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Superunsteerability as a quantifiable resource for random access codes

Chellasamy Jebarathinam, Debarshi Das, Som Kanjilal, R. Srikanth, Debasis Sarkar, Indrani Chattopadhyay, A. S. Majumdar

Published Dec 24, 2018• 0 citations
OpenAlex

Abstract

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 $2 \to 1$ and $3 \to 1$ 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.

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arXiv:1912.09900•Physical Review A•Jul 19, 2023•5 citations
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.
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.
Superunsteerability is a particular kind of spatial quantum correlation that can be observed in a steering scenario in the presence of limited shared randomness. In this work, we define an experimentally measurable quantity in a steering scenario to certify superunsteerability. In the context of certification of randomness with this scenario, we demonstrate that such certification of superunsteerability provides a bound on the amount of genuine randomness generation. On the other hand, superlocality is another kind of spatial quantum correlation that can be observed in a Bell scenario in the presence of limited shared randomness. We identify inequalities to certify superlocality in the Bell scenarios that can be adopted to implement 222-to-111 and 333-to-111 random-access codes. We observe that such certification of superlocality acts as resource for the random-access codes in the presence of limited shared randomness. As a by-product of our certification of superunsteerability and superlocality, we identify a new classification of separable states having quantumness.
Random access code (RAC) is a strategy to access remote data even if one has limited information about it. We derive here the conditions for the optimal performance of two most basic RAC protocols implemented using two-qubit states. The conditions derived are valid for any set of decoding operations. This allows a meaningful comparison between quantum and classical resources in RAC and leads to identifying the condition for quantum advantage. It turns out that the necessary resource is quantum discord of the assisting state, but, importantly, the non-vanishing value of quantum discord in itself does not guarantee quantum advantage for any choice of decoding operations. We argue that simultaneous correlation in mutually unbiased bases as well as a particular notion of nonclassicality based on quantum steering can capture efficiency of the optimal RAC for orthogonal decoding operations.
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.
Recently, the quantumness of local correlations arising from separable states in the context of a Bell scenario has been studied and linked with superlocality [Phys. Rev. A 95, 032120 (2017)]. Here we investigate the quantumness of unsteerable correlations in the context of a given steering scenario. Generalizing the concept of superlocality, we define as supercorrelation the requirement for a larger dimension of the preshared randomness to simulate the correlations than that of the quantum states that generate them. Since unsteerable states form a subset of Bell local states, it is an interesting question whether certain unsteerable states can be supercorrelated. Here, we answer this question in the affirmative. In particular, the quantumness of certain unsteerable correlations can be pointed out by the notion of superunsteerability, the requirement for a larger dimension of the classical variable that the steering party has to preshare with the trusted party for simulating the correlations than that of the quantum states which reproduce them. This provides a generalized approach to quantify the quantumness of unsteerable correlations in convex operational theories.
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.