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New Journal of Physics

Separable states improve protocols with finite randomness

Tan Kok Chuan Bobby, Tomasz Paterek

Published Sep 30, 2014• 13 citations
Publisher

Abstract

It is known from Bellʼs theorem that quantum predictions for some entangled states cannot be mimicked using local hidden variable (LHV) models. From a computer science perspective, LHV models may be interpreted as classical computers operating on a potentially infinite number of correlated bits originating from a common source. As such, Bell inequality violations achieved through entangled states are able to characterize the quantum advantage of certain tasks, so long as the task itself imposes no restriction on the availability of correlated bits. However, if the number of shared bits is limited, additional constraints are placed on the possible LHV models, and separable, i.e. disentangled states may become a useful resource. Bell violations are therefore no longer necessary to achieve a quantum advantage. Here we show that, in particular, separable states improve the so-called random access codes, which is a class of communication problem wherein one party tries to read a portion of the data held by another distant party in the presence of finite shared randomness and limited classical communication. We also show how the bias of classical bits can be used to avoid wrong answers in order to achieve the optimal classical protocol and how the advantage of quantum protocols is linked to quantum discord.

DOI
10.1088/1367-2630/16/9/093063

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It is known from Bellʼs theorem that quantum predictions for some entangled states cannot be mimicked using local hidden variable (LHV) models. From a computer science perspective, LHV models may be interpreted as classical computers operating on a potentially infinite number of correlated bits originating from a common source. As such, Bell inequality violations achieved through entangled states are able to characterize the quantum advantage of certain tasks, so long as the task itself imposes no restriction on the availability of correlated bits. However, if the number of shared bits is limited, additional constraints are placed on the possible LHV models, and separable, i.e. disentangled states may become a useful resource. Bell violations are therefore no longer necessary to achieve a quantum advantage. Here we show that, in particular, separable states improve the so-called random access codes, which is a class of communication problem wherein one party tries to read a portion of the data held by another distant party in the presence of finite shared randomness and limited classical communication. We also show how the bias of classical bits can be used to avoid wrong answers in order to achieve the optimal classical protocol and how the advantage of quantum protocols is linked to quantum discord.
It is known from Bell's theorem that quantum predictions for some entangled states cannot be mimicked using local hidden variable (LHV) models. From a computer science perspective, LHV models may be interpreted as classical computers operating on a potentially infinite number of correlated bits originating from a common source. As such, Bell inequality violations achieved through entangled states are able to characterise the quantum advantage of certain tasks, so long as the task itself imposes no restriction on the availability of correlated bits. However, if the number of shared bits is limited, additional constraints are placed on the possible LHV models and separable, i.e. disentangled, states may become a useful resource. Bell violations are therefore no longer necessary to achieve a quantum advantage. Here we show that in particular, separable states may improve the so-called random access codes, which is a class of communication problems where one party tries to read a portion of the data held by another distant party in presence of finite shared randomness and limited classical communication. We also show how the bias of classical bits can be used to avoid wrong answers in order to achieve the optimal classical protocol and how the advantage of quantum protocols is linked to quantum discord.
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.
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a resource called shared randomness, quantum systems provide an advantage over their classical counterpart. Precisely, we show that appropriate albeit fixed measurements on a shared two-qubit state can generate correlations which cannot be obtained from any possible state on two classical bits. In a resource theoretic set-up, this feature of quantum systems can be interpreted as an advantage in winning a two players co-operative game, which we call the `non-monopolize social subsidy' game. It turns out that the quantum states leading to the desired advantage must possess non-classicality in the form of quantum discord. On the other hand, while distributing such sources of shared randomness between two parties via noisy channels, quantum channels with zero capacity as well as with classical capacity strictly less than unity perform more efficiently than the perfect classical channel. Protocols presented here are noise-robust and hence should be realizable with state-of-the-art quantum devices.
Entanglement is known to boost the efficiency of classical communication. In distributed computation, for instance, exploiting entanglement can reduce the number of communicated bits or increase the probability to obtain a correct answer. Entanglement-assisted classical communication protocols usually consist of two successive rounds: first, a Bell test round, in which the parties measure their local shares of the entangled state, and then a communication round, where they exchange classical messages. Here, we go beyond this standard approach and investigate adaptive uses of entanglement: we allow the receiver to wait for the arrival of the sender's message before measuring their share of the entangled state. We first show that such adaptive protocols improve the success probability in random access codes. Second, we show that once adaptive measurements are used, an entanglement-assisted bit becomes a strictly stronger resource than a qubit in prepare-and-measure scenarios. We briefly discuss the extension of these ideas to scenarios involving quantum communication and we identify resource inequalities.
Quantum entanglement plays a central role in many quantum communication protocols. It allows distant particles to share correlations beyond the limits of classical interactions. Entanglement is essential for superdense coding, quantum teleportation, and secure cryptographic key distribution in quantum communication. It is also a pillar for developing quantum networks, where the management and distribution of entanglement are crucial for connecting distant nodes. Although perfect entanglement is a sought-after ideal, experimental imperatives, including entanglement distribution over long distances, often limit the quality of entangled states. An important question is whether weaker entanglement still offers advantages. First, we study more general tasks than dense coding to show that simpler measurements, combined with entanglement, allow advantageous and sometimes even optimal qubit communication protocols to be obtained. We also demonstrate that simple measurements can generate quantum correlations that cannot be modelled by two classical communication bits and can constitute an optimal protocol with quantum resources. We implement a novel Bell-type inequality tailored for certifying full network non-locality (FNN) to develop certification methods guaranteeing security on an entanglement-based network. Our experiment uses two pairs of polarised entangled photons in a network configuration with three nodes, briefly referred to as a bilocal network scenario. Finally, we show that weakly entangled states can improve communication over a qubit channel using only separate (local) measurements on isotropic non-steerable two-qubit states, without interference, of individual photons, across two communication tasks: secret sharing and its stochastic variant.
We show how nonclassical correlations in local bipartite states can act as a resource for quantum information processing. Considering the task of quantum random access codes (RACs) through separable Bell-diagonal states, we demonstrate the advantage of superunsteerability over classical protocols assisted with two bits of shared randomness. We propose a measure of superunsteerability which quantifies nonclassicality beyond quantum steering and obtain its analytical expression for Bell-diagonal states in the context of two- and three-setting steering scenarios that are directly related to the quantum $2\ensuremath{\rightarrow}1$ and $3\ensuremath{\rightarrow}1$ RAC protocols, respectively. The maximal values of our quantifier yield the optimal quantum efficiency for both of the above protocols, thus showing that superunsteerability provides a precise characterization of the nonclassical resource for implementing RACs with separable Bell-diagonal class of states.