arxiv: 2604.11878 · v1 · submitted 2026-04-13 · 🪐 quant-ph

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Time-Delocalized Local Measurements in an Indefinite Causal Order

Yann Valibouse , Mart\'i Cladera-Rossell\'o , Michael Antesberger , Patrick Lima , Philip Walther , Lee A. Rozema

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Pith reviewed 2026-05-10 16:04 UTC · model grok-4.3

classification 🪐 quant-ph

keywords indefinite causal orderquantum switchlocal measurementstime-delocalized ancillacausal witnessphotonic quantum switchquantum eraser

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The pith

Local measurements realized inside quantum switch preserving indefinite causal order via time-delocalized ancilla

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

This paper introduces a protocol to perform local measurements inside a quantum switch with indefinite causal order. Previous photonic implementations could not extract local results without destroying the superposition of causal orders or delaying readout. By coupling the system photon to a time-delocalized ancilla, the measurement apparatus interacts at two distinct times yet produces a single outcome. The protocol is realized experimentally in a photonic quantum switch using post-selected linear optical gates and a quantum eraser, with preservation of the indefinite causal order certified by a negative causal witness.

Core claim

We experimentally realize a local measurement scheme for the quantum switch by coupling the photon to a time-delocalized ancilla system. Our method ensures that the measurement apparatus interacts with the system at two distinct times and yet yields a single outcome. We use a quantum eraser measurement to preserve the ICO, which we certify by measuring a causal witness and finding a negative value of C_W ≈ -0.305(1). This also provides a general method for path-coherence-preserving measurements with broad applications beyond ICO.

What carries the argument

The time-delocalized ancilla system that couples to the photon in the quantum switch at two times, enabling a single local readout while preserving the superposition of causal orders.

Load-bearing premise

The post-selected linear optical gates and the engineered time-delocalized ancilla coupling preserve the required coherences without introducing uncontrolled decoherence or bias.

What would settle it

Observing a positive causal witness value C_W or absence of interference in the quantum eraser would show that the indefinite causal order was not preserved.

Figures

Figures reproduced from arXiv: 2604.11878 by Lee A. Rozema, Mart\'i Cladera-Rossell\'o, Michael Antesberger, Patrick Lima, Philip Walther, Yann Valibouse.

**Figure 2.** Figure 2: FIG. 2: Experimental implementation [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Characterization of Bob’s Measurements. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Causal witness in the presence of which-path [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

read the original abstract

Processes with indefinite causal order (ICO), such as the quantum switch, are an emerging resource for quantum tasks and a fundamental test bed for studies of temporal correlations in quantum mechanics. A limitation of past photonic implementations of the quantum switch, however, is their inability to perform measurements inside the switch without either destroying the superposition of causal orders or delaying readout until the after the quantum switch. Measurements where the results are read out locally are needed for several applications of ICO, but also for a loophole-free verification of ICO. Here, we overcome past limitations by introducing a $\mathit{local}$ measurement scheme and coupling the photon in the switch to a $\mathit{time-delocalized}$ ancilla system. We experimentally realize this protocol using a photonic quantum switch with post-selected linear optical logic gates. Our method ensures that the measurement apparatus interacts with the system at two distinct times and yet yields a single outcome. We use a quantum eraser measurement to preserve the ICO, which we certify by measuring a causal witness and finding a negative value of $\mathcal{C}_W \approx -0.305 (1)$. Furthermore, by explicitly realizing a time-delocalized ancilla system, our protocol not only enables a new class of quantum switch protocols requiring local readout, but also provides a general method for path-coherence-preserving measurements with broad applications beyond ICO.

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.

Desk Editor's Note private letter to a colleague

The paper gives a workable photonic protocol for local readout inside a quantum switch by pairing a time-delocalized ancilla with a quantum eraser, and they measure a negative causal witness of about -0.3.

read the letter

The main result is an experimental scheme that lets a measurement interact with the switch photon at two different times yet still return a single outcome while keeping the indefinite causal order. They do this by coupling the photon to a time-delocalized ancilla and using a quantum eraser to protect the superposition, then certify the order with a causal witness that comes out negative at roughly -0.305 with a small uncertainty. This is new relative to earlier photonic switches, which either destroyed the causal superposition or postponed any readout until after the device finished. The protocol therefore opens routes to applications that actually need measurements inside the switch rather than only at the end. The experiment itself is straightforward: a linear-optical implementation with post-selection, and the witness value is reported clearly enough to show the central claim is not empty. The soft spot is the post-selection step. Linear-optical gates with heralding can introduce amplitude or phase biases that depend on which events are kept, and the witness is sensitive to exactly those coherences. The abstract does not lay out the full data cuts, efficiency numbers, or checks against selective discarding, so it is not yet obvious that the negative value is free of such artifacts. If the full manuscript has solid controls on that point the result stands; if not, the witness could be inflated. This work is aimed at groups already running photonic ICO experiments or thinking about loophole-free tests and local-readout protocols. A reader who needs a concrete method for measurements inside the switch will find the protocol useful even if they have to adapt the post-selection details. It deserves a serious referee because the experimental advance is concrete and the target application is well-motivated, though reviewers will likely press for more on the post-selection analysis and error budget. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a protocol for local measurements in indefinite causal order (ICO) processes via coupling to a time-delocalized ancilla system, ensuring interaction at distinct times with a single readout outcome. It experimentally implements this in a photonic quantum switch using post-selected linear optical logic gates and a quantum eraser, certifying ICO by measuring a causal witness with value C_W ≈ -0.305(1).

Significance. If the post-selection is shown to be unbiased, the work enables a new class of ICO protocols with local readout, addressing a key limitation of prior photonic implementations and supporting applications in quantum information as well as loophole-free ICO verification. The explicit realization of the time-delocalized ancilla provides a general coherence-preserving measurement technique.

major comments (2)

[§4] §4 (Experimental Implementation): The post-selection efficiency, full data selection criteria, heralding conditions for the linear optical gates, and complete error budget (including potential phase errors or amplitude biases from the quantum eraser) are not provided. This is load-bearing for the central claim, as the reported C_W ≈ -0.305(1) could be affected by selective discarding of events that artificially enhances negativity without preserving the causal superposition coherences.
[§3] §3 (Theoretical Protocol): The coupling of the time-delocalized ancilla to the system is described at a high level, but lacks explicit verification that the single-outcome measurement does not introduce post-selection-dependent collapse of the causal order superposition; a concrete calculation or bound on any introduced decoherence would be needed to support the witness measurement.

minor comments (2)

[Abstract and §2] Notation for the causal witness (C_W vs. mathcal{C}_W) is used inconsistently between abstract and main text; standardize throughout.
[Figures] Figure captions for the experimental setup should explicitly label the post-selection step and its relation to the witness operator to improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and their constructive comments. We address each of the major comments below and have made revisions to incorporate the suggested improvements.

read point-by-point responses

Referee: [§4] §4 (Experimental Implementation): The post-selection efficiency, full data selection criteria, heralding conditions for the linear optical gates, and complete error budget (including potential phase errors or amplitude biases from the quantum eraser) are not provided. This is load-bearing for the central claim, as the reported C_W ≈ -0.305(1) could be affected by selective discarding of events that artificially enhances negativity without preserving the causal superposition coherences.

Authors: We agree that these details are essential to substantiate the central claim. In the revised manuscript we have expanded §4 (and added a supplementary note) with the post-selection efficiency, the complete data selection criteria, the heralding conditions for the linear optical gates, and a full error budget. The budget includes explicit bounds on phase errors and amplitude biases arising from the quantum eraser; we show that the post-selection remains unbiased with respect to the causal-order superposition and does not artificially inflate the negativity of the witness. revision: yes
Referee: [§3] §3 (Theoretical Protocol): The coupling of the time-delocalized ancilla to the system is described at a high level, but lacks explicit verification that the single-outcome measurement does not introduce post-selection-dependent collapse of the causal order superposition; a concrete calculation or bound on any introduced decoherence would be needed to support the witness measurement.

Authors: We appreciate this observation. Although the protocol is outlined in §3, we have added an explicit calculation in the revised version demonstrating that the single-outcome measurement performed by the time-delocalized ancilla does not induce post-selection-dependent collapse of the causal-order superposition. The calculation supplies a quantitative upper bound on any residual decoherence, confirming that the measured witness remains valid. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental measurement of causal witness

full rationale

The paper reports an experimental photonic realization of time-delocalized local measurements inside a quantum switch, using post-selected gates and a quantum eraser to obtain a single-outcome readout while preserving ICO. The central result is the measured value of the causal witness C_W ≈ -0.305(1), which is an empirical datum obtained from the apparatus rather than a theoretical prediction derived from fitted parameters or self-referential definitions. No load-bearing derivation step reduces to its own inputs by construction; the work is self-contained as a physical demonstration whose validity rests on the experimental controls and the independently defined witness operator, not on any tautological renaming or self-citation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The claim rests on standard quantum optics assumptions plus the paper-specific construction of the time-delocalized ancilla and post-selection; no free parameters are explicitly fitted in the abstract, but the ancilla timing and coupling strengths are engineered elements.

axioms (2)

domain assumption Linear optical elements can implement the quantum switch in superposition of causal orders when post-selected
Invoked in the experimental realization section of the abstract.
domain assumption The quantum eraser can erase which-path information without destroying the indefinite causal order
Used to preserve ICO during the local measurement.

invented entities (1)

time-delocalized ancilla system no independent evidence
purpose: To allow the measurement apparatus to interact with the system at two distinct times while producing a single outcome and preserving path coherence
Central new element introduced to overcome the readout limitation; no independent falsifiable prediction outside the experiment is given.

pith-pipeline@v0.9.0 · 5561 in / 1504 out tokens · 111298 ms · 2026-05-10T16:04:49.735057+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

51 extracted references · 23 canonical work pages · 1 internal anchor

[1]

Chiribella, G

G. Chiribella, G. M. D’Ariano, P. Perinotti, and B. Val- iron, Quantum computations without definite causal structure, Physical Review A—Atomic, Molecular, and Optical Physics88, 022318 (2013)

2013
[2]

Oreshkov, F

O. Oreshkov, F. Costa, and ˇC. Brukner, Quantum corre- lations with no causal order, Nature Communications3, 1092 (2012), arXiv:1105.4464 [quant-ph]

work page arXiv 2012
[3]

Experimental aspects of indefinite causal order in quan- tum mechanics, Nature Reviews Physics , 483 (2024)

2024
[4]

Baumeler, A

¨A. Baumeler, A. Feix, and S. Wolf, Maximal incompati- bility of locally classical behavior and global causal order in multiparty scenarios, Physical Review A90, 042106 (2014)

2014
[5]

Baumeler and S

¨A. Baumeler and S. Wolf, The space of logically consis- tent classical processes without causal order, New Jour- nal of Physics18, 013036 (2016)

2016
[6]

Wechs, H

J. Wechs, H. Dourdent, A. A. Abbott, and C. Branciard, Quantum circuits with classical versus quantum control of causal order, PRX Quantum2, 030335 (2021)

2021
[7]

Bavaresco, M

J. Bavaresco, M. Murao, and M. T. Quintino, Unitary channel discrimination beyond group structures: Ad- vantages of sequential and indefinite-causal-order strate- gies, Journal of Mathematical Physics63, 042203 (2022), arXiv:2105.13369 [quant-ph]

work page arXiv 2022
[8]

Ara´ ujo, A

M. Ara´ ujo, A. Feix, F. Costa, andˇC. Brukner, Quantum circuits cannot control unknown operations, New J. Phys. 16, 093026
[9]

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 superposi- tion of multiple temporal orders of photonic gates, PRX Quantum2, 010320 (2021), arXiv:2002.07817 [quant-ph]

work page arXiv 2021
[10]

M. J. Renner and ˇC. Brukner, Computational Advantage from a Quantum Superposition of Qubit Gate Orders, Phys. Rev. Lett.128, 230503 (2022), arXiv:2112.14541 [quant-ph]

work page arXiv 2022
[11]

Baumeler and S

¨A. . Baumeler and S. Wolf, Perfect signaling among three parties violating predefined causal order, inInformation Theory (ISIT), 2014 IEEE International Symposium on (2014) pp. 526–530, arXiv:1312.5916 [quant-ph]

work page arXiv 2014
[12]

A. Feix, M. Ara´ ujo, andˇC. Brukner, Quantum superposi- tion of the order of parties as a communication resource, Phys. Rev. A92, 052326 (2015)

2015
[13]

P. A. Gu´ erin, A. Feix, M. Ara´ ujo, andˇC. Brukner, Expo- nential communication complexity advantage from quan- tum superposition of the direction of communication, Phys. Rev. Lett.117, 100502
[14]

Refrigeration with Indefinite Causal Orders on a Cloud Quantum Computer

D. Felce, V. Vedral, and F. Tennie, Refrigeration with Indefinite Causal Orders on a Cloud Quantum Computer, arXiv e-prints , arXiv:2107.12413 (2021), arXiv:2107.12413 [quant-ph]

work page arXiv 2021
[15]

T. Guha, M. Alimuddin, and P. Parashar, Thermody- namic advancement in the causally inseparable occur- rence of thermal maps, arXiv arXiv:2003.01464

work page arXiv 2003
[16]

Simonov, G

K. Simonov, G. Francica, G. Guarnieri, and M. Pater- nostro, Work extraction from coherently activated maps via quantum switch, Phys. Rev. A105, 032217 (2022)

2022
[17]

Frey, Indefinite causal order aids quantum depolar- izing channel identification, Quantum Information Pro- cessing18, 96 (2019)

M. Frey, Indefinite causal order aids quantum depolar- izing channel identification, Quantum Information Pro- cessing18, 96 (2019)

2019
[18]

Chapeau-Blondeau, Indefinite causal order for quan- tum metrology with quantum thermal noise, Physics Let- ters A447, 128300

F. Chapeau-Blondeau, Indefinite causal order for quan- tum metrology with quantum thermal noise, Physics Let- ters A447, 128300
[19]

X. Zhao, Y. Yang, and G. Chiribella, Quantum metrol- ogy with indefinite causal order, Phys. Rev. Lett.124, 190503
[20]

Spencer-Wood, Indefinite causal key distribution, Journal of Physics A: Mathematical and Theoretical (2025)

H. Spencer-Wood, Indefinite causal key distribution, Journal of Physics A: Mathematical and Theoretical (2025)

2025
[21]

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
[22]

L. M. Procopio, A. Moqanaki, M. Ara´ ujo, F. Costa, I. Alonso Calafell, E. G. Dowd, D. R. Hamel, L. A. Rozema, ˇC. Brukner, and P. Walther, Experimental su- perposition of orders of quantum gates, Nature Commu- nications6, 7913 (2015), arXiv:1412.4006 [quant-ph]

work page arXiv 2015
[23]

Rubino, L

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 Advances3, e1602589 (2017), arXiv:1608.01683 [quant-ph]

work page arXiv 2017
[24]

Rubino, L

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 8 trajectories, Physical Review Research3, 013093 (2021), arXiv:2007.05005 [quant-ph]

work page arXiv 2021
[25]

Rubino, L

G. Rubino, L. A. Rozema, F. Massa, M. Ara´ ujo, M. Zych, ˇC. Brukner, and P. Walther, Experimental en- tanglement of temporal order, Quantum6, 621 (2022), arXiv:1712.06884 [quant-ph]

work page arXiv 2022
[26]

Guo, X.-M

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), arXiv:1811.07526 [quant-ph]

work page arXiv 2020
[27]

Cao, N.-N

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 re- frigeration, Physical Review Research4, L032029 (2022), arXiv:2101.07979 [quant-ph]

work page arXiv 2022
[28]

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, Op- tica10, 561 (2023), arXiv:2202.05346 [quant-ph]

work page arXiv 2023
[29]

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)

2023
[30]

M. An, S. Ru, Y. Wang, Y. Yang, F. Wang, P. Zhang, and F. Li, Noisy quantum parameter estimation with in- definite causal order, Phys. Rev. A109, 012603 (2024)

2024
[31]

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 Exponen- tially Superior Quantum Communication Complexity, Phys. Rev. Lett.122, 120504 (2019), arXiv:1810.10238 [quant-ph]

work page arXiv 2019
[32]

Goswami, C

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
[33]

Goswami, Y

K. Goswami, Y. Cao, G. A. Paz-Silva, J. Romero, and A. G. White, Increasing communication capacity via superposition of order, Phys. Rev. Research2, 033292 (2020)

2020
[34]

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,et al., Experimental super-heisenberg quantum metrology with indefinite gate order, Nature Physics19, 1122 (2023)

2023
[35]

Antesberger, M

M. Antesberger, M. T. Quintino, P. Walther, and L. A. Rozema, Higher-order process matrix tomography of a passively-stable quantum switch, PRX Quantum5, 010325 (2024)

2024
[36]

Toward an Experimental Device-Independent Verification of Indefinite Causal Order

C. Richter, M. Antesberger, H. Cao, P. Walther, and L. A. Rozema, Towards an experimental device- independent verification of indefinite causal order, arXiv preprint arXiv:2506.16949 (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[37]

Ara´ ujo, C

M. Ara´ ujo, C. Branciard, F. Costa, A. Feix, C. Giar- matzi, and ˇC. Brukner, Witnessing causal nonseparabil- ity, New Journal of Physics17, 102001 (2015)

2015
[38]

Purves and A

T. Purves and A. J. Short, Quantum Theory Cannot Vi- olate a Causal Inequality, Phys. Rev. Lett.127, 110402 (2021), arXiv:2101.09107 [quant-ph]

work page arXiv 2021
[39]

Van Der Lugt, J

T. Van Der Lugt, J. Barrett, and G. Chiribella, Device- independent certification of indefinite causal order in the quantum switch, Nature Communications14, 5811 (2023)

2023
[40]

Bavaresco, M

J. Bavaresco, M. Ara´ ujo, ˇC. Brukner, and M. T. Quintino, Semi-device-independent certification of indefinite causal order, Quantum3, 176 (2019), arXiv:1903.10526 [quant-ph]

work page arXiv 2019
[41]

Le´ sniak, R

M. Le´ sniak, R. Kukulski, P. Lewandowska, G. Rajchel- Mieldzio´ c, and M. Wro´ nski, A bipartite quantum key dis- tribution protocol based on indefinite causal order, arXiv preprint arXiv:2603.08204 (2026)

work page arXiv 2026
[42]

Englert, Fringe visibility and which-way informa- tion: An inequality, Physical review letters77, 2154 (1996)

B.-G. Englert, Fringe visibility and which-way informa- tion: An inequality, Physical review letters77, 2154 (1996)

1996
[43]

O. Oreshkov, Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics, Quantum3, 206 (2019), arXiv:1801.07594 [quant-ph]

work page arXiv 2019
[44]

Knill, R

E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature (London)409, 46 (2001)

2001
[45]

T. C. Ralph, N. K. Langford, T. Bell, and A. White, Lin- ear optical controlled-not gate in the coincidence basis, Physical Review A65, 062324 (2002)

2002
[46]

G. J. Pryde, J. L. O’Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, Measuring a Photonic Qubit with- out Destroying It, Phys. Rev. Lett.92, 190402 (2004), arXiv:quant-ph/0312048 [quant-ph]

work page arXiv 2004
[47]

Pryde, J

G. Pryde, J. O’Brien, A. White, T. Ralph, and H. Wise- man, Measurement of quantum weak values of photon polarization, Physical review letters94, 220405 (2005)

2005
[48]

Pittman, B

T. Pittman, B. Jacobs, and J. Franson, Probabilistic quantum logic operations using polarizing beam splitters, Physical Review A64, 062311 (2001)

2001
[49]

S. Barz, I. Kassal, M. Ringbauer, Y. O. Lipp, B. Daki´ c, A. Aspuru-Guzik, and P. Walther, A two-qubit photonic quantum processor and its application to solving systems of linear equations, Scientific reports4, 6115 (2014)

2014
[50]

M. A. Siddiqui, M. Qutubuddin, and T. Qureshi, Complementarity beyond definite causal order (2026), arXiv:2603.27780 [quant-ph]

work page arXiv 2026
[51]

Jha and H

Y. Valibouse, M. Cladera-Rossell´ o, M. Antesberger, P. Walther, and L. A. Rozema, Time-delocalized local measurements in an indefinite causal order, 10.5281/zen- odo.19334935 (2026). 9 Appendix A: Measurement inside the Quantum Switch To perform a measurement of the system polarization, we use an ancilla photon inspired by the von Neumann measurement mod...

work page doi:10.5281/zen- 2026