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arXiv:2102.02709 · Physical Review A

Semi-device-independent certification of entanglement in superdense coding

George Moreno, Ranieri Nery, Carlos de Gois, Rafael Rabelo, Rafael Chaves

Published Feb 25, 2021• 25 citations
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Abstract

Superdense coding is a paradigmatic protocol in quantum information science, employing a quantum communication channel to send classical information more efficiently. As we show here, it can be understood as a particular case of a prepare and measure experiment, a scenario that has attracted growing attention for its fundamental and practical applications. Formulating superdense coding as a prepare and measure scenario allows us to provide a semi-device-independent witness of entanglement that significantly improves over previous tests. Furthermore, we also show how to adapt our results into self-testing of maximally entangled states and also provide a semidefinite program formulation allowing one to efficiently optimize, for any shared quantum state, the probability of success in the superdense coding protocol.

DOI
10.1103/physreva.103.022426

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Superdense coding is a paradigmatic protocol in quantum information science, employing a quantum communication channel to send classical information more efficiently. As we show here, it can be understood as a particular case of a prepare and measure experiment, a scenario that has attracted growing attention for its fundamental and practical applications. Formulating superdense coding as a prepare and measure scenario allows us to provide a semi-device-independent witness of entanglement that significantly improves over previous tests. Furthermore, we also show how to adapt our results into self-testing of maximally entangled states and also provide a semidefinite program formulation allowing one to efficiently optimize, for any shared quantum state, the probability of success in the superdense coding protocol.
An absolutely entangled set (AES) is a collection of states for which at least one member remains entangled under any choice of global unitary transformation. We develop a semi-device-independent framework for certifying this property from dimensionally bounded prepare-and-measure correlations. A witness value above the maximum attainable with separable preparations of a given dimension rules out every non-AES realization. To upperbound this limit, we construct a semidefinite-programming (SDP) hierarchy tailored to separable preparations. For a two-qubit random-access-code witness, the SDP upper bound and the heuristic lower bound coincide to the reported precision, yielding a concrete AES certification. We also formulate a general construction of witnesses for extended preparation sets containing target pure-state AESs. Examples based on equiangular tight frames, a minimal AES, and mutually unbiased bases further illustrate the scope of the method. In summary, our results establish a systematic and experimentally feasible approach to the certification of AESs in semi-device-independent quantum information protocols.
Recently the quantum information science community devoted a lot of attention to the theoretical and practical aspects of generalized measurements, the formalism of all possible quantum operations leading to acquisition of classical information. On the other hand, due to imperfections present in quantum devices, and limited thrust to them, a trend of formulating quantum information tasks in a semi-device-independent manner emerged. In this Rapid Communication we use the concept of quantum random access codes to construct a protocol able to certify the presence of the generalized measurements in a semi-device-independent way without employing quantum entanglement. We use semidefinite programming methods to show robustness of the protocol and characterize its statistical properties. We conclude that it allows for experimental realizations using technology currently available in laboratories.
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 333-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 333-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 nnn-bit PMRAC and may also be extended to other prepare-measure communication games.
A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum correlations in prepare-and-measure scenarios. Inspired by the developments in Bell nonlocality and device-independent information processing, this line of research aims to characterize the possibilities and limits of quantum systems for communication, in particular to precisely capture the advantage they offer over classical systems. In addition to fundamental insights, these ideas also underpin the concept of semi-device-independent quantum information processing. Exploring trade-offs between security, performance and ease-of-implementation, this approach opens promising directions for novel quantum information processing technologies and devices. A number of protocols and proof-of-principle demonstrations have been reported in recent years, in particular for quantum randomness certification and key distribution. Here, we provide a comprehensive introduction to quantum prepare-and-measure correlations and semi-device independent applications.
The ability of quantum devices to preserve or distribute entanglement is essential in employing quantum technologies. Such ability is described and guaranteed by the non-entanglement-breaking (nonEB) feature of participating quantum channels. For quantum information applications relying on entanglement, the certification of the nonEB feature is indispensable in designing, testing, and benchmarking quantum devices. Here, we develop a simple and direct approach for the certification of nonEB quantum channels. By utilizing the prepare-and-measure test, we derive a necessary and sufficient condition for witnessing the nonEB channels, which is applicable in almost all experimental scenarios. The approach not only unifies and simplifies existing methods in the standard scenario and the measurement-device-independent scenario, but also furthers the nonEB channel certification in the semi-device-independent scenario.
We investigate the correlations that can arise between Alice and Bob in prepare-and-measure communication scenarios where the source (Alice) and the measurement device (Bob) can share prior entanglement.The paradigmatic example of such a scenario is the quantum dense-coding protocol, where the communication capacity of a qudit can be doubled if a two-qudit entangled state is shared between Alice and Bob.We provide examples of correlations that actually require more general protocols based on higher-dimensional entangled states.This motivates us to investigate the set of correlations that can be obtained from communicating either a classical or a quantum d-dimensional system in the presence of an unlimited amount of entanglement.We show how such correlations can be characterized by a hierarchy of semidefinite programming relaxations by reducing the problem to a noncommutative polynomial optimization problem.We also introduce an alternative relaxation hierarchy based on the notion of informationally restricted quantum correlations, which, though it represents a strict (nonconverging) relaxation scheme, is less computationally demanding.As an application, we introduce device-independent tests of the dimension of classical and quantum systems that, in contrast to previous results, do not make the implicit assumption that Alice and Bob share no entanglement.We also establish several relations between communication with and without entanglement as resources for creating correlations.