Abstract A random access code (RAC), corresponding to a communication primitive with various applications in quantum information theory, is an instance of a preparation-and-measurement scenario. In this work, we consider (n, d)-RACs constituting an n-length string, constructed from a d size set of letters, and send an encoding of the string in a single d-level physical system and present their quantum advantages. We first characterize optimal classical RACs and prove that a known classical strategy, called majority-encoding-identity-decoding, is optimal. We then construct a quantum protocol by exploiting only two incompatible measurements (the minimal requirement) and show the advantages beyond the classical one. We also discuss the generality of our results and whether quantum advantages are valid for all types of ( n , d ) ↦ 1 RACs.
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.
Random access code (RAC), a primitive for many information processing protocols, enables one party to encode a n -bit string into one bit of message such that another party can retrieve partial information of that string. We introduce the multiparty version of RAC in which the n -bit string is distributed among many parties. For this task, we consider two distinct quantum communication scenarios: one allows shared quantum entanglement among the parties with classical communication, and the other allows communication through a quantum channel. We present several multiparty quantum RAC protocols that outclass its classical counterpart in both the aforementioned scenarios.
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 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) 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.
Quantum mechanics enables information-processing advantages even at the level of a single qubit. A paradigmatic example is the 2$\to$1 random access code (RAC), where a qubit outperforms a classical bit in retrieving encoded information. In the standard form, however, this quantum advantage is restricted to a single receiver, since decoding measurements inevitably destroy the encoded information. Contrary to this, we address how long the information encoded in a single qubit remains accessible even after multiple decoding, each with a quantum advantage. Introducing preparation distinguishability as an operational resource associated with the sender, we show that its interplay with measurement incompatibility on the receiver's side can mitigate measurement-induced disturbance, thereby enabling an arbitrarily long sequence of receivers to each retain a quantum advantage. Our results show that, even under repeated measurements, the information encoded in a qubit need not be entirely exhausted, revealing a stronger communication feature than previously recognised.