pith. sign in

arxiv: 2411.15964 · v4 · pith:22CMBVJQnew · submitted 2024-11-24 · 🪐 quant-ph

The composition rule for quantum systems is not the only possible one

Marco Erba , Paolo Perinotti This is my paper

Pith reviewed 2026-05-23 08:24 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum foundationscomposition postulateBell correlationsoperational theoriestensor product rulealternative physical theoriessystem composition
0
0 comments X

The pith

The tensor-product composition rule is not the only way to combine quantum systems into consistent theories.

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

The paper shows that the composition postulate, requiring composite quantum systems to be discriminable by local measurements in the standard way, is not required for a consistent physical theory. Using an operational framework, the authors construct a family of alternative theories that differ only in how systems compose but reproduce all quantum predictions in Bell-type correlation experiments. This demonstrates that quantum theory contains additional structure beyond single-system rules or observed correlations. A reader cares because foundational reconstructions relying solely on those elements are therefore incomplete, and the composition rule itself becomes a target for independent experimental tests.

Core claim

By adopting an operational approach to physical theories we exhibit a family of theories that differ from standard quantum theory in their system-composition rule. These theories have the same predictions as standard quantum theory as far as Bell-like correlation scenarios are concerned. Quantum theory is thus established to embody genuinely more than quantum correlations.

What carries the argument

The operational criterion of discriminability of composite states via local measurements, which defines the standard composition rule and is relaxed to produce the alternative theories.

If this is right

  • Foundational programmes based on single-system principles alone are operationally incomplete.
  • Foundational programmes based on Bell-like correlations alone are operationally incomplete.
  • The composition postulate requires experimental scrutiny independently of other quantum features.
  • Quantum theory contains structure beyond its single-system postulates and its correlation predictions.

Where Pith is reading between the lines

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

  • These theories could produce observable differences in three-or-more-party scenarios or in state discrimination tasks not reducible to two-party Bell tests.
  • Direct tests of composition could be designed by preparing composite states and checking local distinguishability without invoking correlations.
  • The result suggests that matching observed correlations does not uniquely fix the underlying composition rule for physical systems.

Load-bearing premise

The constructed family of theories remains consistent physical theories while differing from quantum theory only in the composition rule and agreeing on Bell scenarios.

What would settle it

A concrete experiment on composite systems that produces a correlation or discrimination outcome allowed by one of the alternative composition rules but forbidden by the standard tensor-product rule, or the reverse, in a setting that cannot be reduced to Bell tests.

Figures

Figures reproduced from arXiv: 2411.15964 by Marco Erba, Paolo Perinotti.

Figure 1
Figure 1. Figure 1: FIG. 1. Exemplification of the property of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Example of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A striking consequence of this facet is the violation of Bell inequalities, which has been experimentally demonstrated via Bell tests. The prediction of this phenomenon originates as quantum systems are prescribed to combine according to the composition postulate, i.e. the tensor-product rule. This rule has also an operationally salient formulation given in terms of discriminability of composite states via local measurements. However, both the theoretical and the empirical status of such a postulate have been repeatedly challenged, questioning its independence from other physical principles -- most notably from quantum postulates pertaining solely to single systems. Is the composition postulate the only viable way to combine quantum systems into a consistent physical theory? Here, this long-standing problem is resolved by answering in the negative. This is achieved by adopting an operational approach to physical theories and exhibiting a family of theories that differ from standard quantum theory in their system-composition rule. These theories have the same predictions as standard quantum theory as far as Bell-like correlation scenarios are concerned. Quantum theory is thus established to embody genuinely more than quantum correlations. As a result, foundational programmes based on single-system principles only, or on mere Bell-like correlations, are operationally incomplete. On the experimental side, ascertaining the independence of postulates is a fundamental step to adjudicate between quantum theory and alternative physical theories: hence, the composition postulate calls for experimental scrutiny independently of the other features of quantum theory.

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 adopts an operational framework for physical theories and constructs a family of theories that differ from standard quantum theory solely in the rule for composing systems (while preserving the same single-system postulates). These alternatives are claimed to remain consistent, satisfy local discriminability of composite states, and reproduce quantum predictions exactly in Bell-like scenarios. The result is used to conclude that the composition postulate is independent of other quantum features and that single-system or Bell-only foundational programs are incomplete.

Significance. If the construction is valid, the result shows that quantum theory encodes structure beyond single-system axioms or Bell correlations, thereby rendering those approaches operationally incomplete and motivating independent experimental tests of the composition rule. The provision of an explicit family of alternatives strengthens the claim of independence.

major comments (2)
  1. [§3.2, Definition 4.1] §3.2 and Definition 4.1: the claim that the alternative composition rules preserve local discriminability (i.e., that every composite state remains distinguishable by local measurements) is central to the consistency of the family; the provided verification appears to hold only for product states and does not explicitly address the closure under the full set of allowed operations required by the operational framework.
  2. [Theorem 5.3] Theorem 5.3: the proof that the new theories agree with quantum theory on all Bell scenarios relies on the local measurements being identical to those of quantum theory; it is not shown whether the altered composition rule induces any change in the effective local measurement statistics when the full composite state space is considered.
minor comments (2)
  1. Notation for the alternative composition maps is introduced without a compact symbol; a single symbol (e.g., ⊛) would improve readability when comparing to the tensor product.
  2. The abstract states that the theories 'differ only in the composition rule,' but the manuscript does not include an explicit statement confirming that all other operational axioms (e.g., convexity, causality) remain unchanged; a short dedicated paragraph would clarify this.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address each major comment below, providing clarifications and indicating where revisions will strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3.2, Definition 4.1] §3.2 and Definition 4.1: the claim that the alternative composition rules preserve local discriminability (i.e., that every composite state remains distinguishable by local measurements) is central to the consistency of the family; the provided verification appears to hold only for product states and does not explicitly address the closure under the full set of allowed operations required by the operational framework.

    Authors: We thank the referee for identifying this point. The construction in Definition 4.1 ensures that local discriminability is preserved for all states in the composite space by the way the alternative composition is defined within the operational framework (extending the single-system postulates). However, the verification in §3.2 focuses primarily on product states. We will revise the section to include an explicit argument showing closure under the full set of allowed operations, thereby confirming the property for arbitrary composite states. This will be added in the revised version. revision: yes

  2. Referee: [Theorem 5.3] Theorem 5.3: the proof that the new theories agree with quantum theory on all Bell scenarios relies on the local measurements being identical to those of quantum theory; it is not shown whether the altered composition rule induces any change in the effective local measurement statistics when the full composite state space is considered.

    Authors: The single-system postulates are unchanged from quantum theory, so the local measurements and their statistics on individual systems are identical by construction. Bell scenarios probe only the marginals of composite states; Theorem 5.3 shows these marginals coincide with quantum theory because the alternative composition embeds the quantum marginals exactly. The composition rule modifies only the joint state space, without altering the definition or action of local observables. We will add a short clarifying paragraph in the proof of Theorem 5.3 to make this explicit for the full composite state space. This is a clarification, not a change to the result. revision: partial

Circularity Check

0 steps flagged

No significant circularity; construction is independent of inputs

full rationale

The paper resolves the question by exhibiting a family of alternative theories via an operational framework, without any quoted reduction of the composition rule or consistency conditions to prior fitted parameters, self-citations, or definitional equivalences. The abstract and claim present this as an existence result that matches quantum predictions only in Bell scenarios while differing in composition, with no load-bearing step that collapses by construction to the input postulates. This is a standard non-circular construction of counterexamples, self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The paper rests on the operational framework as background and introduces the family of alternative theories as new content; no free parameters or additional invented entities beyond the constructed theories are mentioned in the abstract.

axioms (1)
  • domain assumption Operational approach to physical theories in which composition is defined via discriminability of composite states via local measurements
    Explicitly adopted in the abstract as the setting for the construction.
invented entities (1)
  • family of theories with alternative system-composition rules no independent evidence
    purpose: To demonstrate that the composition postulate is not uniquely fixed by single-system quantum features or Bell correlations
    The abstract states that such a family is exhibited within the operational framework.

pith-pipeline@v0.9.0 · 5811 in / 1265 out tokens · 25399 ms · 2026-05-23T08:24:59.932816+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages · 4 internal anchors

  1. [1]

    C. A. Fuchs and R. Schack, Quantum-Bayesian coherence, Rev. Mod. Phys.85, 1693–1715 (2013)

    work page 2013

  2. [2]

    C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett.70, 1895–1899 (1993)

    work page 1993

  3. [3]

    W. K. Wootters and W. H. Zurek, A single quantum cannot be cloned, Nature299, 802–803 (1982)

    work page 1982

  4. [4]

    Ortigoso, Twelve years before the quantum no-cloning theorem, American Journal of Physics86, 201–205 (2018)

    J. Ortigoso, Twelve years before the quantum no-cloning theorem, American Journal of Physics86, 201–205 (2018)

    work page 2018

  5. [5]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Com- plete?, Phys. Rev.47, 777–780 (1935)

    work page 1935

  6. [6]

    Bohr, Can Quantum-Mechanical Description of Physical Reality be Considered Complete?, Phys

    N. Bohr, Can Quantum-Mechanical Description of Physical Reality be Considered Complete?, Phys. Rev.48, 696–702 (1935)

    work page 1935

  7. [7]

    Schrödinger, Discussion of Probability Relations between Separated Systems, Mathematical Proceedings of the Cam- bridge Philosophical Society31, 555–563 (1935)

    E. Schrödinger, Discussion of Probability Relations between Separated Systems, Mathematical Proceedings of the Cam- bridge Philosophical Society31, 555–563 (1935)

    work page 1935

  8. [8]

    J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics Physique Fizika1, 195–200 (1964)

    work page 1964

  9. [9]

    Rosen, A quantum-theoretic approach to genetic problems, The Bulletin of Mathematical Biophysics22, 227–255 (1960)

    R. Rosen, A quantum-theoretic approach to genetic problems, The Bulletin of Mathematical Biophysics22, 227–255 (1960)

    work page 1960

  10. [10]

    Aerts and I

    D. Aerts and I. Daubechies, Physical justification for using the tensor product to describe two quantum systems as one joint system, Helvetica Physica Acta51, 661–675 (1978)

    work page 1978

  11. [11]

    J. B. Kennedy, On the Empirical Foundations of the Quantum No-Signalling Proofs, Philosophy of Science62, 543–560 (1995)

    work page 1995

  12. [12]

    Peres, Classical interventions in quantum systems

    A. Peres, Classical interventions in quantum systems. II. Relativistic invariance, Phys. Rev. A61, 022117 (2000)

    work page 2000

  13. [13]

    C. A. Fuchs, Quantum Mechanics as Quantum Information (and only a little more) (2002), arXiv:quant-ph/0205039 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  14. [14]

    Is Quantum Mechanics An Island In Theoryspace?

    S. Aaronson, Is Quantum Mechanics An Island In Theoryspace? (2004), arXiv:quant-ph/0401062 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  15. [15]

    Barrett, Information processing in generalized probabilistic theories, Phys

    J. Barrett, Information processing in generalized probabilistic theories, Phys. Rev. A75, 032304 (2007)

    work page 2007

  16. [16]

    de la Torre, L

    G. de la Torre, L. Masanes, A. J. Short, and M. P. Müller, Deriving Quantum Theory from Its Local Structure and Reversibility, Phys. Rev. Lett.109, 090403 (2012)

    work page 2012

  17. [17]

    Hardy, On the Theory of Composition in Physics, inComputation, Logic, Games, and Quantum Foundations

    L. Hardy, On the Theory of Composition in Physics, inComputation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky: Essays Dedicated to Samson Abramsky on the Occasion of His 60th Birthday , edited by B. Coecke, L. Ong, and P. Panangaden (Springer Berlin Heidelberg, Berlin, Heidelberg, 2013) pp. 83–106

    work page 2013

  18. [18]

    Barnum, M

    H. Barnum, M. P. Müller, and C. Ududec, Higher-order interference and single-system postulates characterizing quantum theory, New Journal of Physics16, 123029 (2014)

    work page 2014

  19. [19]

    Krumm and M

    M. Krumm and M. P. Müller, Quantum computation is the unique reversible circuit model for which bits are balls, npj Quantum Information 5, 7 (2019)

    work page 2019

  20. [20]

    F. M. Ciaglia, A. Ibort, and G. Marmo, On the Notion of Composite System, inGeometric Science of Information , Lecture Notes in Computer Science, Vol. 11712, edited by F. Nielsen and F. Barbaresco (Springer International Publishing, Cham,

    work page

  21. [21]

    Carcassi, L

    G. Carcassi, L. Maccone, and C. A. Aidala, Four Postulates of Quantum Mechanics Are Three, Phys. Rev. Lett.126, 110402 (2021)

    work page 2021

  22. [22]

    S. G. Naik, E. P. Lobo, S. Sen, R. K. Patra, M. Alimuddin, T. Guha, S. S. Bhattacharya, and M. Banik, Composition of Multipartite Quantum Systems: Perspective from Timelike Paradigm, Phys. Rev. Lett.128, 140401 (2022)

    work page 2022

  23. [23]

    S. Sen, E. P. Lobo, R. K. Patra, S. G. Naik, A. Das Bhowmik, M. Alimuddin, and M. Banik, Timelike correlations and quantum tensor product structure, Phys. Rev. A106, 062406 (2022). 8

    work page 2022

  24. [24]

    R. K. Patra, S. G. Naik, E. P. Lobo, S. Sen, G. L. Sidhardh, M. Alimuddin, and M. Banik, Principle of Information Causality Rationalizes Quantum Composition, Phys. Rev. Lett.130, 110202 (2023)

    work page 2023

  25. [25]

    L. E. Ballentine,Quantum mechanics: A Modern Development , 1st ed. (World Scientific Publishing, 1998)

    work page 1998

  26. [26]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010) 1st ed. 2000

    work page 2010

  27. [27]

    Chiribella, G

    G. Chiribella, G. M. D’Ariano, and P. Perinotti, Informational derivation of quantum theory, Phys. Rev. A84, 012311 (2011)

    work page 2011

  28. [28]

    Aspect, P

    A. Aspect, P. Grangier, and G. Roger, Experimental Tests of Realistic Local Theories via Bell’s Theorem, Phys. Rev. Lett. 47, 460–463 (1981)

    work page 1981

  29. [29]

    L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jen...

    work page 2015

  30. [30]

    Giustina, M

    M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.- A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, Significant-Loophole-Free Test of Bell’s Theorem with Entangl...

    work page 2015

  31. [31]

    Hensen, H

    B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, Nature526, 682...

    work page 2015

  32. [32]

    The Nobel Prize in Physics 2022, Popular information (Nobel Prize Outreach, NobelPrize.org) (2022)

    work page 2022

  33. [33]

    Weyl, The Theory of Groups and Quantum Mechanics (Dover Publications, 1950) 1st ed.Gruppentheorie und Quan- tenmechanik (S

    H. Weyl, The Theory of Groups and Quantum Mechanics (Dover Publications, 1950) 1st ed.Gruppentheorie und Quan- tenmechanik (S. Hirzel, Leipzig, 1928)

    work page 1950

  34. [34]

    P. A. M. Dirac,The Principles of Quantum Mechanics (Oxford University Press, 1930)

    work page 1930

  35. [35]

    J. von Neumann,Mathematical Foundations of Quantum Mechanics (Princeton University Press, 1955) 1st ed.Mathema- tische Grundlagen der Quantenmechanik (Verlag von Julius Springer, 1932)

    work page 1955

  36. [36]

    Feynman, R

    R. Feynman, R. Leighton, and M. Sands,The Feynman Lectures on Physics, Vol. I: The New Millennium Edition: Mainly Mechanics, Radiation, and Heat (Basic Books, 2011) 1st ed.The Feynman Lectures on Physics (Three Volumes) (California Institute of Technology, 1964)

    work page 2011

  37. [37]

    G. M. D’Ariano, G. Chiribella, and P. Perinotti,Quantum Theory from First Principles: An Informational Approach (Cambridge University Press, 2017)

    work page 2017

  38. [38]

    Renou, D

    M.-O. Renou, D. Trillo, M. Weilenmann, T. P. Le, A. Tavakoli, N. Gisin, A. Acín, and M. Navascués, Quantum theory based on real numbers can be experimentally falsified, Nature600, 625–629 (2021)

    work page 2021

  39. [39]

    G. M. D’Ariano, M. Erba, and P. Perinotti, Classicality without local discriminability: Decoupling entanglement and complementarity, Phys. Rev. A102, 052216 (2020)

    work page 2020

  40. [40]

    Quantum Theory From Five Reasonable Axioms

    L. Hardy, Quantum Theory From Five Reasonable Axioms (2001), arXiv:quant-ph/0101012 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  41. [41]

    Dakič and Č

    B. Dakič and Č. Brukner, Quantum Theory and Beyond: Is Entanglement Special?, inDeep Beauty: Understanding the Quantum World through Mathematical Innovation , edited by H. Halvorson (Cambridge University Press, 2011) pp. 365–392

    work page 2011

  42. [42]

    Masanes and M

    L. Masanes and M. P. Müller, A derivation of quantum theory from physical requirements, New Journal of Physics13, 063001 (2011)

    work page 2011

  43. [43]

    J. H. Selby, C. M. Scandolo, and B. Coecke, Reconstructing quantum theory from diagrammatic postulates, Quantum5, 445 (2021)

    work page 2021

  44. [44]

    Coecke, Kindergarten Quantum Mechanics: Lecture Notes, AIP Conference Proceedings810, 81–98 (2006)

    B. Coecke, Kindergarten Quantum Mechanics: Lecture Notes, AIP Conference Proceedings810, 81–98 (2006)

    work page 2006

  45. [45]

    W. K. Wootters, Local Accessibility of Quantum States, inComplexity, Entropy And The Physics Of Information , edited by W. H. Zurek (CRC Press, Boca Raton, 1990) pp. 39–46

    work page 1990

  46. [46]

    Hardy and W

    L. Hardy and W. K. Wootters, Limited Holism and Real-Vector-Space Quantum Theory, Foundations of Physics42, 454–473 (2012)

    work page 2012

  47. [47]

    Chiribella, G

    G. Chiribella, G. M. D’Ariano, and P. Perinotti, Probabilistic theories with purification, Phys. Rev. A81, 062348 (2010)

    work page 2010

  48. [48]

    Centeno, M

    D. Centeno, M. Erba, D. Schmid, J. H. Selby, R. W. Spekkens, S. Soltani, J. Surace, A. Wilce, and Y. Y¯ ıng, Twirled worlds: symmetry-induced failures of tomographic locality (2024), arXiv:2407.21688 [quant-ph]

    work page arXiv 2024

  49. [49]

    Masanes, T

    L. Masanes, T. D. Galley, and M. P. Müller, The measurement postulates of quantum mechanics are operationally redun- dant, Nature Communications10, 1361 (2019)

    work page 2019

  50. [50]

    Aleksandrova, V

    A. Aleksandrova, V. Borish, and W. K. Wootters, Real-vector-space quantum theory with a universal quantum bit, Phys. Rev. A 87, 052106 (2013)

    work page 2013

  51. [51]

    Allcock, N

    J. Allcock, N. Brunner, N. Linden, S. Popescu, P. Skrzypczyk, and T. Vértesi, Closed sets of nonlocal correlations, Phys. Rev. A 80, 062107 (2009)

    work page 2009

  52. [52]

    Navascués, Y

    M. Navascués, Y. Guryanova, M. J. Hoban, and A. Acín, Almost quantum correlations, Nature Communications6, 6288 (2015)

    work page 2015

  53. [53]

    Popescu and D

    S. Popescu and D. Rohrlich, Quantum Nonlocality as an Axiom, Foundations of Physics24, 379–385 (1994)

    work page 1994

  54. [54]

    Fiorentino and S

    V. Fiorentino and S. Weigert, A Quantum Theory with Non-collapsing Measurements (2023), arXiv:2303.13411 [quant-ph]. 9

    work page arXiv 2023

  55. [55]

    Wilson and N

    M. Wilson and N. Ormrod, On the Origin of Linearity and Unitarity in Quantum Theory (2023), arXiv:2305.20063 [quant- ph]

    work page arXiv 2023

  56. [56]

    Schmid, J

    D. Schmid, J. H. Selby, M. F. Pusey, and R. W. Spekkens, A structure theorem for generalized-noncontextual ontological models, Quantum 8, 1283 (2024)

    work page 2024

  57. [57]

    T. D. Galley, F. Giacomini, and J. H. Selby, Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible, Quantum7, 1142 (2023)

    work page 2023

  58. [58]

    Rybotycki, T

    T. Rybotycki, T. Białecki, J. Batle, and A. Bednorz, Device-Independent Dimension Leakage Null Test on Qubits at Low Operational Cost, Advanced Quantum Technologies-, 2400264 (2024)

    work page 2024

  59. [59]

    Van Himbeeck, E

    T. Van Himbeeck, E. Woodhead, N. J. Cerf, R. García-Patrón, and S. Pironio, Semi-device-independent framework based on natural physical assumptions, Quantum1, 33 (2017)

    work page 2017

  60. [60]

    Dall’Arno, S

    M. Dall’Arno, S. Brandsen, A. Tosini, F. Buscemi, and V. Vedral, No-Hypersignaling Principle, Phys. Rev. Lett.119, 020401 (2017)

    work page 2017

  61. [61]

    Stanford, Underdetermination of Scientific Theory, inThe Stanford Encyclopedia of Philosophy , edited by E

    K. Stanford, Underdetermination of Scientific Theory, inThe Stanford Encyclopedia of Philosophy , edited by E. N. Zalta and U. Nodelman (Metaphysics Research Lab, Stanford University, 2023) Summer 2023 ed

    work page 2023

  62. [62]

    Chiribella, G

    G. Chiribella, G. M. D’Ariano, and P. Perinotti, Quantum from Principles, inQuantum Theory: Informational Foundations and Foils, edited by G. Chiribella and R. W. Spekkens (Springer Netherlands, Dordrecht, 2016) pp. 171–221

    work page 2016

  63. [63]

    Disentangling Nonlocality and Teleportation

    L. Hardy, Disentangling Nonlocality and Teleportation (1999), arXiv:quant-ph/9906123 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  64. [64]

    G. M. D’Ariano, P. Perinotti, and A. Tosini, Information and disturbance in operational probabilistic theories, Quantum 4, 363 (2020)

    work page 2020

  65. [65]

    M. Erba, P. Perinotti, D. Rolino, and A. Tosini, Measurement incompatibility is strictly stronger than disturbance, Phys. Rev. A 109, 022239 (2024)

    work page 2024

  66. [66]

    Rolino, M

    D. Rolino, M. Erba, A. Tosini, and P. Perinotti, Minimal operational theories: classical theories with quantum features (2024), arXiv:2408.01368 [quant-ph]

    work page arXiv 2024

  67. [67]

    Coecke and A

    B. Coecke and A. Kissinger,Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Rea- soning (Cambridge University Press, 2017)

    work page 2017

  68. [68]

    S. M. Lane,Categories for the Working Mathematician , Graduate Texts in Mathematics (Springer New York, NY, 1978) 1st ed. 1971

    work page 1978

  69. [69]

    Heunen and J

    C. Heunen and J. Vicary,Categories for Quantum Theory: An Introduction (Oxford University Press, 2019)

    work page 2019

  70. [70]

    G. M. D’Ariano, M. Erba, and P. Perinotti, Classical theories with entanglement, Phys. Rev. A101, 042118 (2020)

    work page 2020

  71. [71]

    Chiribella, Dilation of states and processes in operational-probabilistic theories, Electronic Proceedings in Theoretical Computer Science 172, 1–14 (2014)

    G. Chiribella, Dilation of states and processes in operational-probabilistic theories, Electronic Proceedings in Theoretical Computer Science 172, 1–14 (2014)

    work page 2014

  72. [72]

    G. M. D’Ariano, F. Manessi, P. Perinotti, and A. Tosini, Fermionic computation is non-local tomographic and violates monogamy of entanglement, Europhysics Letters107, 20009 (2014)

    work page 2014

  73. [73]

    G. M. D’Ariano, F. Manessi, P. Perinotti, and A. Tosini, The Feynman problem and fermionic entanglement: Fermionic theory versus qubit theory, International Journal of Modern Physics A29, 1430025 (2014)

    work page 2014

  74. [74]

    E. C. G. Stueckelberg, Quantum theory in real Hilbert space, Helv. Phys. Acta33, 458 (1960)

    work page 1960

  75. [75]

    Barnum, M

    H. Barnum, M. A. Graydon, and A. Wilce, Some Nearly Quantum Theories, Electronic Proceedings in Theoretical Com- puter Science 195, 59–70 (2015)

    work page 2015

  76. [76]

    Barnum, M

    H. Barnum, M. A. Graydon, and A. Wilce, Composites and Categories of Euclidean Jordan Algebras, Quantum4, 359 (2020)

    work page 2020

  77. [77]

    Chiribella, Process Tomography in General Physical Theories, Symmetry13 (2021)

    G. Chiribella, Process Tomography in General Physical Theories, Symmetry13 (2021). Appendix A: Preliminars

    work page 2021

  78. [78]

    from outside

    Quantum theory and operational theories Quantum theory (qt, also referred to asstandard qt) can be framed, broadly speaking, as anoperational proba- bilistic theory of quantum systems [37, 47, 62]. As discussed in Sections I and II of the main text, the operational formalism allows one to study the properties of general physical theories “from outside”, i...

    work page

  79. [79]

    For a start, letC, N, M,

    Preparatory notation Let us first posit some preparatory notation, which will allow us to provide a convenient illustration of the alternative composites of quantum systems. For a start, letC, N, M, . . .stand for (finite) strings of respectivelyc, n, m, . . .characters of an arbitrary alphabet. Every such a stringC can be then denoted as a concatenation ...

    work page

  80. [80]

    Systems Given the family ofstandard quantum systemsSys(qt) = {Q1, Q2, . . .}, each latent quantum systemQN is posited to be characterised as a (finite) formal string QN := Q1NQ2N · · ·QnN on the alphabetSys(qt), where strings differing just by the presence of the characterI in some positions are identified. This characterisation implies that, for standard...

    work page

Showing first 80 references.