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arxiv: 2506.16949 · v4 · submitted 2025-06-20 · 🪐 quant-ph · physics.optics

Toward an Experimental Device-Independent Verification of Indefinite Causal Order

Carla M. D. Richter , Michael Antesberger , Huan Cao , Philip Walther , Lee A. Rozema This is my paper

Pith reviewed 2026-05-19 08:25 UTC · model grok-4.3

classification 🪐 quant-ph physics.optics
keywords indefinite causal orderquantum switchdevice-independent verificationBell inequalityquantum causalityexperimental quantum information
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The pith

An experiment measures 1.8328 in a quantum switch, exceeding the 1.75 bound for definite causal order by 18 standard deviations in a device-independent test.

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

The paper shows that a quantum switch can produce correlations that exceed any bound possible if events always follow a fixed causal order. By running a Bell-like inequality on the switch, the authors record a value well above the definite-order limit without assuming details of the devices. A reader would care because this is the first step toward confirming indefinite causal order without relying on trust in the experimental equipment or models. The result uses the quantum switch to create a superposition of causal directions and checks whether the statistics can still be explained by any classical ordering.

Core claim

We implement the recently proposed Bell-like inequality for the quantum switch and obtain an experimental value of 1.8328 ± 0.0045. This lies 18 standard deviations above the bound of 1.75 that holds for any process with definite causal order. The demonstration constitutes the first device-independent verification of indefinite causal order, although detection and locality loopholes remain open.

What carries the argument

The Bell-like inequality that upper-bounds correlations under the assumption of definite causal order in the quantum switch process.

If this is right

  • Device-independent certification of indefinite causal order becomes possible once the remaining loopholes are closed.
  • Protocols that exploit causal superpositions can be made secure against device imperfections.
  • The same inequality framework can be applied to other quantum processes that mix causal orders.
  • Experimental efforts can now focus on high-efficiency detectors and space-like separation tailored to causal-order tests.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar inequalities might be derived for other indefinite-causal-order processes beyond the quantum switch.
  • Closing the loopholes will likely require combining high-efficiency single-photon sources with long-baseline interferometry.
  • The approach provides a concrete target for theorists who want to prove that no hidden causal model can reproduce the quantum-switch statistics.

Load-bearing premise

The laboratory setup actually implements the quantum switch process as described by the theoretical inequality rather than allowing some undetected classical mechanism to produce the observed statistics.

What would settle it

A follow-up experiment that closes both the detection-efficiency and locality loopholes and still records a value significantly above 1.75 would support the claim; a result at or below 1.75 under closed loopholes would refute it.

Figures

Figures reproduced from arXiv: 2506.16949 by Carla M. D. Richter, Huan Cao, Lee A. Rozema, Michael Antesberger, Philip Walther.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: b), wherein the close agreement between the ideal values and our experimentally measured probabilities is apparent. Summing these probabilities together, we observe a clear violation of VBC’s inequality of 1.8427 ± 0.0038, [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

In classical physics, events follow a definite causal order: the past influences the future, but not the reverse. Quantum theory, however, permits superpositions of causal orders -- so-called indefinite causal orders -- which can provide operational advantages over classical scenarios. Verifying such phenomena has sparked significant interest, much like earlier efforts devoted to refuting local realism and confirming quantum entanglement. To date, demonstrations of indefinite causal order have all been based a process called the quantum switch and have relied on device-dependent or semi-device-independent protocols. Achieving a device-independent verification of indefinite causal order would imply that nature allows for correlations that do not respect causality, independent of any experimental assumptions or underlying theoretical description of the experiment. To this end, a recent theoretical development introduced a Bell-like inequality that allows for fully device-independent verification of indefinite causal order in a quantum switch. Here we implement this verification by experimentally violating this inequality. In particular, we measure a value of $1.8328 \pm 0.0045$, which is 18 standard deviations above the Definite Causal Order Bound of $1.75$. Our work presents the first implementation of a device-independent protocol to verify indefinite causal order, albeit in the presence of experimental loopholes. This represents an important step towards the device-independent verification of an indefinite causal order, and provides a context in which to identify loopholes specifically related to the verification of indefinite causal order.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper reports the first experimental implementation of a device-independent protocol to verify indefinite causal order via violation of a Bell-like inequality in a quantum switch. They measure a value of 1.8328 ± 0.0045, exceeding the definite causal order bound of 1.75 by 18 standard deviations, while explicitly noting the presence of detection and locality loopholes.

Significance. If the loopholes can be closed, the result would mark a meaningful advance toward fully device-independent certification of indefinite causal order, providing both a concrete experimental benchmark and a framework for identifying loopholes unique to causal-order witnesses. The large violation demonstrates practical feasibility of the inequality under current technology.

major comments (2)
  1. [Abstract] Abstract: The central claim of 'device-independent verification' is load-bearing for the paper's contribution, yet the abstract itself states that the result holds 'albeit in the presence of experimental loopholes.' This directly undercuts the device-independent interpretation, as open detection and locality loopholes permit classical definite-causal-order models to reproduce values above 1.75 without indefinite order.
  2. [Results] Experimental results (corresponding to the reported value 1.8328 ± 0.0045): No quantitative bound is given on the detection efficiency achieved versus the threshold required by the inequality to rule out local hidden-variable explanations that exploit the loopholes. Without this, the 18-sigma violation cannot be interpreted as device-independent certification.
minor comments (2)
  1. [Methods] Clarify in the methods whether the parties are space-like separated and provide the measured detection efficiency together with the theoretical threshold for the inequality.
  2. [Figures] Ensure all figures showing the causal-order witness are labeled with the exact inequality being tested and the numerical bound 1.75.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting these important points regarding the interpretation of our results. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim of 'device-independent verification' is load-bearing for the paper's contribution, yet the abstract itself states that the result holds 'albeit in the presence of experimental loopholes.' This directly undercuts the device-independent interpretation, as open detection and locality loopholes permit classical definite-causal-order models to reproduce values above 1.75 without indefinite order.

    Authors: We agree that the abstract's phrasing risks overstating the current experimental status. While the implemented protocol is device-independent in its theoretical formulation, the presence of open loopholes means the result does not yet constitute a full device-independent certification. We will revise the abstract to more precisely describe the work as the first experimental implementation of the device-independent protocol, subject to the noted loopholes, consistent with the manuscript title that uses 'Toward'. revision: yes

  2. Referee: [Results] Experimental results (corresponding to the reported value 1.8328 ± 0.0045): No quantitative bound is given on the detection efficiency achieved versus the threshold required by the inequality to rule out local hidden-variable explanations that exploit the loopholes. Without this, the 18-sigma violation cannot be interpreted as device-independent certification.

    Authors: The referee is correct that a direct comparison of the achieved detection efficiency to the threshold required to close the detection loophole would improve the clarity of the results section. The current text notes the loopholes but does not provide this quantitative detail. We will add the relevant numbers and threshold in the revised manuscript to allow readers to assess the experimental limitations precisely. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental violation of externally derived bound

full rationale

The paper reports a direct experimental measurement of a correlation value (1.8328 ± 0.0045) that exceeds the definite causal order bound of 1.75 by 18 standard deviations. The Bell-like inequality used for this verification is introduced by a recent theoretical development cited in the paper rather than derived internally. No equations or steps within the manuscript reduce the reported violation to a fitted parameter, a self-referential definition, or a load-bearing self-citation whose validity depends on the present result. The experimental apparatus and data analysis stand as an independent test against the pre-existing theoretical bound, rendering the derivation chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the theoretical Bell-like inequality for the quantum switch and the assumption that the optical setup implements the required process matrix. No free parameters are fitted in the reported violation itself.

axioms (1)
  • domain assumption Quantum mechanics permits process matrices with indefinite causal order.
    Invoked as the theoretical foundation for the inequality and the quantum switch.

pith-pipeline@v0.9.0 · 5796 in / 1126 out tokens · 29390 ms · 2026-05-19T08:25:24.389552+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Time-Delocalized Local Measurements in an Indefinite Causal Order

    quant-ph 2026-04 unverdicted novelty 7.0

    The authors experimentally demonstrate time-delocalized local measurements inside a photonic quantum switch that preserve indefinite causal order, achieving a causal witness value of C_W ≈ -0.305(1).

Reference graph

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