Measurement incompatibility and steering are necessary and sufficient for operational contextuality

Tavakoli, Armin; Uola, Roope

doi:10.1103/physrevresearch.2.013011

Cited by 57 publications

(41 citation statements)

References 56 publications

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“…Specifically, contextuality provides an advantage to the maximum copying fidelity. Our result directly links contextuality to a quantum advantage [5,12,13].…”

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confidence: 61%

Contextual advantage for state-dependent cloning

Lostaglio

Senno

2020

Quantum

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A number of noncontextual models exist which reproduce different subsets of quantum theory and admit a no-cloning theorem. Therefore, if one chooses noncontextuality as one's notion of classicality, no-cloning cannot be regarded as a nonclassical phenomenon. In this work, however, we show that there are aspects of the phenomenology of quantum state cloning which are indeed nonclassical according to this principle. Specifically, we focus on the task of state-dependent cloning and prove that the optimal cloning fidelity predicted by quantum theory cannot be explained by any noncontextual model. We derive a noise-robust noncontextuality inequality whose violation by quantum theory not only implies a quantum advantage for the task of state-dependent cloning relative to noncontextual models, but also provides an experimental witness of noncontextuality.An important guiding principle for quantum theorists is the identification of genuine nonclassical effects certified by rigorous theorems. Given a quantum phenomenon, the relevant question is: Are there classical models able to reproduce the observed operational data? Here we investigate this question in the context of a cloning experiment.

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“…Specifically, contextuality provides an advantage to the maximum copying fidelity. Our result directly links contextuality to a quantum advantage [5,12,13].…”

mentioning

confidence: 61%

Contextual advantage for state-dependent cloning

Lostaglio

Senno

2020

Quantum

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“…It is important to notice that whenever two measurements are compatible, they cannot be used to produce quantum advantage in tasks like Bell nonlocality [5] or Einstein-Podolsky-Rosen steering [6,7]. Moreover, it was recently shown that joint measurability is equivalent to a specific notion of classicality, namely, preparation non-contextuality [8,9]. Hence, one may think of compatible measurements as 'classical' , and incompatible measurements as a resource for the above tasks.…”

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confidence: 99%

Incompatibility robustness of quantum measurements: a unified framework

2019

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In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e. measurements that cannot be simultaneously performed on a single copy of the system. It is then natural to ask what the most incompatible quantum measurements are. To answer this question, several measures have been proposed to quantify how incompatible a set of measurements is, however their properties are not well-understood. In this work, we develop a general framework that encompasses all the commonly used measures of incompatibility based on robustness to noise. Moreover, we propose several conditions that a measure of incompatibility should satisfy, and investigate whether the existing measures comply with them. We find that some of the widely used measures do not fulfil these basic requirements. We also show that when looking for the most incompatible pairs of measurements, we obtain different answers depending on the exact measure. For one of the measures, we analytically prove that projective measurements onto two mutually unbiased bases are among the most incompatible pairs in every dimension. However, for some of the remaining measures we find that some peculiar measurements turn out to be even more incompatible.performed simultaneously by performing the parent measurement. If such a parent measurement does not exist, we say that the measurements are incompatible (or not jointly measurable). We remark here that other notions of compatibility, such as commutativity, non-disturbance and coexistence, are also used in the literature [1,3]; let us for completeness briefly explain how they are related. Commutativity of a measurement pair implies nondisturbance, which in turn implies joint measurability, which then implies coexistence. Moreover, it is known that none of the converse implications hold in general, therefore these notions are strictly distinct [4]. In this work we focus solely on the notion of joint measurability, because the existence (or not) of a parent measurement has a clear operational meaning. Therefore, throughout the present paper we use the terms '(in) compatibility' and '(non-)joint measurability' interchangeably. It is important to notice that whenever two measurements are compatible, they cannot be used to produce quantum advantage in tasks like Bell nonlocality [5] or Einstein-Podolsky-Rosen steering [6,7]. Moreover, it was recently shown that joint measurability is equivalent to a specific notion of classicality, namely, preparation non-contextuality [8,9]. Hence, one may think of compatible measurements as 'classical' , and incompatible measurements as a resource for the above tasks. Therefore, it is of fundamental importance to characterise and understand the structure of incompatible measurements.What is particularly important is to go beyond the dichotomy of compatible and incompatible measurements, and quantify to what extent a pair of measurements is incompatible. A natural framework for this qua...

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“…Note here that, obliviousness in an operational theory can equivalently be represented as the obliviousness at the level of ontic states if the ontological model of that operational theory is preparation non-contextual [17]. In this connection, it is also worthwhile to note that, in two-input-two-output Bell scenario the preparation non-contextuality assumption in an ontological model of quantum theory can also be viewed as locality condition [28,29]. We may call it as trivial preparation non-contextuality condition.…”

Section: Introductionmentioning

confidence: 99%

Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness

Pan

2021

Preprint

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We provide an interesting two-party parity oblivious communication game whose success probability is solely determined by the Bell expression. The parity-oblivious condition in an operational quantum theory implies the preparation non-contextuality in an ontological model of it. We find that the aforementioned Bell expression has two upper bounds in an ontological model; the usual local bound and a non-trivial preparation non-contextual bound arising from the non-trivial parityoblivious condition, which is smaller that the local bound. We first demonstrate the communication game when both Alice and Bob perform three measurements of dichotomic observables in their respective sites. The optimal quantum value of the Bell expression in this scenario enables us to deviceindependently self-test the maximally entangled state and trine-set of observables, three-outcome qubit positive-operator-valued-measures (POVMs) and 1.58 bit of local randomness. Further, we generalize the above communication game in that both Alice and Bob perform the same but arbitrary (odd) number (n > 3) of measurements. Based on the optimal quantum value of the relevant Bell expression for any arbitrary n, we have also demonstrated device-independent self-testing of state and measurements.

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Measurement incompatibility and steering are necessary and sufficient for operational contextuality

Cited by 57 publications

References 56 publications

Contextual advantage for state-dependent cloning

Contextual advantage for state-dependent cloning

Incompatibility robustness of quantum measurements: a unified framework

Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness

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