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.
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.
We present a hitherto unexplored semi-device-independent (SDI) self-testing protocol designed to certify unitary operations within a variant of prepare-measure framework. We consider a communication game which we refer to as a variant of
3-bit prepare-measure random access code (PMRAC) involving two parties, Alice and Bob, who share a prior two-qubit quantum state. Alice encodes her message by applying unitary operations on her subsystem and sends it to Bob. To decode the message, Bob performs a measurement on the whole system. We demonstrate that the optimal quantum advantage of the variant of
3-bit PMRAC over the classical bound enables the self-testing of Alice's unitary operations and Bob's measurements. The derivation of the optimal quantum success probability is fully analytical. The approach is so elegant that it can be generalized for any arbitrary
n-bit PMRAC and may also be extended to other prepare-measure communication games.
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.
$n\ensuremath{\rightarrow}m$ random access code (RAC) is an information task to encode an
n-bit random message into a shorter
m-bit string. Resulting from the compression loss from
n to
m bits, there exists success probabilities for the string receiver to recover any bits of the initial message. It has been shown that success probabilities of bit recovery can be enhanced by employing quantum resources. Here we present experimental realizations of $2\ensuremath{\rightarrow}1$ and $3\ensuremath{\rightarrow}1$ distributed entanglement-assisted random access codes (EARACs) with a two-photon entangled source. The average success probabilities obtained in our experiment are
0.8491(41) for a $2\ensuremath{\rightarrow}1$ EARAC and
0.7724(34) for a $3\ensuremath{\rightarrow}1$ EARAC, exceeding the classical counterparts, respectively. Moreover, through the existing experimental data, success probabilities for
n varying from 4 to 10 (
m=1) are estimated.
Abstract We consider two classes of quantum generalisations of random access code (RAC) and study the bounds for probabilities of success for such tasks. It provides a useful framework for the study of certain information processing tasks with constrained resources. The first class is based on a RAC with quantum inputs and output known as the no-signalling quantum RAC (NS-QRAC) box (Grudka et al 2015 Phys. Rev. A 92 052312), where unbounded entanglement and constrained classical communication are allowed. We show that it can be seen as quantum teleportation with constrained classical communication and provide a lower quantum bound for the success probability. We consider two modifications to the NS-QRAC scenario: the first, where unbounded entanglement and constrained quantum communication is allowed and the second, where bounded entanglement and unconstrained classical communication is allowed. We find a monogamy relation for the transmission fidelities, which—in contrast to the usual communication schemes—involves multiple senders and a single receiver. We provide an upper bounds for the latter and a lower one for the former. The second class is based on a RAC with a quantum channel and shared entanglement (Tavakoli et al 2021 PRX Quantum 2 040357). We study the set of tasks where two inputs made of two digits of d-base are encoded over a qudit and a maximally entangled state. We show that such tasks can be seen as quantum dense-coding with constrained quantum communication and explicit protocols, which give lower quantum bounds for the tasks’ efficiency, in dimensions d = 2 , 3 , 4 . The employed encoding utilises Gray codes.
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.