Observers of quantum systems cannot agree to disagree

Contreras-Tejada, Patricia; Scarpa, Giannicola; Kubicki, Aleksander M.; Brandenburger, Adam; Mura, Pierfrancesco La

doi:10.1038/s41467-021-27134-6

Cited by 6 publications

(4 citation statements)

References 29 publications

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“…We end with some comments on the realizability of common certainty of disagreement (CCD) as in theorem 4.2. In the physical domain, it can be shown that CCD is impossible when observing quantum systems, but possible when observing superquantum (no-signalling) systems [ 28 ]. In the language of this paper, we can say that quantum mechanics somehow controls the ‘extent’ of negativity in phase-space probability representations so that CCD cannot arise.…”

Section: Discussionmentioning

confidence: 99%

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Agreement and disagreement in a non-classical world

Brandenburger,

Contreras-Tejada,

La Mura

et al. 2024

Phil. Trans. R. Soc. A.

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The Agreement Theorem Aumann (1976 Ann. Stat. 4 , 1236–1239. ( doi:10.1214/aos/1176343654 )) states that if two Bayesian agents start with a common prior, then they cannot have common knowledge that they hold different posterior probabilities of some underlying event of interest. In short, the two agents cannot ‘agree to disagree’. This result applies in the classical domain where classical probability theory applies. But in non-classical domains, such as the quantum world, classical probability theory does not apply. Inspired principally by their use in quantum mechanics, we employ signed probabilities to investigate the epistemics of the non-classical world. We find that here, too, it cannot be common knowledge that two agents assign different probabilities to an event of interest. However, in a non-classical domain, unlike the classical case, it can be common certainty that two agents assign different probabilities to an event of interest. Finally, in a non-classical domain, it cannot be common certainty that two agents assign different probabilities, if communication of their common certainty is possible—even if communication does not take place. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

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Section: Discussionmentioning

confidence: 99%

“…This finding suggests there may be promise in proposing the impossibility of CCD (of ‘agreeing to disagree’) as an axiom in the program to derive quantum mechanics from underlying physical principles. (See [ 28 ] for further discussion and references to the axiomatization programme.)…”

Section: Discussionmentioning

confidence: 99%

Agreement and disagreement in a non-classical world

Brandenburger,

Contreras-Tejada,

La Mura

et al. 2024

Phil. Trans. R. Soc. A.

Self Cite

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“…John Bell's seminal work [1][2][3][4][5][6] has triggered a rich tradition of experimental studies [7][8][9][10][11][12][13] as well as theoretical and interpretational work [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. To derive his famous inequalities, he has taken a realist worldview, making the additional assumption of free choice and locality, as formally defined by precise equations in a hidden variable model.…”

Section: Introductionmentioning

confidence: 99%

Quantifying and Interpreting Connection Strength in Macro- and Microscopic Systems: Lessons from Bell’s Approach

Gallus

Błasiak

Pothos

2022

Entropy

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Bell inequalities were created with the goal of improving the understanding of foundational questions in quantum mechanics. To this end, they are typically applied to measurement results generated from entangled systems of particles. They can, however, also be used as a statistical tool for macroscopic systems, where they can describe the connection strength between two components of a system under a causal model. We show that, in principle, data from macroscopic observations analyzed with Bell’ s approach can invalidate certain causal models. To illustrate this use, we describe a macroscopic game setting, without a quantum mechanical measurement process, and analyze it using the framework of Bell experiments. In the macroscopic game, violations of the inequalities can be created by cheating with classically defined strategies. In the physical context, the meaning of violations is less clear and is still vigorously debated. We discuss two measures for optimal strategies to generate a given statistic that violates the inequalities. We show their mathematical equivalence and how they can be computed from CHSH-quantities alone, if non-signaling applies. As a macroscopic example from the financial world, we show how the unfair use of insider knowledge could be picked up using Bell statistics. Finally, in the discussion of realist interpretations of quantum mechanical Bell experiments, cheating strategies are often expressed through the ideas of free choice and locality. In this regard, violations of free choice and locality can be interpreted as two sides of the same coin, which underscores the view that the meaning these terms are given in Bell’s approach should not be confused with their everyday use. In general, we conclude that Bell’s approach also carries lessons for understanding macroscopic systems of which the connectedness conforms to different causal structures.

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“…The NPA hierarchy is an extremely useful tool, but is not described in terms of either information-theoretic or physical principles. As a result, many principles followed such as information causality [22], macroscopic locality [23], local orthogonality [24,25], and no common certainty of disagreement [26]. An obstacle to the development of such principles is the almost-quantum set of common-cause boxes [27], which have not yet violated any of the proposed principles.…”

Section: Introductionmentioning

confidence: 99%

On characterising assemblages in Einstein–Podolsky–Rosen scenarios

Rossi¹,

Hoban²,

Sainz³

2022

J. Phys. A: Math. Theor.

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Characterising non-classical quantum phenomena is crucial not only from a fundamental perspective, but also to better understand its capabilities for information processing and communication tasks. In this work, we focus on exploring the characterisation of Einstein-Podolsky-Rosen inference (a.k.a. steering): a signature of non-classicality manifested when one or more parties in a Bell scenario have their systems and measurements described by quantum theory, rather than being treated as black boxes. We propose a way of characterising common-cause assemblages from the correlations that arise when the trusted party performs tomographicallycomplete measurements on their share of the experiment, and discuss the advantages and challenges of this approach. Within this framework, we show that so-called almost quantum assemblages satisfy the principle of macroscopic noncontextuality, and demonstrate that a subset of almost quantum correlations recover almost quantum assemblages in this approach.

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Observers of quantum systems cannot agree to disagree

Cited by 6 publications

References 29 publications

Agreement and disagreement in a non-classical world

Agreement and disagreement in a non-classical world

Quantifying and Interpreting Connection Strength in Macro- and Microscopic Systems: Lessons from Bell’s Approach

On characterising assemblages in Einstein–Podolsky–Rosen scenarios

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