Contextuality of General Probabilistic Theories

Shähandeh, Farid

doi:10.1103/prxquantum.2.010330

Cited by 35 publications

(37 citation statements)

References 47 publications

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“…This follows from Theorem 1 because a noncontextual simulation is an embedding (see Lemma 2 and Definition 3). Furthermore, our results on exact embeddings into quantum theory (in Section V below) imply as a simple consequence (Corollary 3) a result that has also been found in [63][64][65]: that the only unrestricted GPTs that are exactly embeddable into classical probability theory are the classical GPTs, i.e. the C n .…”

Section: A Equivalence Of Simulations and Ontological Modelssupporting

confidence: 80%

Testing quantum theory with generalized noncontextuality

Mueller¹,

Garner²

2021

Preprint

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It is a fundamental prediction of quantum theory that states of physical systems are described by complex vectors or density operators on a Hilbert space. However, many experiments admit effective descriptions in terms of other state spaces, such as classical probability distributions or quantum systems with superselection rules. Here, we ask which probabilistic theories could reasonably be found as effective descriptions of physical systems if nature is fundamentally quantum. To this end, we employ a generalized version of noncontextuality: processes that are statistically indistinguishable in an effective theory should not require explanation by multiple distinguishable processes in a more fundamental theory. We formulate this principle in terms of embeddings and simulations of one probabilistic theory by another, show how this concept subsumes standard notions of contextuality, and prove a multitude of fundamental results on the exact and approximate embedding of theories (in particular into quantum theory). We show how results on Bell inequalities can be used for the robust certification of generalized contextuality. From this, we propose an experimental test of quantum theory by probing single physical systems without assuming access to a tomographically complete set of procedures, arguably avoiding a significant loophole of earlier approaches.

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Section: A Equivalence Of Simulations and Ontological Modelssupporting

confidence: 80%

Testing quantum theory with generalized noncontextuality

Mueller¹,

Garner²

2021

Preprint

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“…And indeed, thanks to the above observation x+y 2 = x + y−x 2 ∈ x + A. This proves (24). As an immediate consequence of this together with Q * (n, A, X), observe that the convex bodies x+B 2 , indexed by x ∈ X, are all disjoint and moreover contained in B, because this is convex.…”

Section: The Proofsupporting

confidence: 58%

“…• We are not examining non-local correlations or entanglement-like features available in different GPTs, which are often the subject of enquiry in the GPT literature [23,24,25,26,27,8,9]. However, although we are only considering the geometries of single systems, it is worth emphasising that these do impact upon which non-local correlations can be attained [28,29,27,8,9].…”

Section: Definition 2 (General Probabilistic Theories)mentioning

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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“…This lemma was independently shown in[34], where it is considered as a GTT for GPTs.Accepted in Quantum 2021-11-12, click title to verify. Published under CC-BY 4.0.…”

mentioning

confidence: 99%

General Probabilistic Theories with a Gleason-type Theorem

Wright

Weigert

2021

Quantum

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Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We identify the class of general probabilistic theories which also admit Gleason-type theorems. It contains theories satisfying the no-restriction hypothesis as well as others which can simulate such an unrestricted theory arbitrarily well when allowing for post-selection on measurement outcomes. Our result also implies that the standard no-restriction hypothesis applied to effects is not equivalent to the dual no-restriction hypothesis applied to states which is found to be less restrictive.

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Contextuality of General Probabilistic Theories

Cited by 35 publications

References 47 publications

Testing quantum theory with generalized noncontextuality

Testing quantum theory with generalized noncontextuality

A Post-Quantum Associative Memory

General Probabilistic Theories with a Gleason-type Theorem

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