nie, X. Zhu, K. Huang, K. Tang, X. Long, Z. Lin, Y. Tian, C. Qiu, C. Xi, X. Yang, J. Li, Y. Dong, T. Xin, and D. Lu, “Experimental realization of a quantum refrigerator driven by indefinite causal orders”, Phys. Rev. Lett. 129, 100603 (2022)

    2022

  21. [27]

    Experimental validation of enhanced information capacity by quantum switch in accordance with thermodynamic laws

    C. Xi, X. Liu, H. Liu, K. Huang, X. Long, D. Ebler, X. Nie, O. Dahlsten, and D. Lu, “Experimental validation of enhanced information capacity by quantum switch in accordance with thermodynamic laws”, Phys. Rev. Lett. 133, 040401 (2024)

    2024

  22. [28]

    Experimental aspects of indefinite causal order in quantum mechanics

    L. A. Rozema, T. Str¨ omberg, H. Cao, Y. Guo, B.-H. Liu, and P. Walther, “Experimental aspects of indefinite causal order in quantum mechanics”, Nature Reviews Physics 6, 483–499 (2024)

    2024

  23. [29]

    Computational advantage from quantum-controlled ordering of gates

    M. Ara´ ujo, F. Costa, and ˇC. Brukner, “Computational advantage from quantum-controlled ordering of gates”, Phys. Rev. Lett. 113, 250402 (2014)

    2014

  24. [30]

    Sending classical information via three noisy channels in superposition of causal orders

    L. M. Procopio, F. Delgado, M. Enr ´ ıquez, N. Belabas, and J. A. Levenson, “Sending classical information via three noisy channels in superposition of causal orders”, Phys. Rev. A 101, 012346 (2020)

    2020

  25. [31]

    Classical communication with indefinite causal order for N completely depolarizing channels

    S. Sazim, M. Sedlak, K. Singh, and A. K. Pati, “Classical communication with indefinite causal order for N completely depolarizing channels”, Phys. Rev. A 103, 062610 (2021)

    2021

  26. [32]

    A diagrammatic approach to information transmission in generalised switches

    M. Wilson and G. Chiribella, “A diagrammatic approach to information transmission in generalised switches”, in Proceedings 17th international conference on quantum physics and logic, paris, france, june 2 - 6, 2020, Vol. 340, edited by B. Valiron, S. Mansfield, P. Arrighi, and...

    2021

  27. [34]

    Quantum communication using a quantum switch of quantum switches

    D. Das and S. Bandyopadhyay, “Quantum communication using a quantum switch of quantum switches”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 478, 10.1098/rspa.2022.0231 (2022)

    2022

  28. [35]

    Enhancing quantum state discrimination with indefinite causal order

    S. Kechrimparis, J. Moran, A. Karsa, C. Lee, and H. Kwon, “Enhancing quantum state discrimination with indefinite causal order”, New Journal of Physics 26, 123030 (2024)

    2024

  29. [36]

    Kechrimparis, J

    S. Kechrimparis, J. Moran, and H. Kwon, Probabilistic channel distillation via indefinite causal order, arXiv:2501.13696, 2025

    2025 arXiv

  30. [37]

    Computational advantage from the quantum superposition of multiple temporal orders of photonic gates

    M. M. Taddei, J. Cari˜ ne, D. Mart ´ ınez, T. Garc ´ ıa, N. Guerrero, A. A. Abbott, M. Ara´ ujo, C. Branciard, E. S. G´ omez, S. P. Walborn, L. Aolita, and G. Lima, “Computational advantage from the quantum superposition of multiple temporal orders of photonic gates”, PRX Quan...

    2021

  31. [38]

    Perfect discrimination of no-signalling channels via quantum superposition of causal structures

    G. Chiribella, “Perfect discrimination of no-signalling channels via quantum superposition of causal structures”, Phys. Rev. A 86, 040301 (2012)

    2012

  32. [39]

    Computational advantage from a quantum superposition of qubit gate orders

    M. J. Renner and ˇC. Brukner, “Computational advantage from a quantum superposition of qubit gate orders”, Phys. Rev. Lett. 128, 230503 (2022)

    2022

  33. [40]

    Universal quantum rewinding protocol with an arbitrarily high probability of success

    D. Trillo, B. Dive, and M. Navascu´ es, “Universal quantum rewinding protocol with an arbitrarily high probability of success”, Phys. Rev. Lett. 130, 110201 (2023)

    2023

  34. [41]

    Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations

    M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations”, Phys. Rev. Lett. 123, 210502 (2019)

    2019

  35. [42]

    Probabilistic exact universal quantum circuits for transforming unitary operations

    M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Probabilistic exact universal quantum circuits for transforming unitary operations”, Phys. Rev. A 100, 062339 (2019)

    2019

  36. [43]

    Deterministic transformations between unitary operations: exponential advantage with adaptive quantum circuits and the power of indefinite causality

    M. T. Quintino and D. Ebler, “Deterministic transformations between unitary operations: exponential advantage with adaptive quantum circuits and the power of indefinite causality”, Quantum 6, 679 (2022). 16

    2022

  37. [44]

    Quantum superposition of causal structures as a universal resource for local implementation of nonlocal quantum operations

    P. Ghosal, A. Ghosal, D. Das, and A. G. Maity, “Quantum superposition of causal structures as a universal resource for local implementation of nonlocal quantum operations”, Phys. Rev. A 107, 022613 (2023)

    2023

  38. [45]

    Quantum query complexity of boolean functions under indefinite causal order

    A. A. Abbott, M. Mhalla, and P. Pocreau, “Quantum query complexity of boolean functions under indefinite causal order”, Phys. Rev. Res. 6, L032020 (2024)

    2024

  39. [46]

    Quantum machine learning with indefinite causal order

    N. Ma, P. Z. Zhao, and J. Gong, “Quantum machine learning with indefinite causal order”, Phys. Rev. A 110, 052406 (2024)

    2024

  40. [47]

    Enhancement of nonstabilizerness within indefinite causal order

    Y. Mo, C. Zhu, Z. Liu, M. Jing, and X. Wang, “Enhancement of nonstabilizerness within indefinite causal order”, Phys. Rev. A 109, 062428 (2024)

    2024

  41. [48]

    Quantum gate teleportation with the superposition of causal order

    W.-Q. Liu and H.-R. Wei, “Quantum gate teleportation with the superposition of causal order”, Phys. Rev. Appl. 23, 014064 (2025)

    2025

  42. [49]

    Quantum superposition of the order of parties as a communication resource

    A. Feix, M. Ara´ ujo, and C. ˇC. Brukner, “Quantum superposition of the order of parties as a communication resource”, Phys. Rev. A 92, 052326 (2015)

    2015

  43. [50]

    Exponential communication complexity advantage from quantum superposition of the direction of communication

    P. A. Gu´ erin, A. Feix, M. Ara´ ujo, and ˇC. Brukner, “Exponential communication complexity advantage from quantum superposition of the direction of communication”, Phys. Rev. Lett. 117, 100502 (2016)

    2016

  44. [51]

    Enhanced communication with the assistance of indefinite causal order

    D. Ebler, S. Salek, and G. Chiribella, “Enhanced communication with the assistance of indefinite causal order”, Phys. Rev. Lett. 120, 120502 (2018)

    2018

  45. [52]

    Communication enhancement through quantum coherent control of n channels in an indefinite causal-order scenario

    L. M. Procopio, F. Delgado, M. Enr ´ ıquez, N. Belabas, and J. A. Levenson, “Communication enhancement through quantum coherent control of n channels in an indefinite causal-order scenario”, Entropy 21, 10.3390/e21101012 (2019)

    2019 doi

  46. [53]

    Multifold behavior of the information transmission by the quantum 3-switch

    L. M. Procopio, F. Delgado, M. Enr ´ ıquez, and N. Belabas, “Multifold behavior of the information transmission by the quantum 3-switch”, Quantum Information Processing 20, 219 (2021)

    2021

  47. [54]

    Quantum and classical data transmission through completely depolarizing channels in a superposition of cyclic orders

    G. Chiribella, M. Wilson, and H. F. Chau, “Quantum and classical data transmission through completely depolarizing channels in a superposition of cyclic orders”, Phys. Rev. Lett. 127, 190502 (2021)

    2021

  48. [55]

    Performance characterization of pauli channels assisted by indefinite causal order and post-measurement

    F. Delgado and C. Cardoso-Isidoro, “Performance characterization of pauli channels assisted by indefinite causal order and post-measurement”, Quantum Inf. Comput. 20, 1261–1280 (2020)

    2020

  49. [56]

    Indefinite causal order enables perfect quantum communication with zero capacity channels

    G. Chiribella, M. Banik, S. S. Bhattacharya, T. Guha, M. Alimuddin, A. Roy, S. Saha, S. Agrawal, and G. Kar, “Indefinite causal order enables perfect quantum communication with zero capacity channels”, New Journal of Physics 23, 033039 (2021)

    2021

  50. [57]

    Thermodynamics of quantum switch information capacity activation

    X. Liu, D. Ebler, and O. Dahlsten, “Thermodynamics of quantum switch information capacity activation”, Phys. Rev. Lett. 129, 230604 (2022)

    2022

  51. [58]

    Beyond shannon limits: quantum communications through quantum paths

    M. Caleffi, K. Simonov, and A. S. Cacciapuoti, “Beyond shannon limits: quantum communications through quantum paths”, IEEE Journal on Selected Areas in Communications 41, 2707–2724 (2023)

    2023

  52. [59]

    Quantum switch for the quantum internet: noiseless communications through noisy channels

    M. Caleffi and A. S. Cacciapuoti, “Quantum switch for the quantum internet: noiseless communications through noisy channels”, IEEE Journal on Selected Areas in Communications 38, 575–588 (2020)

    2020

  53. [60]

    Toward the advantages of quantum trajectories on entanglement distribution in quantum networks

    R. Xu, R.-G. Zhou, and Y. Li, “Toward the advantages of quantum trajectories on entanglement distribution in quantum networks”, IEEE Transactions on Wireless Communications 22, 5170–5184 (2023)

    2023

  54. [61]

    Superposition of causal order enables quantum advantage in teleportation under very noisy channels

    C. Mukhopadhyay and A. K. Pati, “Superposition of causal order enables quantum advantage in teleportation under very noisy channels”, Journal of Physics Communications 4, 105003 (2020)

    2020

  55. [62]

    Continuous variable teleportation with indefinite causal order

    M. Ban, “Continuous variable teleportation with indefinite causal order”, Quantum Information Processing 21, 367 (2022)

    2022

  56. [63]

    Quantum teleportation in higher dimension and entanglement distribution via quantum switches

    I. Dey and N. Marchetti, “Quantum teleportation in higher dimension and entanglement distribution via quantum switches”, IET Quantum Communication 6, e12122 (2025)

    2025

  57. [64]

    The entanglement-assisted communication capacity over quantum trajectories

    D. Chandra, M. Caleffi, and A. S. Cacciapuoti, “The entanglement-assisted communication capacity over quantum trajectories”, IEEE Transactions on Wireless Communications 21, 3632–3647 (2022)

    2022

  58. [65]

    Improvement in quantum communication using quantum switch

    A. Mitra, H. Badhani, and S. Ghosh, “Improvement in quantum communication using quantum switch”, Physica Scripta 98, 045101 (2023). 17

    2023

  59. [66]

    General communication enhancement via the quantum switch

    Z. Wu, J. Fullwood, Z. Ma, S.-Q. Zhou, Q. Zhao, and G. Chiribella, “General communication enhancement via the quantum switch”, Phys. Rev. A 111, 012605 (2025)

    2025

  60. [67]

    Quantum shannon theory with superpositions of trajectories

    G. Chiribella and H. Kristj´ ansson, “Quantum shannon theory with superpositions of trajectories”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, 20180903 (2019)

    2019

  61. [68]

    Communication through coherent control of quantum channels

    A. A. Abbott, J. Wechs, D. Horsman, M. Mhalla, and C. Branciard, “Communication through coherent control of quantum channels”, Quantum 4, 333 (2020)

    2020

  62. [69]

    Channel capacity enhancement with indefinite causal order

    N. Loizeau and A. Grinbaum, “Channel capacity enhancement with indefinite causal order”, Phys. Rev. A 101, 012340 (2020)

    2020

  63. [70]

    Experimental communication through superposition of quantum channels

    A. O. T. Pang, N. Lupu-Gladstein, H. Ferretti, Y. B. Yilmaz, A. Brodutch, and A. M. Steinberg, “Experimental communication through superposition of quantum channels”, Quantum 7, 1125 (2023)

    2023

  64. [71]

    Communication through quantum-controlled noise

    P. A. Gu´ erin, G. Rubino, andˇC. Brukner, “Communication through quantum-controlled noise”, Phys. Rev. A 99, 062317 (2019)

    2019

  65. [72]

    Quantum switch instabilities with an open control

    O. A. D. Molitor, A. H. A. Malavazi, R. D. Baldij˜ ao, A. C. Orthey, I. L. Paiva, and P. R. Dieguez, “Quantum switch instabilities with an open control”, Communications Physics 7, 373 (2024)

    2024

  66. [73]

    Deterministic generation of multipartite entanglement via causal activation in the quantum internet

    S. Koudia, A. S. Cacciapuoti, and M. Caleffi, “Deterministic generation of multipartite entanglement via causal activation in the quantum internet”, IEEE Access 11, 73863–73878 (2023)

    2023

  67. [74]

    Coherent control of the causal order of entanglement distillation

    Z. Zuo, M. Hanks, and M. S. Kim, “Coherent control of the causal order of entanglement distillation”, Phys. Rev. A 108, 062601 (2023)

    2023

  68. [75]

    Spencer-Wood, Indefinite causal key distribution , arXiv:2303.03893., 2024

    H. Spencer-Wood, Indefinite causal key distribution , arXiv:2303.03893., 2024

    2024

  69. [76]

    S. G. Naik, S. Sen, R. K. Patra, A. Chakraborty, M. Alimuddin, M. Banik, and P. Ghosal, Local- data-hiding and causal inseparability: probing indefinite causal structures with cryptographic primitives, arXiv:2407.20543., 2024

    2024 arXiv

  70. [77]

    Quantum refrigeration with indefinite causal order

    D. Felce and V. Vedral, “Quantum refrigeration with indefinite causal order”, Phys. Rev. Lett. 125, 070603 (2020)

    2020

  71. [78]

    Indefinite causal order aids quantum depolarizing channel identification

    M. Frey, “Indefinite causal order aids quantum depolarizing channel identification”, Quantum Information Processing 18, 96 (2019)

    2019

  72. [79]

    Mukhopadhyay, M

    C. Mukhopadhyay, M. K. Gupta, and A. K. Pati, Superposition of causal order as a metrological resource for quantum thermometry , arXiv:1812.07508., 2018

    2018 arXiv

  73. [80]

    Quantum metrology with indefinite causal order

    X. Zhao, Y. Yang, and G. Chiribella, “Quantum metrology with indefinite causal order”, Phys. Rev. Lett. 124, 190503 (2020)

    2020

  74. [81]

    Noisy quantum metrology with the assistance of indefinite causal order

    F. Chapeau-Blondeau, “Noisy quantum metrology with the assistance of indefinite causal order”, Phys. Rev. A 103, 032615 (2021)

    2021

  75. [82]

    Indefinite causal order for quantum metrology with quantum thermal noise

    F. Chapeau-Blondeau, “Indefinite causal order for quantum metrology with quantum thermal noise”, Physics Letters A 447, 128300 (2022)

    2022

  76. [83]

    Indefinite causal order for quantum phase estimation with pauli noise

    F. Chapeau-Blondeau, “Indefinite causal order for quantum phase estimation with pauli noise”, Fluctuation and Noise Letters 22, 10.1142/s0219477523500360 (2023)

    2023 doi

  77. [84]

    Indefinite causal order for parameter estimation of channel with depolarization noise

    Y. Yuan, “Indefinite causal order for parameter estimation of channel with depolarization noise”, Physics Letters A 531, 130163 (2025)

    2025

  78. [85]

    Quantum fisher information of phase estimation in the presence of indefinite causal order

    M. Ban, “Quantum fisher information of phase estimation in the presence of indefinite causal order”, Physics Letters A 468, 128749 (2023)

    2023

  79. [86]

    Phase estimation for a single-mode photon influenced by completely thermalizing channels with indefinite causal order

    M. Ban, “Phase estimation for a single-mode photon influenced by completely thermalizing channels with indefinite causal order”, Physics Letters A 521, 129744 (2024)

    2024

  80. [87]

    Measurement with indefinite causal order and the sagnac interferometer

    S. M. Barnett, S. Croke, and S. Franke-Arnold, “Measurement with indefinite causal order and the sagnac interferometer”, Phil. Trans. R. Soc. A 382, 20240447 (2024)

    2024

  81. [88]

    Evading noise in multiparameter quantum metrology with indefinite causal order

    A. Z. Goldberg, K. Heshami, and L. L. S´ anchez-Soto, “Evading noise in multiparameter quantum metrology with indefinite causal order”, Phys. Rev. Res. 5, 033198 (2023)

    2023

  82. [89]

    Quantum non-gaussianity from an indefnite causal order of gaussian operations

    S. Koudia and A. Gharbi, “Quantum non-gaussianity from an indefnite causal order of gaussian operations”, International Journal of Quantum Information 19, 2150026 (2021)

    2021

  83. [90]

    Measuring incompatibility and clustering quantum observables with a quantum switch

    N. Gao, D. Li, A. Mishra, J. Yan, K. Simonov, and G. Chiribella, “Measuring incompatibility and clustering quantum observables with a quantum switch”, Phys. Rev. Lett. 130, 170201 (2023)

    2023

  84. [91]

    Quantum correlations with no causal order

    O. Oreshkov, F. Costa, and ˇC. Brukner, “Quantum correlations with no causal order”, Nature Communications 3, 1092 (2012). 18

    2012

  85. [92]

    Witnesses of causal nonseparability: an introduction and a few case studies

    C. Branciard, “Witnesses of causal nonseparability: an introduction and a few case studies”, Scientific Reports 6, 26018 (2016)

    2016

  86. [93]

    A purification postulate for quantum mechanics with indefinite causal order

    M. Ara´ ujo, A. Feix, M. Navascu´ es, and ˇC. Brukner, “A purification postulate for quantum mechanics with indefinite causal order”, Quantum 1, 10 (2017)

    2017

  87. [94]

    Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics

    O. Oreshkov, “Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics”, Quantum 3, 206 (2019)

    2019

  88. [95]

    Quantum theory cannot violate a causal inequality

    T. Purves and A. J. Short, “Quantum theory cannot violate a causal inequality”, Phys. Rev. Lett. 127, 110402 (2021)

    2021

  89. [96]

    Existence of processes violating causal inequalities on time-delocalised subsystems

    J. Wechs, C. Branciard, and O. Oreshkov, “Existence of processes violating causal inequalities on time-delocalised subsystems”, Nature Communications 14, 1471 (2023)

    2023

  90. [97]

    Witnessing causal nonseparability

    M. Ara´ ujo, C. Branciard, F. Costa, A. Feix, C. Giarmatzi, and ˇC. Brukner, “Witnessing causal nonseparability”, New Journal of Physics 17, 102001 (2015)

    2015

  91. [98]

    Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders

    N. Paunkovi´ c and M. Vojinovi´ c, “Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders”, Quantum 4, 275 (2020)

    2020

  92. [99]

    Fundamental limits for realizing quantum processes in spacetime

    V. Vilasini and R. Renner, “Fundamental limits for realizing quantum processes in spacetime”, Phys. Rev. Lett. 133, 080201 (2024)

    2024

  93. [100]

    Quantum circuits with classical versus quantum control of causal order

    J. Wechs, H. Dourdent, A. A. Abbott, and C. Branciard, “Quantum circuits with classical versus quantum control of causal order”, PRX Quantum 2, 030335 (2021)

    2021

  94. [101]

    Causal and causally separable processes

    O. Oreshkov and C. Giarmatzi, “Causal and causally separable processes”, New Journal of Physics 18, 093020 (2016)

    2016

  95. [102]

    Genuinely multipartite noncausality

    A. A. Abbott, J. Wechs, F. Costa, and C. Branciard, “Genuinely multipartite noncausality”, Quantum 1, 39 (2017)

    2017

  96. [103]

    Maximal incompatibility of locally classical behavior and global causal order in multiparty scenarios

    ¨A. Baumeler, A. Feix, and S. Wolf, “Maximal incompatibility of locally classical behavior and global causal order in multiparty scenarios”, Phys. Rev. A 90, 042106 (2014)

    2014

  97. [104]

    The space of logically consistent classical processes without causal order

    ¨A. Baumeler and S. Wolf, “The space of logically consistent classical processes without causal order”, New Journal of Physics 18, 013036 (2016)

    2016

  98. [105]

    On the definition and characterisation of multipartite causal (non)separability

    J. Wechs, A. A. Abbott, and C. Branciard, “On the definition and characterisation of multipartite causal (non)separability”, New Journal of Physics 21, 013027 (2019)

    2019

  99. [106]

    Indefinite causal structures for continuous- variable systems

    F. Giacomini, E. Castro-Ruiz, and ˇC. Brukner, “Indefinite causal structures for continuous- variable systems”, New Journal of Physics 18, 113026 (2016)

    2016

  100. [107]

    Composition rules for quantum processes: a no-go theorem

    P. A. Gu´ erin, M. Krumm, C. Budroni, and ˇC. Brukner, “Composition rules for quantum processes: a no-go theorem”, New Journal of Physics 21, 012001 (2019)

    2019

  101. [108]

    Strategies for single-shot discrimination of process matrices

    P. Lewandowska, L. Pawela, and Z. Pucha la, “Strategies for single-shot discrimination of process matrices”, Scientific Reports 13, 3046 (2023)

    2023

  102. [109]

    Revisiting dynamics of quantum causal structures—when can causal order evolve?

    J. H. Selby, A. B. Sainz, and P. Horodecki, “Revisiting dynamics of quantum causal structures—when can causal order evolve?”, Entropy 26, 10.3390/e26080643 (2024)

    2024 doi

  103. [110]

    Observer-dependent locality of quantum events

    P. A. Gu´ erin and ˇC. Brukner, “Observer-dependent locality of quantum events”, New Journal of Physics 20, 103031 (2018)

    2018

  104. [111]

    Wechs and O

    J. Wechs and O. Oreshkov, Subsystem decompositions of quantum evolutions and transformations between causal perspectives, arXiv:2411.16504., 2024

    2024 arXiv

  105. [112]

    Entanglement detection

    O. G¨ uhne and G. T´ oth, “Entanglement detection”, Physics Reports474, 1–75 (2009)

    2009

  106. [113]

    The simplest causal inequalities and their violation

    C. Branciard, M. Ara´ ujo, A. Feix, F. Costa, and ˇC. Brukner, “The simplest causal inequalities and their violation”, New Journal of Physics 18, 013008 (2016)

    2016

  107. [114]

    Multipartite causal correlations: polytopes and inequalities

    A. A. Abbott, C. Giarmatzi, F. Costa, and C. Branciard, “Multipartite causal correlations: polytopes and inequalities”, Phys. Rev. A 94, 032131 (2016)

    2016

  108. [115]

    Quantum generalizations of bell’s inequality

    B. S. Cirel’son, “Quantum generalizations of bell’s inequality”, Letters in Mathematical Physics 4, 93–100 (1980)

    1980

  109. [116]

    Bounding quantum correlations with indefinite causal order

    ˇC. Brukner, “Bounding quantum correlations with indefinite causal order”, New Journal of Physics 17, 083034 (2015)

    2015

  110. [117]

    Liu and G

    Z. Liu and G. Chiribella, Tsirelson bounds for quantum correlations with indefinite causal order, arXiv:2403.02749, 2024

    2024 arXiv

  111. [118]

    Device-independent certification of indefinite causal order in the quantum switch

    T. van der Lugt, J. Barrett, and G. Chiribella, “Device-independent certification of indefinite causal order in the quantum switch”, Nature Communications 14, 5811 (2023)

    2023

  112. [119]

    Semi-device-independent certification of indefinite causal order

    J. Bavaresco, M. Ara´ ujo, ˇC. Brukner, and M. T. Quintino, “Semi-device-independent certification of indefinite causal order”, Quantum 3, 176 (2019). 19

    2019

  113. [120]

    Semi-device-independent certification of causal nonseparability with trusted quantum inputs

    H. Dourdent, A. A. Abbott, N. Brunner, I. ˇSupi´ c, and C. Branciard, “Semi-device-independent certification of causal nonseparability with trusted quantum inputs”, Phys. Rev. Lett. 129, 090402 (2022)

    2022

  114. [121]

    Network-Device-Independent Certification of Causal Nonseparability

    H. Dourdent, A. A. Abbott, I. ˇSupi´ c, and C. Branciard, “Network-Device-Independent Certification of Causal Nonseparability”, Quantum 8, 1514 (2024)

    2024

  115. [122]

    Possibilistic and maximal indefinite causal order in the quantum switch

    T. van der Lugt and N. Ormrod, “Possibilistic and maximal indefinite causal order in the quantum switch”, Quantum 8, 1543 (2024)

    2024

  116. [123]

    Incompatible results of quantum measurements

    A. Peres, “Incompatible results of quantum measurements”, Physics Letters A 151, 107–108 (1990)

    1990

  117. [124]

    Quantum mysteries revisited

    N. D. Mermin, “Quantum mysteries revisited”, American Journal of Physics 58, 731–734 (1990)

    1990

  118. [125]

    Bell’s theorem for temporal order

    M. Zych, F. Costa, I. Pikovski, and ˇC. Brukner, “Bell’s theorem for temporal order”, Nature Communications 10, 3772 (2019)

    2019

  119. [126]

    Gravitational quantum switch on a superposition of spherical shells

    N. S. M´ oller, B. Sahdo, and N. Yokomizo, “Gravitational quantum switch on a superposition of spherical shells”, Quantum 8, 1248 (2024)

    2024

  120. [127]

    Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems

    E. Castro-Ruiz, F. Giacomini, A. Belenchia, and ˇC. Brukner, “Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems”, Nature Communications 11, 2672 (2020)

    2020

  121. [128]

    Quantum switch in the gravity of earth

    N. S. M´ oller, B. Sahdo, and N. Yokomizo, “Quantum switch in the gravity of earth”, Phys. Rev. A 104, 042414 (2021)

    2021

  122. [129]

    Simulating indefinite causal order with rindler observers

    A. Dimi´ c, M. Milivojevi´ c, D. Goˇ canin, N. S. M´ oller, andˇC. Brukner, “Simulating indefinite causal order with rindler observers”, Frontiers in Physics 8, 10.3389/fphy.2020.525333 (2020)

    2020

  123. [130]

    Embedding cyclic information-theoretic structures in acyclic space- times: no-go results for indefinite causality

    V. Vilasini and R. Renner, “Embedding cyclic information-theoretic structures in acyclic space- times: no-go results for indefinite causality”, Phys. Rev. A 110, 022227 (2024)

    2024

  124. [131]

    Mapping indefinite causal order processes to composable quantum protocols in a spacetime

    M. Salzger and V. Vilasini, “Mapping indefinite causal order processes to composable quantum protocols in a spacetime”, New Journal of Physics, 10.1088/1367-2630/ad9d6f (2024)

    2024 doi

  125. [133]

    de la Hamette, V

    A.-C. de la Hamette, V. Kabel, and ˇC. Brukner, What an event is not: unravelling the identity of events in quantum theory and gravity , arXiv:2404.00159., 2024

    2024 arXiv

  126. [134]

    Fedida, A.-C

    S. Fedida, A.-C. de la Hamette, V. Kabel, and ˇC. Brukner, Knot invariants and indefinite causal order, arXiv:2409.11448, 2024

    2024

  127. [135]

    Quantum superpositions of minkowski spacetime

    J. Foo, C. S. Arabaci, M. Zych, and R. B. Mann, “Quantum superpositions of minkowski spacetime”, Phys. Rev. D 107, 045014 (2023)

    2023

  128. [136]

    X. Liu, C. Zeng, and J. Wang, Generation of quantum entanglement in superposed diamond spacetime, arXiv:2501.00246, 2024

    2024 arXiv

  129. [137]

    J. Foo, R. B. Mann, and M. Zych, Relativity and decoherence of spacetime superpositions , arXiv:2302.03259, 2023. 20

    2023 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.