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arXiv:2204.05537 · Physical Review A

Role of nonclassical temporal correlation in powering quantum random access codes

Subhankar Bera, Ananda G. Maity, Shiladitya Mal, A. S. Majumdar

Published Oct 25, 2022• 2 citations
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Abstract

We explore the fundamental origin of the quantum advantage behind random access code. We propose new temporal inequalities compatible with noninvasive-realist models and show that any nonzero quantum advantage of $n\ensuremath{\mapsto}1$ random access code in the presence of shared randomness is equivalent to the violation of the corresponding temporal inequality. As a consequence of this connection, we also prove that the maximal success probability of $n\ensuremath{\mapsto}1$ random access code can be obtained when the maximal violation of the corresponding inequality is achieved. We further show that any nonzero quantum advantage of $n\ensuremath{\mapsto}1$ random access code, or in other words, any nonzero violation of the corresponding temporal inequality, can certify genuine randomness.

DOI
10.1103/physreva.106.042439

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We explore the fundamental origin of the quantum advantage behind random access code. We propose new temporal inequalities compatible with noninvasive-realist models and show that any nonzero quantum advantage of n\ensuremath↦1n\ensuremath{\mapsto}1n\ensuremath↦1 random access code in the presence of shared randomness is equivalent to the violation of the corresponding temporal inequality. As a consequence of this connection, we also prove that the maximal success probability of n\ensuremath↦1n\ensuremath{\mapsto}1n\ensuremath↦1 random access code can be obtained when the maximal violation of the corresponding inequality is achieved. We further show that any nonzero quantum advantage of n\ensuremath↦1n\ensuremath{\mapsto}1n\ensuremath↦1 random access code, or in other words, any nonzero violation of the corresponding temporal inequality, can certify genuine randomness.
We provide the first explicit identification and quantitative characterization of the physical origin of the quantum advantage in the Random Access Code (RAC) protocol. This is achieved by formulating the protocol in terms of intraparticle entanglement between co-measurable degrees of freedom of a single particle and establishing a fundamental correspondence between the protocol's success probability and the underlying resource powering it. For this purpose, we use a relevant Bell-type inequality derived from the assumption of noncontextuality of measurement outcomes. The formulated analysis reveals that the magnitude of quantum-mechanical violation of this inequality, signifying a form of quantum contextuality, is quantitatively commensurate with the ``quantum enhancement" of success probability in any intraparticle entanglement-assisted nnn-bit RAC protocol. In particular, the maximal success probability achievable in a quantum n↦1n \mapsto 1n↦1 RAC protocol corresponds to the maximal quantum violation of the relevant Bell-type inequality. Our framework not only demonstrates how quantum contextuality entailed by intraparticle entanglement serves as an effective resource for enhancing RAC performance, but also offers a significant operational advantage: the proposed scheme is readily implementable in a single-particle interferometric setup requiring coherence preservation only for a single particle, rather than between spatially separated entangled systems.
We explore implications of the nonclassicality of unsteerable correlations as a resource for quantum information processing. The notion of superunsteerability furnishes an operational characterization of nonclassicality beyond steering in the presence of finite shared randomness. Considering the task of quantum random access codes (RAC) through separable Bell-diagonal states, we demonstrate the advantage of superunsteerability over classical protocols assisted with two-bits of shared randomness. We propose a quantifier of superunsteerability and obtain its analytical expression in the context of the two- and three-setting steering scenarios that are directly related to the quantum 2→12 \to 12→1 and 3→13 \to 13→1 RAC protocols, respectively. The maximal values of our quantifier yield optimal quantum efficiency for both protocols, thus showing that superunsteerability provides a precise characterization of the nonclassical resource for implementing RACs with separable states.
A random access code (RAC) is an important communication protocol to obtain information about a randomly specified substring of an nnn-bit string, while only having limited information about the nnn-bit string. Quantum RACs usually utilize either communication of quantum bits or a shared-in-advance quantum state used in conjunction with classical communication. Here we consider the latter version of the quantum protocols under the constraint of single-bit communication and with a shared arbitrary state of two qubits. Taking the worst-case success probability as the figure of merit, we demonstrate that any state with an invertible correlation matrix can be used to outperform the best classical RAC for n=3n=3n=3. We derive an additional condition sufficient to beat the best classical performance in the case of n=2n=2n=2. In particular, separable states turn out to be a useful resource behind the quantum advantage for n=2,3n=2,3n=2,3. For $n\ensuremath{\ge}4$, RACs assisted with a single copy of a quantum state do not outperform the classical RACs.
It is one of the peculiar features of quantum physics that some sets of measurements are incompatible in the sense that they cannot be performed simultaneously. Incompatibility is an important quantum resource as it enables Bell nonlocality and steering. Here we show that incompatibility is crucial also in certain communication tasks; we prove that quantum random access code performs better than its classical counterpart only when incompatible quantum measurements are used in the decoding task. As a consequence, evaluating the average success probability for quantum random access code provides a semi-device-independent test for the detection of quantum incompatibility. We further demonstrate that any incompatible pair of projective measurements gives an advantage over all classical strategies. Finally, we establish a connection between the maximal average success probability for quantum random access code and earlier quantities introduced to assess incompatibility.
We develop a framework for characterizing quantum temporal correlations in a general temporal scenario, in which an initial quantum state is measured, sent through a quantum channel, and finally measured again. This framework does not make any assumptions on the system nor on the measurements, namely, it is device independent. It is versatile enough, however, to allow for the addition of further constraints in a semi-device-independent setting. Our framework serves as a natural tool for quantum certification in a temporal scenario when the quantum devices involved are uncharacterized or partially characterized. It can hence also be used for characterizing quantum temporal correlations when one assumes an additional constraint of no-signalling in time, there are upper bounds on the involved systems' dimensions, rank constraints-for which we prove genuine quantum separations over local hidden variable models-or further linear constraints. We present a number of applications, including bounding the maximal violation of temporal Bell inequalities, quantifying temporal steerability, and bounding the maximum successful probability in quantum randomness access codes.
We show how nonclassical correlations in local bipartite states can act as a resource for quantum information processing. Considering the task of quantum random access codes (RACs) through separable Bell-diagonal states, we demonstrate the advantage of superunsteerability over classical protocols assisted with two bits of shared randomness. We propose a measure of superunsteerability which quantifies nonclassicality beyond quantum steering and obtain its analytical expression for Bell-diagonal states in the context of two- and three-setting steering scenarios that are directly related to the quantum $2\ensuremath{\rightarrow}1$ and $3\ensuremath{\rightarrow}1$ RAC protocols, respectively. The maximal values of our quantifier yield the optimal quantum efficiency for both of the above protocols, thus showing that superunsteerability provides a precise characterization of the nonclassical resource for implementing RACs with separable Bell-diagonal class of states.