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→1 and
3→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
n-bit string, while only having limited information about the
n-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=3. We derive an additional condition sufficient to beat the best classical performance in the case of
n=2. In particular, separable states turn out to be a useful resource behind the quantum advantage for
n=2,3. For $n\ensuremath{\ge}4$, RACs assisted with a single copy of a quantum state do not outperform the classical RACs.
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
n-bit RAC protocol. In particular, the maximal success probability achievable in a quantum
n↦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.
A random access code (RAC) is a communication task in which the sender encodes a random message into a shorter one to be decoded by the receiver so that a randomly chosen character of the original message is recovered with some probability. Both the message and the character to be recovered are assumed to be uniformly distributed. In this paper, we extend this protocol by allowing more general distributions of these inputs, which alters the encoding and decoding strategies optimizing the protocol performance, with either classical or quantum resources. We approach the problem of optimizing the performance of these biased RACs with both numerical and analytical tools. On the numerical front, we present algorithms that allow a numerical evaluation of the optimal performance over both classical and quantum strategies and provide a Python package designed to implement them, called RAC-tools. We then use this numerical tool to investigate single-parameter families of biased RACs in the ${n}^{2}\ensuremath{\mapsto}1$ and ${2}^{d}\ensuremath{\mapsto}1$ scenarios. For RACs in the ${n}^{2}\ensuremath{\mapsto}1$ scenario, we derive a general upper bound for the cases in which the inputs are not correlated, which coincides with the quantum value for
n=2 and in some cases for
n=3. Moreover, it is shown that attaining this upper bound self-tests pairs or triples of rank-1 projective measurements, respectively. An analogous upper bound is derived for the value of RACs in the ${2}^{d}\ensuremath{\mapsto}1$ scenario, which is shown to be always attainable using mutually unbiased measurements if the distribution of input strings is unbiased.
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.
A random access code (RAC) encodes an
L-bit string into a
k-bit message,
L>k, so that any requested bit can be recovered with high probability; a quantum RAC (QRAC) uses
k qubits instead. We give a geometric characterization of optimal classical
(L,k)-RACs under average and worst-case decoding criteria. The average criterion is reduced to choosing
2k representatives in
{0,1}L, while the worst-case criterion is reduced to a minimax problem over
2k points in
[0,1]L with a distance-like objective. This framework proves optimality for several parameter families, with many optimal constructions arising from standard infinite families of binary linear codes. It also yields two explicit classical--quantum separations. First, for every
L>1, we construct a
(L,1)-QRAC whose average decoding success probability strictly exceeds the optimal classical value. Second, for the family
(2k−1,k), we prove worst-case optimality of a classical RAC and construct a QRAC with strictly larger worst-case success probability. For the family
(L,L−1), the framework identifies a classical RAC that is average-case optimal and, under a stated conjecture, also worst-case optimal. The same viewpoint further recovers explicit
(L,L−1)-QRACs attaining a previously conjectured upper-bound value.