General probabilistic theories: An introduction

Plávala, Martin

doi:10.48550/arxiv.2103.07469

Cited by 29 publications

(61 citation statements)

References 128 publications

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“…VI, we expect accessible GPT fragments to be a valuable tool for theory-agnostic tomography [10][11][12]. We also expect accessible GPT fragments to be critical for the development of a resource theory of generalized contextuality 4 .…”

Section: Introductionmentioning

confidence: 94%

“…The framework is built on a minimal set of operational principles, based primarily on the fact that any physical theory must, at a minimum, make probabilistic predictions about the outcomes of experiments. This framework has been employed, for example, to study the principles that underlie quantum advantages for information processing [2,4,5].…”

Section: Introductionmentioning

confidence: 99%

“…3 That is, for each possible outcome of the original measurement, its inefficient counterpart has a nonzero probability of performing as expected, and a probability of failure (which is nonzero for at least one outcome), in which case it returns a 'null' outcome. 4 Indeed, it was for this purpose that we originally conceived of them. 5 Strictly, the GPTs that are cone-equivalent to an unrestricted [3] GPT correspond to the noisy-unrestricted GPTs of Ref.…”

Section: Introductionmentioning

confidence: 99%

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Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

Selby¹,

Schmid²,

Wolfe³

et al. 2021

Preprint

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The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all physically possible processes. We here consider the question of how to provide a GPT-like characterization of a particular experimental setup within a given physical theory. We show that the resulting characterization is not generally a GPT in and of itself-rather, it is described by a more general mathematical object that we introduce and term an accessible GPT fragment. We then introduce an equivalence relation, termed cone equivalence, between accessible GPT fragments (and, as a special case, between standard GPTs). We give a number of examples of experimental scenarios that are best described using accessible GPT fragments, and where moreover cone-equivalence arises naturally. We then prove that an accessible GPT fragment admits of a classical explanation if and only if every other fragment that is cone-equivalent to it also admits of a classical explanation. Finally, we leverage this result to prove several fundamental results regarding the experimental requirements for witnessing the failure of generalized noncontextuality. In particular, we prove that neither incompatibility among measurements nor the assumption of freedom of choice is necessary for witnessing failures of generalized noncontextuality, and, moreover, that such failures can be witnessed even using arbitrarily inefficient detectors.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

Selby¹,

Schmid²,

Wolfe³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…We point the interested reader to Ref. [13,21,15] for more details and a thorough operational justification of the construction described here.…”

Section: General Probabilistic Theoriesmentioning

confidence: 99%

“…In order to achieve this, following recent developments [4,5,6,7,8,9] we will utilise the formalism of general probabilistic theories (GPTs). Within this mathematical framework, it is possible to model a vast family of physical theories, including classical probability theory, quantum mechanics; and more exotic theories such as generalised bits [10], spherical models [6], and Popescu-Rohrlich (PR) boxes [11,12], to name a few [13,14,15].…”

Section: Introductionmentioning

confidence: 99%

A Post-Quantum Associative Memory

Lami¹,

Goldwater²,

Adesso³

2022

Preprint

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Associative memories are devices storing information that can be fully retrieved given partial disclosure of it. We examine a toy model of associative memory and the ultimate limitations it is subjected to within the framework of general probabilistic theories (GPTs), which represent the most general class of physical theories satisfying some basic operational axioms. We ask ourselves how large the dimension of a GPT should be so that it can accommodate 2 m states with the property that any N of them are perfectly distinguishable. Invoking an old result by Danzer and Grünbaum, we prove that when N = 2 the optimal answer to this question is m + 1, to be compared with O(2 m ) when the theory is required to be either classical or quantum. This yields an example of a task where GPTs outperform both classical and quantum theory exponentially. The same problem for N ≥ 3 is left open.

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Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure

Arai

Hayashi

2023

New J. Phys.

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An experimental verification of the maximally entangled state ensures that the constructed state is close to the maximally entangled state, but it does not guarantee that the state is exactly the same as the maximally entangled state. Further, the entanglement structure is not uniquely determined in general probabilistic theories even if we impose that the local subsystems are fully equal to quantum systems. Therefore, the existence of the maximally entangled state depends on whether the standard entanglement structure is valid. To examine this issue, we introduce pseudo standard entanglement structure as a structure of quantum composite system under natural assumptions based on the existence of projective measurements and the existence of approximations of all maximally entangled standard states. Surprisingly, there exist infinitely many pseudo standard entanglement structures different from the standard entanglement structure. In our setting, any maximally entangled state can be arbitrarily approximated by an entangled state that belongs to our obtained pseudo standard entanglement structure. That is, experimental verification does not exclude the possibility of our obtained pseudo standard entanglement structure that is different from the standard entanglement structure. On the other hand, such pseudo structures never possess global unitary symmetry, i.e., global unitary symmetry is essential condition for the standard entanglement structure.

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General probabilistic theories: An introduction

Cited by 29 publications

References 128 publications

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

A Post-Quantum Associative Memory

Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure

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