Almost Quantum Correlations are Inconsistent with Specker's Principle

Gonda, Tomáš; Kunjwal, Ravi; Schmid, David; Wolfe, Elie; Sainz, Ana Belén

doi:10.22331/q-2018-08-27-87

Cited by 16 publications

(25 citation statements)

References 40 publications

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“…This is, for example, the reading adopted in Ref. [49], where the failure of Specker's principle in any almost quantum theory was demonstrated. On the other hand, we will often also refer to the "joint measurability" of a set of measurement events, by which we mean that this set of measurement events is a subset of the set of measurement outcomes for some choice of measurement setting.…”

Section: Distinguishing Two Consequences Of Specker's Principle: Strumentioning

confidence: 82%

“…We know that an almost quantum theory cannot satisfy Specker's principle [49] but it satisfies statistical Specker's principle (or consistent exclusivity). An open question that remains is:…”

Section: Almost Quantum Theorymentioning

confidence: 99%

“…If one restricted joint measurability of A (x) and B (y) to just commutativity -a sufficient but not necessary condition for joint measurability 49 [44] -we would take the above choice of the product POVM as a "natural" one. Being a product of trivial POVMs, this choice will never lead to a violation of the CHSHtype inequality for this scenario.…”

Section: C2 Chsh-type Contextuality Scenario: 4cyclementioning

confidence: 99%

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Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements

Kunjwal

2019

Quantum

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We develop a hypergraph-theoretic framework for Spekkens contextuality applied to Kochen-Specker (KS) type scenarios that goes beyond the Cabello-Severini-Winter (CSW) framework.To do this, we add new hypergraph-theoretic ingredients to the CSW framework. We then obtain noise-robust noncontextuality inequalities in this generalized framework by applying the assumption of (Spekkens) noncontextuality to both preparations and measurements. The resulting framework goes beyond the CSW framework in both senses, conceptual and technical. On the conceptual level: 1) as in any treatment based on the generalized notion of noncontextualityà la Spekkens, we relax the assumption of outcome determinism inherent to the Kochen-Specker theorem but retain measurement noncontextuality, besides introducing preparation noncontextuality, 2) we do not require the exclusivity principle -that pairwise exclusive measurement events must all be mutually exclusive -as a fundamental constraint on measurement events of interest in an experimental test of contextuality, given that this property is not true of general quantum measurements, and 3) as a result, we do not need to presume that measurement events of interest are "sharp" (for any definition of sharpness), where this notion of sharpness is meant to imply the exclusivity principle. On the technical level, we go beyond the CSW framework in the following senses: 1) we introduce a source events hypergraph -besides the measurement events hypergraph usually considered -and define a new operational quantity Corr that appears in our inequalities, 2) we define a new hypergraph invariant -the weighted max-predictability -that is necessary for our analysis and appears in our inequalities, and 3) our noise-robust noncontextuality inequalities quantify tradeoff relations between three operational quantities -Corr, R, and p 0 -only one of which (namely, R) corresponds to the Bell-Ravi Kunjwal: rkunjwal@perimeterinstitute.ca Kochen-Specker functionals appearing in the CSW framework; when Corr = 1, the inequalities formally reduce to CSW type bounds on R. Along the way, we also consider in detail the scope of our framework vis-à-vis the CSW framework, particularly the role of Specker's principle in the CSW framework, i.e., what the principle means for an operational theory satisfying it and why we don't impose it in our framework.

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Section: Distinguishing Two Consequences Of Specker's Principle: Strumentioning

confidence: 82%

Section: Almost Quantum Theorymentioning

confidence: 99%

Section: C2 Chsh-type Contextuality Scenario: 4cyclementioning

confidence: 99%

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Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements

Kunjwal

2019

Quantum

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“…Before such a project can be undertaken, however, one needs a better understanding of the scope of joint measurability structures that can be real-ized by quantum systems of limited Hilbert space dimension, particularly if one is keen to build experimental tests and quantum information protocols based on such joint measurability structures. Such an understanding can also potentially aid the elucidation of facts about joint measurability that are particular to quantum theory in the broader landscape of general probabilistic theories [31][32][33][34][35]. Already, in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Already, in Ref. [35], it was shown that considering the joint measurability structure corresponding to a complete graph on four vertices is enough to separate almost quantum correlations (generalized to include single laboratory situations) [36,37] from those correlations that can be realized with projective measurements in quantum theory [37]. This result was taken as a failure of Specker's principle [35,38]-that any set of pairwise compatible measurements is globally compatible-for any measurements underlying almost quantum correlations.…”

Section: Introductionmentioning

confidence: 99%

Joint measurability structures realizable with qubit measurements: Incompatibility via marginal surgery

Nikola

Kunjwal

2020

Phys. Rev. Research

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Measurements in quantum theory exhibit incompatibility, i.e., they can fail to be jointly measurable. An intuitive way to represent the (in)compatibility relations among a set of measurements is via a hypergraph representing their joint measurability structure: its vertices represent measurements and its hyperedges represent (all and only) subsets of compatible measurements. Projective measurements in quantum theory realize (all and only) joint measurability structures that are graphs. On the other hand, general measurements represented by positive operator-valued measures (POVMs) can realize arbitrary joint measurability structures. Here we explore the scope of joint measurability structures realizable with qubit POVMs. We develop a technique that we term marginal surgery to obtain nontrivial joint measurability structures starting from a set of compatible measurements. We show explicit examples of marginal surgery on a special set of qubit POVMs to construct joint measurability structures such as N-cycle and N-Specker scenarios for any integer N 3. We also show the realizability of various joint measurability structures with N ∈ {4, 5, 6} vertices. In particular, we show that all possible joint measurability structures with N = 4 vertices are realizable. We conjecture that all joint measurability structures are realizable with qubit POVMs. This contrasts with the unbounded dimension required in R. Kunjwal et al. [Phys. Rev. A 89, 052126 (2014)]. Our results also render this previous construction maximally efficient in terms of the required Hilbert space dimension. We also obtain a sufficient condition for the joint measurability of any set of binary qubit POVMs which powers many of our results and should be of independent interest.

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Constrained measurement incompatibility from generalised contextuality of steered preparation

Mukherjee,

Pan

2024

New J. Phys.

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In a bipartite Bell scenario involving two local measurements per party and two outcome per measurement, the measurement incompatibility in one wing is both necessary and sufficient to reveal the nonlocality. However, such a one-to-one correspondence fails when one of the observers performs more than two measurements. In such a scenario, the measurement incompatibility is necessary but not sufficient to reveal the nonlocality. In this work, within the formalism of general probabilistic theory (GPT), we demonstrate that unlike the nonlocality, the incompatibility of $N$ arbitrary measurements in one wing is both necessary and sufficient for revealing the generalised contextuality for the sub-system in the other wing. Further, we formulate an elegant form of inequality for any GPT that is necessary for $N$-wise compatibility of $N$ arbitrary observables. Moreover, we argue that any theory that violates the proposed inequality possess a degree of incompatibility that can be quantified through the amount of violation. We claim that it is the generalised contextuality that provides a restriction to the allowed degree of measurement incompatibility of any viable theory of nature and thereby super-select the quantum theory. Finally, we discuss the geometrical implications of our results.

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Almost Quantum Correlations are Inconsistent with Specker's Principle

Cited by 16 publications

References 40 publications

Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements

Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements

Joint measurability structures realizable with qubit measurements: Incompatibility via marginal surgery

Constrained measurement incompatibility from generalised contextuality of steered preparation

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