Preparation contextuality as an essential feature underlying quantum communication advantage

Saha, Debashis; Chaturvedi, Anubhav

doi:10.1103/physreva.100.022108

Cited by 42 publications

(35 citation statements)

References 18 publications

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“…Also, it is worth noting that a number of works have (in different ways) shown that outcome statistics that violate a Bell inequality is a proof of preparation contextuality [18,23,24,42]. In Appendix A, we note that this fact follows immediately from ontological models and the no-signaling principle (see also Ref.…”

Section: Resultsmentioning

confidence: 83%

“…It is interesting to note that tests of preparation contextuality can be formulated as communication tasks between two separated parties, in which the receiver is kept oblivious about parts of the sender's input [23][24][25]. Such obliviousness corresponds to different contexts for the states.…”

Section: Resultsmentioning

confidence: 99%

“…Contextuality (in its broad sense) in quantum theory is closely related to e.g. advantages in quantum computation [19][20][21][22], advantages in particular communication tasks [23][24][25][26], quantum zero-error communication [27] and anomalous weak values [28].…”

Section: Introductionmentioning

confidence: 99%

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Measurement incompatibility and steering are necessary and sufficient for operational contextuality

Tavakoli

Uola

2020

Phys. Rev. Research

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Contextuality is a signature of operational nonclassicality in the outcome statistics of an experiment. This notion of nonclassicality applies to a breadth of physical phenomena. Here, we establish its relation to two fundamental nonclassical entities in quantum theory; measurement incompatibility and steering. We show that each is necessary and sufficient the failure of operational contextuality. We exploit the established connection to contextuality to provide a novel approach to problems in measurement incompatibility and steering.

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Section: Resultsmentioning

confidence: 83%

Section: Resultsmentioning

confidence: 99%

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Measurement incompatibility and steering are necessary and sufficient for operational contextuality

Tavakoli

Uola

2020

Phys. Rev. Research

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“…Moreover, we show preparation contextuality is the necessary resource for advantage in OC tasks. Taking into account the recent works [44,53], one may attempt to provide a complete resource theory of quantum contextuality in the context of communication tasks.…”

Section: Resultsmentioning

confidence: 99%

“…The proof of this fact is discussed in section 4. It is also noteworthy that there exists a generic relation of quantum advantage between these two communication scenarios [44].…”

Section: Oblivious Communicationmentioning

confidence: 99%

State independent contextuality advances one-way communication

2019

Self Cite

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Although 'quantum contextuality' is one of the most fundamental non-classical feature, its generic role in information processing and computation is an open quest. In this article, we present a family of distributed computing tasks pertaining to every logical proof of Kochen-Specker (KS) contextuality in two different one-way communication scenarios: (I) communication of bounded dimensional system, (II) communication of unbounded dimensional system while keeping certain information oblivious, namely, oblivious communication (OC). As the later remains largely unexplored, we introduce a general framework for OC tasks and provide a methodology for obtaining an upper bound on the success of OC tasks in classical communication. We show that quantum communication comprised of every KS set of vectors outperforms classical communication and perfectly accomplish the task in both the aforementioned scenarios. We explicitly discuss the communication tasks pertaining to the simplest state independent contextuality sets of dimension three and four. Our results establish an operational significance to single system contextuality and open up the possibility of semi-device independent quantum information processing based on that. Alongside, we identify any advantage in OC tasks as a witness of preparation contextuality. communicated system (classical or quantum) is restricted to certain value, and (II) oblivious communication (OC) upon the constraint that certain information about the sender's input is unrevealed in communication. As the later remains largely unexplored, we provide a method to obtain optimal bounds on the success probability of OC tasks in classical communication. Moving to the central part of the article we introduce a family of oneway communication tasks, which we refer to as vertex equality problem, based on the orthogonal graphs of vector sets with SIC property. We show that quantum communication comprised of every KS set of vectors outperforms classical communication in both the aforementioned scenarios. While the result holds for any SIC proof involving rank-one projectors in the former scenario, we extend this result for the simplest SIC proof in the later scenario. Significantly, OC does not impose any restriction on the dimension of the communicated system. This implies that even unbounded classical resource cannot reproduce quantum contextual statistics satisfying certain oblivious conditions. We explicitly derive the optimal classical strategies for the vertex equality problem pertaining to Cabello-Estebaranz-GarciaAlcaine (CEG-18) [26] and Yu-Oh (YO-13) [6] vector sets. Nevertheless, we provide the analytical expression of the optimal success probability in classical communication, applicable to a general vertex equality problem. We also study the robustness of quantum communication advantage with respect to white noise and discuss the applicability of quantum contextuality in semi-device independent information processing [27,28]. Besides, we generalize the observation made in [13] that preparation ...

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Logical proof of quantum correlations requiring entanglement measurements

Sohbi

Kim

2019

Phys. Rev. A

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We present a logical type of proof of contextuality for a two-qubit state. We formulate a paradox that cannot be verified by a two-qubit system with local measurements while it is possible by using entanglement measurements. With our scheme we achieve p Hardy ≈ 0.167, which is the highest probability obtained for a system of similar dimension. Our approach uses graph theory and the global exclusivity principle to give an interpretation of logical type of proofs of quantum correlations. We review the Hardy paradox and find connection to the KCBS inequality. We apply the same method to build a paradox based the CHSH inequality.Contextuality refers to the property of measurements statistics to have their outcomes depending on the set of measurements that are simultaneously performed. Originally discovered by Bell, Kochen and Specker [1,2], it uses the notion of compatibility, which refers to the property of several measurements to be performed simultaneously. Recent efforts have been made on understanding contextuality using a graph theory approach [3-6]. Contextuality has shown an advantage in quantum computing [7][8][9][10], in quantum cryptography [11,12], quantum communication [13,14] and state discrimination [15].Contextuality generalizes non-locality [4] and the ability to experimentally observe these two fundamental properties of quantum physics is an important point when it comes to their uses in information technology tasks. It is then one of the most fundamental challenge to develop tools to characterize and classify measurements statistics belonging to different theories. A common technic to witness non-locality and contextuality is through inequalities of measurements statistics. Another possibility is by using logical arguments [16][17][18][19][20], where a set of conditions if satisfied assert the non-local or contextual nature of the system considered. While it is clear that a verification of non-locality or contextuality with a logical proof implies the violation of an inequality [21], the inverse is not straightforward to answer.When such properties are observed on spatially separated systems, entanglement is a needed resource. Entangled states and local measurements are a sufficient resource to observe non-locality. Moreover, a quantum measurement can also have entanglement properties when its eigenstates are entangled. This is a crucial key in the architectures of quantum network using quantum repeaters [22], where independent sources send entangled photons to distant parties. When entanglement measurements are performed on pair of photons from different sources it can create entanglement between initially uncorrelated parties. In particular Bell state measurements can create maximally entangled states and can also be self-tested device-independently [23,24].Recent advances on the classification of correlations * sohbi@kias.re.kr

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Preparation contextuality as an essential feature underlying quantum communication advantage

Cited by 42 publications

References 18 publications

Measurement incompatibility and steering are necessary and sufficient for operational contextuality

Measurement incompatibility and steering are necessary and sufficient for operational contextuality

State independent contextuality advances one-way communication

Logical proof of quantum correlations requiring entanglement measurements

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