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arXiv:2605.13350

Random Access Code protocols: Quantum advantage related to intraparticle entanglement-based contextuality

Nilaj Saha, Sumit Mukherjee, Dipankar Home

quant-phmath-phSubmitted May 13, 2026• Announced May 14, 2026• 0 citations• Revised May 16, 2026 (v2)
v1 · May 13, 2026v2 · May 16, 2026v3 · Jun 30, 2026
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Abstract

The quantum enhancement of success probability in the Random Access Code (RAC) protocols remains unexplored from two important perspectives. First, the use of entanglement between two co-measurable degrees of freedom of a single particle (intraparticle entanglement) in achieving such quantum enhancement has not been investigated. Second, no explicit quantitative correspondence has been established between the predicted/observed quantum advantage and the underlying quantum resource responsible for it. In this work, we address both these aspects simultaneously by harnessing a single-particle resource. For this purpose, the RAC protocol is formulated in terms of intraparticle entanglement between, for instance, spin/polarization and path degrees of freedom of a single particle. Within this framework, a relevant Bell-type inequality, derived from the assumption of noncontextuality for single particle path-spin measurements, is used. Based on these ingredients, the formulated analysis reveals that the magnitude of quantum-mechanical violation of such Bell-type 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 of a quantum $n \mapsto 1$ RAC protocol corresponds to the maximal quantum violation of the relevant Bell-type inequality. This correspondence is empirically testable using a readily implementable single-particle interferometric setup requiring coherence preservation only for a single particle.

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The quantum enhancement of success probability in the Random Access Code (RAC) protocols remains unexplored from two important perspectives. First, the use of entanglement between two co-measurable degrees of freedom of a single particle (intraparticle entanglement) in achieving such quantum enhancement has not been investigated. Second, no explicit quantitative correspondence has been established between the predicted/observed quantum advantage and the underlying quantum resource responsible for it. In this work, we address both these aspects simultaneously by harnessing a single-particle resource. For this purpose, the RAC protocol is formulated in terms of intraparticle entanglement between, for instance, spin/polarization and path degrees of freedom of a single particle. Within this framework, a relevant Bell-type inequality, derived from the assumption of noncontextuality for single particle path-spin measurements, is used. Based on these ingredients, the formulated analysis reveals that the magnitude of quantum-mechanical violation of such Bell-type 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 of a quantum n↦1n \mapsto 1n↦1 RAC protocol corresponds to the maximal quantum violation of the relevant Bell-type inequality. This correspondence is empirically testable using a readily implementable single-particle interferometric setup requiring coherence preservation only for a single particle.
Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the entanglement-assisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific cases where one outperforms the other. In this article, we study a family of $3\ensuremath{\rightarrow}1$ distributed RACs [J. Bowles, N. Brunner, and M. Paw\l{}owski, Phys. Rev. A 92, 022351 (2015)] and present its general construction of both the QRAC and the EARAC. We demonstrate that, depending on the function of inputs that is sought, if QRAC achieves the maximal success probability then EARAC fails to do so and vice versa. Moreover, a tripartite Bell-type inequality associated with the EARAC variants reveals the genuine multipartite nonlocality exhibited by our protocol. We conclude with an experimental realization of the $3\ensuremath{\rightarrow}1$ distributed QRAC that achieves higher success probabilities than the maximum possible with EARACs for a number of tasks.
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.
The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations, we demonstrate monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.
We develop a family of semi-device-independent (SDI) entanglement-assisted prepare-measure (PM) communication games involving two parties, within the n→ln\rightarrow ln→l random-access code (RAC) framework where the sender Alice holds a n-bit string and communicates l<nl<nl<n bits or qubits to the receiver Bob. In contrast to the standard quantum PMRAC, here the parties share a prior entanglement, and Alice applies quantum operations on her sub-system to encode her inputs and sends to Bob. We first consider the 4→l4\rightarrow l4→l entanglement-assisted PMRAC with l=1l=1l=1 and 222 and derive the optimal quantum success probabilities using an elegant analytical technique. We demonstrate quantum supremacy over both classical RACs and conventional quantum PMRACs. Moreover, we exhibit that the optimal quantum advantage allows one to certify Alice's unitary operations. We then derive an upper bound on the quantum success probabilities for 5→l5\rightarrow l5→l entanglement-assisted PMRAC with l=1,2l=1,2l=1,2 and 333. Further, we extend the demonstration of quantum advantage for n→n−2n\rightarrow n-2n→n−2 case where n is arbitrary.
Abstract We develop a family of semi-device-independent (SDI) entanglement-assisted prepare-measure (PM) communication games involving two parties, within the n → l random-access code (RAC) framework where the sender Alice holds a n -bit string and communicates l < n bits or qubits to the receiver Bob. In contrast to the standard quantum PMRAC, here the parties share a prior entanglement, and Alice applies quantum operations on her sub-system to encode her inputs and sends to Bob. We first consider the 4 → l entanglement-assisted PMRAC with l = 1 and 2 and derive the optimal quantum success probabilities using an elegant analytical technique. We demonstrate quantum supremacy over both classical RACs and conventional quantum PMRACs. Moreover, we exhibit that the optimal quantum advantage allows one to certify Alice’s unitary operations. We then derive an upper bound on the quantum success probabilities for 5 → l entanglement-assisted PMRAC with l = 1 , 2 and 3 . Further, we extend the demonstration of quantum advantage for n → n − 2 case where n is arbitrary.
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.