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Physical Review A

Experimental generation of entanglement-assisted quantum random access code

Xiao-Run Wang, Luyan Wu, Chenxi Liu, Tongjun Liu, Jian Li, Qin Wang

Published May 9, 2019• 8 citations
Publisher

Abstract

$n\ensuremath{\rightarrow}m$ 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.

DOI
10.1103/physreva.99.052313

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n\ensuremath→mn\ensuremath{\rightarrow}mn\ensuremath→m random access code (RAC) is an information task to encode an nnn-bit random message into a shorter mmm-bit string. Resulting from the compression loss from nnn to mmm 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→12\ensuremath{\rightarrow}12\ensuremath→1 and 3\ensuremath→13\ensuremath{\rightarrow}13\ensuremath→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)0.8491(41)0.8491(41) for a 2\ensuremath→12\ensuremath{\rightarrow}12\ensuremath→1 EARAC and 0.7724(34)0.7724(34)0.7724(34) for a 3\ensuremath→13\ensuremath{\rightarrow}13\ensuremath→1 EARAC, exceeding the classical counterparts, respectively. Moreover, through the existing experimental data, success probabilities for nnn varying from 4 to 10 (m=1m=1m=1) are estimated.
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.
An n↦pm random access code (RAC) is an encoding of n bits into m bits such that any initial bit can be recovered with probability at least p , while in a quantum RAC (QRAC), the n bits are encoded into m qubits. Since its proposal, the idea of RACs was generalized in many different ways, e.g. allowing the use of shared entanglement (called entanglement-assisted random access code, or simply EARAC) or recovering multiple bits instead of one. In this paper we generalize the idea of RACs to recovering the value of a given Boolean function f on any subset of fixed size of the initial bits, which we call f -random access codes. We study and give protocols for f -random access codes with classical ( f -RAC) and quantum ( f -QRAC) encoding, together with many different resources, e.g. private or shared randomness, shared entanglement ( f -EARAC) and Popescu-Rohrlich boxes ( f -PRRAC). The success probability of our protocols is characterized by the noise stability of the Boolean function f . Moreover, we give an upper bound on the success probability of any f -QRAC with shared randomness that matches its success probability up to a multiplicative constant (and f -RACs by extension), meaning that quantum protocols can only achieve a limited advantage over their classical counterparts.
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.
Entanglement-assisted random access codes (EARACs) compress a large amount of bits, such that any chosen one of them can be recovered with a large probability of success. They have been used for information theoretic treatments of semi-device-independent randomness certification and other communication complexity problems. For high-dimensional problems, the access request distribution can be used to obtain better performance, which until now could only be achieved through numerical methods. This paper makes an analytical account of access request distribution for arbitrary input sizes. We introduce entanglement-assisted almost-random access codes (EAARACs), which maximize the average probability of access under an arbitrary distribution of requests, thus refining EARACs and generalizing the methods used in the study of low-dimensional communication complexity problems. We analytically find the optimal probability of success for EAARACs under arbitrary request distributions and provide an illustrative numerical example.
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) encodes an LLL-bit string into a kkk-bit message, L>kL>kL>k, so that any requested bit can be recovered with high probability; a quantum RAC (QRAC) uses kkk qubits instead. We give a geometric characterization of optimal classical (L,k)(L,k)(L,k)-RACs under average and worst-case decoding criteria. The average criterion is reduced to choosing 2k2^k2k representatives in {0,1}L\{0,1\}^L{0,1}L, while the worst-case criterion is reduced to a minimax problem over 2k2^k2k points in [0,1]L[0,1]^L[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>1L>1L>1, we construct a (L,1)(L,1)(L,1)-QRAC whose average decoding success probability strictly exceeds the optimal classical value. Second, for the family (2k−1,k)(2^k-1,k)(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)(L,L-1)(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)(L,L-1)(L,L−1)-QRACs attaining a previously conjectured upper-bound value.