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arXiv:1504.08105 · Physical Review Letters

Quantum Random Access Codes Using Single d -Level Systems

Armin Tavakoli, Alley Hameedi, Breno Marques, Mohamed Bourennane

Published Apr 29, 2015• 128 citations
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Abstract

Random access codes (RACs) are used by a party to, with limited communication, access an arbitrary subset of information held by another party. Quantum resources are known to enable RACs that break classical limitations. Here, we study quantum and classical RACs with high-level communication. We derive average performances of classical RACs and present families of high-level quantum RACs. Our results show that high-level quantum systems can significantly increase the advantage of quantum RACs over their classical counterparts. We demonstrate our findings in an experimental realization of a quantum RAC with four-level communication.

DOI
10.1103/physrevlett.114.170502

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Random access codes (RACs) are used by a party to, with limited communication, access an arbitrary subset of information held by another party. Quantum resources are known to enable RACs that break classical limitations. Here, we study quantum and classical RACs with high-level communication. We derive average performances of classical RACs and present families of high-level quantum RACs. Our results show that high-level quantum systems can significantly increase the advantage of quantum RACs over their classical counterparts. We demonstrate our findings in an experimental realization of a quantum RAC with four-level communication.
We investigate the task of ddd-level random access codes (ddd-RACs) and consider the possibility of encoding classical strings of ddd-level symbols (dits) into a quantum system of dimension d′d'd′ strictly less than ddd. We show that the average success probability of recovering one (randomly chosen) dit from the encoded string can be larger than that obtained in the best classical protocol for the task. Our result is intriguing as we know from Holevo's theorem (and more recently from Frenkel-Weiner's result [Commun. Math. Phys. 340, 563 (2015)]) that there exist communication scenarios wherein quantum resources prove to be of no advantage over classical resources. A distinguishing feature of our protocol is that it establishes a stronger quantum advantage in contrast to the existing quantum ddd-RACs where ddd-level quantum systems are shown to be advantageous over their classical ddd-level counterparts.
Quantum information is a highly interesting and fast emerging field that involves processing information encoded into quantum systems and their subsequent use in various information tasks. The use of quantum resources such as superposition and entanglement have shown to enhance information processing capabilities beyond classical means in a number of communication, information and computation tasks. In this thesis, we have used single photons to study the advantage of d-level quantum systems (qudits) for a communication task commonly known as random access codes (RACs). A successful experimental demonstration of quantum random access codes (QRACs) with four dimensions is realized to demonstrate that the higher dimensional QRACs not only outperform the classical RACs but also provide an advantage over their quantum bit (qubit) counterparts. QRACs are also studied in regards to two specific applications: certification of true randomness and for testing the non-classicality of quantum systems. A method for increased certification of generated randomness is realized for the former and a successful experimental demonstration of a test of non-classicality with arbitrarily low detection efficiency is provided for the latter. This is followed by an implementation of a QRAC in a one-path communication network consisting of preparation, transformation and measurement devices. We have shown that the distributed QRAC provides optimal success probabilities for a number of tasks. Moreover, a novel quantum protocol for the solution to the problem of dining cryptographers and anonymous veto voting is also presented. This single photon transmission based protocol provides an efficient solution, which is experimentally demonstrated for a 3-party description. Lastly, Nitrogen-Vacancy (NV) center in diamond is studied as a potential resource for single photon emission and two methods to enhance the photon collection efficiency are successfully explored. Due to this enhancement, single photons from an NV center may also be used in similar single quantum system based communication experiments.
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 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.
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.
An (n,m,p)(n,m,p)(n,m,p) random access code (RAC) makes it possible to encode nnn bits in an mmm-bit message in such a way that a receiver of the message can guess any of the original nnn bits with probability ppp greater than 12\frac{1}{2}21​. In quantum RACs (QRACs), one transmits nnn qubits. The full set of primitive entanglement-assisted random access codes (EARACs) is introduced, in which parties are allowed to share a two-qubit singlet. It is shown that via a concatenation of these, one can build for any nnn an (n,1,p)(n,1,p)(n,1,p) EARAC. QRACs for n>3n>3n>3 exist only if parties also share classical randomness. We show that EARACs outperform the best of known QRACs not only in the success probabilities but also in the amount of communication needed in the preparatory stage of the protocol. Upper bounds on the performance of EARACs are given and shown to limit also QRACs.