Pith. sign in

REVIEW 3 major objections 4 minor 58 references

Probing the Physical Reality of Projective Measurements

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Repeated measurements on a spin chain can discriminate between instantaneous wave-function collapse and a continuous, collapse-free description of measurement.

desk verdict A solid, near-term testable protocol for distinguishing projective collapse from one specific decoherence-based collapse-free model—but the paper's universal claim about all collapse-free theories is unsupported and likely false. read the letter →

arxiv 2506.20618 v1 pith:A4DB32CH submitted 2025-06-25 quant-ph cond-mat.quant-gas

Leonard Werner Pingen , Mattia Moroder , Sebastian Paeckel This is my paper · ORCID
classification quant-phcond-mat.quant-gas MSC 81P1581P16 PACS 03.65.Ta03.65.Yz
keywords repeatedmeasurementsprojectivemeasurementwave-functioncollapsedecoherencetransverse-fieldIsingmodelrepeated-measurementstatisticscoherent-subspaceoverlapanalogquantumsimulation
topics The Measurement Problem
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 argues that the textbook rule—measurement instantly collapses the wave function onto an eigenstate—can be tested with repeated measurements on a small spin chain, using only frequencies already available in analog quantum simulators. In the transverse-field Ising model, a measurement of a quasi-conserved mode occupation should, under projective collapse, be confirmed again with probability at least $P_{\min}^n$ after $n$ repeats. The authors construct a continuous, collapse-free description in which only the classical, incoherent part of the state is projected and the coherent part evolves unitarily; that model yields a much smaller upper bound on repeated confirmations, already separated from the projective case after about ten measurements. If the separation is real, any theory that removes explicit wave-function collapse should reproduce the faster-decaying statistics, and current experiments could decide the question.

What carries the argument

The repeated-measurement statistics (RMS), the probability of confirming the first outcome at every later shot, is the discriminating observable. The projective bound follows from the quasi-conserved character of the eigenmode projectors $\hat\Pi_\nu$, whose commutator with the Hamiltonian bounds the survival probability via $t_{\rm bound} \sim (1-P_{\min})/(\sqrt{2} N_\nu J)$. For the collapse-free side, the machinery is the coherent-subspace overlap (CSO), the Frobenius norm of the off-diagonal blocks of the reduced density matrix between the $\Pi_\nu=0$ and $\Pi_\nu=1$ sectors, together with the convex decomposition $\hat\rho=\alpha \hat\rho_c+(1-\alpha)\hat\rho_{ic}$ in which a measurement leaves the boundary state $\hat\rho_c$ invariant and projects only the maximally mixed part $\hat\rho_{ic}\propto 1$. The channel produces the upper bound $P_{\rm dec}^{\max}$ that the paper compares with the projective lower bound.

What would settle it

Run the protocol for $n=10$ on an $N=8$-site transverse-field Ising chain with $J=25\,$Hz, quench to $\xi=1$, and measure the occupation of mode $k=1$ at intervals $t_{\rm bound}\approx 0.0152/J$, repeating the whole sequence enough times to estimate $P(w_{10}=1)$. If the observed confirm probability is above $(0.99)^{10}\approx0.904$, the collapse-free upper bound is violated; if it falls clearly below that value, the instantaneous-projection description is falsified.

Watch

Extended reading notes

Core claim

The central claim is that projective collapse is not phenomenologically indistinguishable from a continuous, decoherence-only account of measurements. For a subsystem of $N$ spins in the transverse-field Ising chain, measuring the occupation $\hat\Pi_\nu$ of an eigenmode of the isolated open chain gives an inter-measurement time $t_{\rm bound}\propto\sqrt{N}$, so perfect confirmation is nearly guaranteed within that window. Under standard projective measurements the probability $P_{\rm proj}(w_n=1)$ of confirming the initial outcome $n$ consecutive times is bounded below by $(P_{\min})^n$, decaying slowly; under the paper's collapse-free channel the upper bound $P_{\rm dec}^{\max}(w_n=1)$ decays far faster. The authors take this gap, visible after $O(10)$ measurements, as evidence that instantaneous projection is a substantive physical assumption that can be separated empirically from any continuous replacement.

Load-bearing premise

All the collapse-free bounds rest on the choice that a measurement acts only on the completely mixed, classical part of the state and leaves the coherent part's dynamics untouched; a different no-collapse theory that also modifies the coherent part could produce statistics closer to the projective case and erase the predicted gap.

Editorial extensions

If this is right

  • With $N=8$ spins, $P_{\min}=0.99$ and $J=25\,$Hz, the required interval is about $0.6\,$ms, so the ten-shot protocol fits inside realistic coherence windows of optical-lattice and Rydberg simulators.
  • Ten consecutive confirmations should appear with probability above $(0.99)^{10}\approx 0.904$ for projective collapse, while the collapse-free bound is already orders of magnitude lower at that point, so the two hypotheses give non-overlapping predictions.
  • Measuring only local spin-z projections instead of the non-local mode occupations still leaves a contradiction between the bounds, though with lower acceptance rates; optimized local axes can restore higher acceptance and larger gaps.
  • Because the continuous model uses only continuity of the coherent part and absence of explicit collapse, the paper argues the fast-decaying statistics are a generic signature of any collapse-free reformulation, not an artifact of its particular decoherence channel.

Reading between the lines

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

  • Beyond the paper's protocol, the same RMS comparison could be run on platforms where the measurement axis is continuously tunable, using the optimized local basis from the supplemental material to maximize the gap while keeping acceptance usable.
  • The protocol could also be adapted to other integrable and near-integrable chains with quasi-conserved local operators; the expected one-dimensional timescale scaling $t_{\rm bound}\propto\sqrt{N}$ suggests the discriminating window widens with subsystem size, though higher-dimensional systems shorten it.
  • A null result in favor of projective statistics would not prove that collapse is an instantaneous physical mechanism; it would only rule out the broad class of continuous collapse-free channels that preserve the coherent component, whereas a positive result would require revisiting the role of the measurement postulate in practical simulations.
  • The authors do not discuss combining the RMS gap with Zeno-type suppression; because repeated measurements already freeze transitions, the protocol could double as a quantitative probe of the Zeno crossover between projective and continuous descriptions.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes an experimental protocol, based on repeated measurements of quasi-conserved fermionic-mode occupations in a transverse-field Ising chain, to test whether the instantaneous-projection postulate of quantum measurement is physically accurate. Under projective measurements, the probability of confirming the initial outcome n consecutive times is lower-bounded by (P_min)^n, with the inter-measurement time controlled by subsystem size (Eq. S1.18). The authors then introduce a decoherence-based, collapse-free measurement channel (Eq. 5 / Eq. S1.29) that leaves the boundary component of the reduced density matrix invariant and projects only the maximally mixed component, and they report that the resulting repeated-measurement statistics decay much faster (Fig. 2). They conclude that this separation should be qualitatively replicated by any modification of standard quantum theory lacking explicit wave-function collapses, making the protocol a discriminator of the physical reality of projective collapse.

Significance. If the central claim were established, the protocol would be of considerable interest: it gives a concrete, experimentally accessible route, using Rydberg arrays or optical lattices, to probe a foundational assumption with O(10) repeated measurements. The projective-side analysis is a genuine strength: Eq. (S1.18) follows from a clean operator-norm commutator bound, no data fitting is involved, and the t_bound ~ sqrt(N)/J scaling is explicit and checkable. The significance is, however, contingent on the general collapse-free claim, which the manuscript does not support. As it stands, the paper establishes at most a separation between projective measurements and one particular continuous decoherence-based channel, and that separation itself is not fully derived for the multi-step curve shown in Fig. 2.

major comments (3)
  1. [Abstract, Conclusions, Eq. (5)] The central claim that the decoherence-based RMS should be qualititatively replicated by any modification of standard quantum theory lacking explicit wave-function collapses is not established and, as stated, is contradicted by a collapse-free theory the paper itself cites. The update rule Eq. (5), detailed in Eq. (S1.29), is a specific measurement postulate: it leaves the boundary component rho_c(t) invariant and projects only the maximally mixed component. The Supplemental Material acknowledges that the decomposition Eq. (4) is 'somewhat arbitrary.' Nothing in the assumption 'no collapse' forces this channel. In Bohmian mechanics (Refs. [13,14]), the universal wavefunction does not collapse, yet after a unitary system-pointer interaction the conditional wavefunction for the selected particle configuration is the projected eigenstate; the probability of confirming the outcome on subsequent rounds therefore follows the projective bound (P_min)^n, not P_max_dec. The protocol can discriminate projective collapse from the authors' specific continuous channel, but not from all collapse-free theories. The abstract's universality statement and the sentence 'we expect our findings to be independent of the specific choice of the theory' therefore overreach the derivation and should be either proven or explicitly withdrawn.
  2. [Fig. 2; 'A Continuous Formulation' section] The multi-step upper bound P_max_dec(w_n=1) displayed in Fig. 2 is not derived in the main text or the Supplemental Material. The supplement ends with one-step lower bounds on P_dec for a single measurement, Eqs. (S1.30), and the surrounding text does not describe how the channel Eq. (S1.29) is iterated across n measurements, nor how the n-step curve is computed. Since the central quantitative claim is that the two statistics separate after O(10) measurements, this missing derivation is load-bearing. The authors should provide either an explicit recursion for the post-measurement state under repeated applications of Eq. (S1.29) or an analytic bound on P_dec(w_n=1), so that the curve in Fig. 2 can be verified.
  3. [Eq. (4) and Eq. (S1.29)] The choice rho_ic proportional to the identity is not the only incoherent state with vanishing CSO for a given measurement, and the bound P_max_dec is not shown to be robust under alternative choices of the incoherent component. Because the universality claim rests on P_max_dec being a property of any collapse-free theory, the authors should either prove that the bound is independent of the decomposition Eq. (4) within their stated class of continuous theories, or explicitly restrict the conclusion to the maximally-mixed decomposition. The present text leaves the impression that the numerical separation in Fig. 2 depends on a particular, admittedly arbitrary, modeling choice.
minor comments (4)
  1. [Fig. 1 caption] Fig. 1 contains a typo: 'field strenghth' should be 'field strength'.
  2. [Conclusions] In the conclusions, 'We have analyzed the RMS the one-dimensional TFIM' is missing a preposition; it should read 'the RMS of the one-dimensional TFIM'.
  3. [Supplemental Material, Eq. (S1.40)] The recursion for the minimum overlap in Eq. (S1.40) is stated without proof; please provide a derivation or a reference for this step.
  4. [Supplemental Material, 'Practical measurements'] The word 'orthorgonal' appears twice in this section and should be corrected to 'orthogonal'.

Circularity Check

1 steps flagged · score 6.0 of 10

The universal 'any collapse-free theory' claim reduces to the paper's own continuous-measurement channel (Eq. 5), while the concrete P_proj and P_dec bounds are derived, not fitted.

  1. self definitional [Abstract; Continuous Formulation Eqs. (4)-(5); Supplemental Eq. (S1.29); Conclusions]
    "Our findings imply that the significantly different measurement statistics in the collapse-free description should be qualitatively replicated by any modification of standard quantum theory that is lacking explicit wave-function collapses. ... We emphasize that the key ingredient for this conclusion is solely the absence of explicit wave-function collapses and thus not restricted to our specific decoherence-based proposal."

    The paper operationalizes 'collapse-free' as Eq. (5): a measurement leaves the coherent boundary part alpha rho_c invariant and projects only the maximally-mixed incoherent part (1-alpha) rho_ic. The faster-decaying bound P_max_dec is a mathematical consequence of this channel. The conclusion that every theory lacking explicit collapses must reproduce P_max_dec is then asserted by saying the 'key ingredient ... solely the absence of explicit wave-function collapses'. That is a definitional identification: unless 'no collapse' is equated with Eq.

full rationale

The projective-side derivation is self-contained: t_bound and P_proj(w_n=1) >= (P_min)^n follow from the commutator bound in the Supplemental Material (Eqs. S1.14-S1.18), with no fitted parameter. The decoherence-side numbers likewise follow from the explicitly stated channel Eq. (5)/Eq. (S1.29); the authors call this a 'proposed measurement postulate', so the derived P_max_dec is a theorem relative to that postulate, not a disguised fit. There are no self-citations and no benchmark fitting in the paper. The one genuinely circular move is the step from 'our continuous channel yields P_max_dec' to 'any modification of standard quantum theory lacking explicit wave-function collapses should replicate P_max_dec'. That step identifies the absence of collapse with the specific rule that the coherent boundary component is left invariant and only the maximally-mixed component is projected. The paper itself notes the decomposition is 'somewhat arbitrary', and it lists Bohmian mechanics as a collapse-free theory; in Bohmian mechanics the conditional wavefunction after a measurement is the projected eigenstate, so the repeated-measurement statistics equal the projective bound, not P_max_dec. Hence the universal prediction is true only if 'collapse-free' is defined as Eq. (5), making that central claim circular by definition, even though the concrete model-based comparison is an honest derivation.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard QM machinery for the projective side and on the authors' new decoherence-based measurement postulate for the collapse-free side. All parameters in the figures are chosen by hand, not fitted. No new physical entities are introduced.

free parameters (3)
  • P_min = 0.99
    Target confirmation probability used to set t_bound via Eq. (S1.18); chosen by hand, not fitted.
  • Subsystem size N = 8
    Size used for Fig. 2 and timescale estimate; chosen to make t_bound experimentally accessible (approximately 0.0152/J).
  • Quench parameter xi = 1
    Quench to the critical point maximizes initial CSO (Fig. 3); chosen by hand.
assumptions (5)
  • standard math Standard quantum mechanics: unitary Schrodinger evolution and Born rule for projective measurements.
    Used throughout the projective-measurement analysis and to justify the initial state and measurement statistics.
  • domain assumption Local thermalization of the TFIM with algebraic decay of the CSO proportional to t^{-3/2}.
    Used to claim perfect decoherence for quenches with xi >= 1 (Eq. S1.27), relying on Refs [37,38].
  • ad hoc to paper Decoherence-based measurement postulate: a measurement leaves boundary states of the density-matrix set invariant and projects only the maximally mixed component (Eq. S1.29).
    Core new assumption; not derived from first principles, and the authors acknowledge the decomposition is somewhat arbitrary.
  • standard math The maximally mixed state is the unique state with zero CSO for any measurement.
    Used to justify the choice of the incoherent component and to argue for the naturalness of the channel.
  • ad hoc to paper Any collapse-free theory will qualitatively replicate the statistics of this specific continuous model.
    Generalization claim in the abstract and conclusions; not proven, only argued from the absence of explicit collapses.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Probing the Physical Reality of Projective Measurements." pith.science (2026). https://pith.science/paper/A4DB32CH

@misc{pith2026250620618,
  author       = {Pith},
  title        = {Pith review of: Probing the Physical Reality of Projective Measurements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A4DB32CH}},
  note         = {Machine review of arXiv:2506.20618}
}
read the original abstract

We propose a protocol to test whether the postulate of a measurement acting as an instantaneous projection onto an eigenstate of the measurement apparatus is compatible with physical reality. This approach is solely based on repeated measurements of local quantities with frequencies that are within reach of analog quantum simulation platforms, for instance Rydberg atom arrays or ultracold gases in optical lattices. Crucially, we also develop a continuous description of a quantum measurement finding that its repeated-measurement statistics (RMS) drastically differ from the projective case. This description is based on very general assumptions about quantum systems, most importantly maintaining continuous dynamics of the coherent part of the state. Our findings imply that the significantly different measurement statistics in the collapse-free description should be qualitatively replicated by any modification of standard quantum theory that is lacking explicit wave-function collapses.

Figures

Figures reproduced from arXiv: 2506.20618 by the authors.

Figure 1
Figure 1. FIG. 1. The repeated-measurement protocol. We initially prepare a chain of aligned spin-1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Lower ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Coherent-subspace overlap (CSO) for a quench to [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references · 32 canonical work pages

  1. [1]

    von Neumann,Mathematical Foundations of Quantum Mechanics(Princeton University Press, Princeton, NJ,

    J. von Neumann,Mathematical Foundations of Quantum Mechanics(Princeton University Press, Princeton, NJ,

  2. [2]

    E. P. Wigner, American Journal of Physics31, 6 (1963)

    1963

  3. [3]

    Schlosshauer, Rev

    M. Schlosshauer, Rev. Mod. Phys.76, 1267 (2005)

    2005

  4. [4]

    Brukner, (2015), arXiv:1507.05255 [quant-ph]

    C. Brukner, (2015), arXiv:1507.05255 [quant-ph]

    arXiv 2015

  5. [5]

    A. A. Tomaz, R. S. Mattos, and M. Barbatti, (2025), arXiv:2502.19278 [quant-ph]

    arXiv 2025

  6. [6]

    Everett,The Many-Worlds Interpretation of Quantum Mechanics: The Theory of the Universal Wave Function, Ph.D

    H. Everett,The Many-Worlds Interpretation of Quantum Mechanics: The Theory of the Universal Wave Function, Ph.D. thesis, Princeton University (1956)

    work page 1956

  7. [7]

    Rovelli, International Journal of Theoretical Physics 35, 1637 (1996)

    C. Rovelli, International Journal of Theoretical Physics 35, 1637 (1996)

    1996

  8. [8]

    Information and funda- mental elements of the structure of quantum theory,

    ˇC. Brukner and A. Zeilinger, “Information and funda- mental elements of the structure of quantum theory,” in Time, Quantum and Information, edited by L. Castell and O. Ischebeck (Springer Berlin Heidelberg, Berlin, Heidelberg, 2003) pp. 323–354

    work page 2003

Show all 58 references
  1. [9]

    G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986)

    1986

  2. [10]

    Bassi and G

    A. Bassi and G. Ghirardi, Physics Reports379, 257 (2003)

    2003

  3. [11]

    Penrose, General Relativity and Gravitation28, 581 (1996)

    R. Penrose, General Relativity and Gravitation28, 581 (1996)

    1996

  4. [12]

    Oppenheim, Phys

    J. Oppenheim, Phys. Rev. X13, 041040 (2023)

    2023

  5. [13]

    Bohm, Phys

    D. Bohm, Phys. Rev.85, 166 (1952)

    1952

  6. [14]

    D¨ urr and S

    D. D¨ urr and S. Teufel,Bohmian Mechanics: The Physics and Mathematics of Quantum Theory(Springer, 2009)

    2009

  7. [15]

    H. D. Zeh, Foundations of Physics1, 69 (1970)

    1970

  8. [16]

    H. D. Zeh, Foundations of Physics3, 109–116 (1973)

    1973

  9. [17]

    W. H. Zurek, Reviews of Modern Physics75, 715–775 (2003)

    2003

  10. [18]

    M. Fuwa, S. Takeda, M. Zwierz, H. M. Wiseman, and A. Furusawa, Nature Communications6, 6665 (2015)

    2015

  11. [19]

    Garrisi, M

    F. Garrisi, M. P. Massara, A. Zambianchi, M. Galli, D. Bajoni, A. Rimini, and O. Nicrosini, Scientific Re- ports9, 11897 (2019)

    2019

  12. [20]

    Strasberg, K

    P. Strasberg, K. Modi, and M. Skotiniotis, European Journal of Physics43, 035404 (2022)

    2022

  13. [21]

    Shettell, F

    N. Shettell, F. Centrone, and L. P. Garc ´ ıa-Pintos, Quan- tum7, 1182 (2023)

    2023

  14. [22]

    Guryanova, N

    Y. Guryanova, N. Friis, and M. Huber, Quantum4, 222 (2020)

    2020

  15. [23]

    Schwarzhans, F

    E. Schwarzhans, F. C. Binder, M. Huber, and M. P. E. Lock, (2023), arXiv:2302.11253 [quant-ph]

    2023

  16. [24]

    J. R. Hance and S. Hossenfelder, Journal of Physics Com- munications6, 102001 (2022)

    2022

  17. [25]

    Six measurement problems of quantum mechanics,

    F. A. Muller, “Six measurement problems of quantum mechanics,” inNon-Reflexive Logics, Non-Individuals, and the Philosophy of Quantum Mechanics: Essays in 6 Honour of the Philosophy of D´ ecio Krause, edited by J. R. B. Arenhart and R. W. Arroyo (Springer Inter- national Publi...

    2023

  18. [26]

    Schlosshauer, Physics Reports831, 1–57 (2019)

    M. Schlosshauer, Physics Reports831, 1–57 (2019)

    2019

  19. [27]

    W. H. Zurek, Phys. Rev. D24, 1516 (1981)

    1981

  20. [28]

    E. Joos, H. D. Zeh, C. Kiefer, D. J. W. Giulini, J. Kupsch, and I.-O. Stamatescu,Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd ed. (Springer, Berlin, Heidelberg, 2003)

    2003

  21. [29]

    Gross and I

    C. Gross and I. Bloch, Science357, 995 (2017)

    2017

  22. [30]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature551, 579 (2017)

    2017

  23. [31]

    [49–56], for details on the quench protocol, the projection-based and the decoherence-based measurement statistics and optimiza- tions facilitating the experimental realization

    See the Supplemental Material at [URL will be inserted by publisher], which includes Refs. [49–56], for details on the quench protocol, the projection-based and the decoherence-based measurement statistics and optimiza- tions facilitating the experimental realization

  24. [32]

    Meinert, M

    F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Wein- mann, A. J. Daley, and H.-C. N¨ agerl, Phys. Rev. Lett. 111, 053003 (2013)

    2013

  25. [33]

    Misra and E

    B. Misra and E. C. G. Sudarshan, Journal of Mathemat- ical Physics18, 756 (1977)

    1977

  26. [34]

    Sch¨ afer, I

    F. Sch¨ afer, I. Herrera, S. Cherukattil, C. Lovecchio, F. S. Cataliotti, F. Caruso, and A. Smerzi, Nature Communi- cations5, 3194 (2014)

    2014

  27. [35]

    N. Kalb, J. Cramer, D. J. Twitchen, M. Markham, R. Hanson, and T. H. Taminiau, Nature Communica- tions7, 13111 (2016)

    2016

  28. [36]

    Bell, Physics World3, 33 (1990)

    J. Bell, Physics World3, 33 (1990)

    1990

  29. [37]

    Calabrese, F

    P. Calabrese, F. H. L. Essler, and M. Fagotti, Journal of Statistical Mechanics: Theory and Experiment2012, P07022 (2012)

    2012

  30. [38]

    Fagotti and F

    M. Fagotti and F. H. L. Essler, Phys. Rev. B87, 245107 (2013)

    2013

  31. [39]

    Kimura and A

    G. Kimura and A. Kossakowski, Open Systems & Infor- mation Dynamics12, 207–229 (2005)

    2005

  32. [40]

    Borish, O

    V. Borish, O. Markovi´ c, J. A. Hines, S. V. Rajagopal, and M. Schleier-Smith, Physical Review Letters124 (2020), 10.1103/physrevlett.124.063601

    2020 doi

  33. [41]

    Scholl, M

    P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, A. M. L¨ auchli, and A. Browaeys, Nature595, 233 (2021)

    2021

  34. [42]

    Q. Xu, J. P. Bonilla Ataides, C. A. Pattison, N. Raveen- dran, D. Bluvstein, J. Wurtz, B. Vasi´ c, M. D. Lukin, L. Jiang, and H. Zhou, Nature Physics20, 1084 (2024)

    2024

  35. [43]

    Bloch, J

    I. Bloch, J. Dalibard, and S. Nascimb` ene, Nature Physics 8, 267 (2012)

    2012

  36. [44]

    Y.-A. Chen, S. Nascimb` ene, M. Aidelsburger, M. Atala, S. Trotzky, and I. Bloch, Phys. Rev. Lett.107, 210405 (2011)

    2011

  37. [45]

    R. Liao, F. Xiong, and X. Chen, Phys. Rev. A103, 043312 (2021)

    2021

  38. [46]

    Miessen, D

    A. Miessen, D. J. Egger, I. Tavernelli, and G. Mazzola, PRX Quantum5, 040320 (2024)

    2024

  39. [47]

    Acharya, D

    R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, G. Bortoli, A. Bourassa,...

    2025

  40. [48]

    Digital quantum magnetism at the frontier of classical simulations,

    R. Haghshenas, E. Chertkov, M. Mills, W. Kadow, S.- H. Lin, Y.-H. Chen, C. Cade, I. Niesen, T. Beguˇ si´ c, M. S. Rudolph, C. Cirstoiu, K. Hemery, C. M. Keever, M. Lubasch, E. Granet, C. H. Baldwin, J. P. Bartolotta, M. Bohn, J. Cline, M. DeCross, J. M. Dreiling, C. Foltz, D. ...

    2025 arXiv

  41. [49]

    Pfeuty, Annals of Physics57, 79 (1970)

    P. Pfeuty, Annals of Physics57, 79 (1970)

    1970

  42. [50]

    He and H

    Y. He and H. Guo, Journal of Statistical Mechanics: The- ory and Experiment2017, 093101 (2017)

    2017

  43. [51]

    E. Lieb, T. Schultz, and D. Mattis, Annals of Physics 16, 407 (1961)

    1961

  44. [52]

    L. G. Molinari, (2023), arXiv:1710.09248 [math-ph]

    2023 arXiv

  45. [53]

    Peschel, Journal of Physics A: Mathematical and Gen- eral36, L205–L208 (2003)

    I. Peschel, Journal of Physics A: Mathematical and Gen- eral36, L205–L208 (2003)

    2003

  46. [54]

    W. H. Zurek, Phys. Rev. D26, 1862 (1982)

    1982

  47. [55]

    Baumgratz, M

    T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett.113, 140401 (2014)

    2014

  48. [56]

    Fagotti and P

    M. Fagotti and P. Calabrese, Journal of Statistical Me- chanics: Theory and Experiment2010, P04016 (2010)

    2010

  49. [57]

    Probing the Physical Reality of Projective Measurements

    G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett.90, 227902 (2003). 8 Supplemental Material for “Probing the Physical Reality of Projective Measurements” The transverse-field Ising model We consider the one-dimensional transverse-field Ising model (TFIM) ˆH=−J ...

    2003

  50. [1955]

    translated by Robert T. Beyer

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.