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International Conference on Mechatronics and Computer Technology Engineering (MCTE)

Discrimination of entangled quantum states

Chufan Zhang

Published Dec 16, 2022• 0 citations
Publisher

Abstract

Quantum state discrimination is one of the most important tasks in quantum information theory and applications. It is the key step of quantum protocols such as teleportation, quantum computing and cryptography. In this paper, we investigate the discrimination of two Bell states, and two GHZ states. Our results can be extended to multipartite entangled states.

DOI
10.1117/12.2661054

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Quantum state discrimination is one of the most important tasks in quantum information theory and applications. It is the key step of quantum protocols such as teleportation, quantum computing and cryptography. In this paper, we investigate the discrimination of two Bell states, and two GHZ states. Our results can be extended to multipartite entangled states.
The variety of multipartite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view, classifications have been introduced. Accordingly, here we derive criteria and demonstrate how to experimentally discriminate an observed state against the ones of certain other classes of multipartite entangled states. Our method, originating in Bell inequalities, adds an important tool for the characterization of multiparty entanglement.
Entanglement-assisted discrimination of orthogonal quantum states exhibiting quantum nonlocality is a frontier topic in quantum information theory. In this paper, we investigate the role of multipartite entanglement and develop resource-efficient LOCC discrimination protocols for nonlocal sets of orthogonal states, including multipartite orthogonal product-state sets and entangled-state sets with different nonlocal features. By incorporating controlled-NOT (CNOT) operations into the discrimination procedure, we construct protocols for genuinely nonlocal GHZ bases in four- and five-qubit systems that require only a single EPR pair. For the same target sets, we compare different entanglement-assisted schemes and identify those with lower entanglement consumption. We further observe that, on average, protocols avoiding teleportation consume fewer resources than teleportation-based approaches. In addition, when higher-partite GHZ-type resources (with n>3n>3n>3) are available among suitable subsystems, they can in some cases reduce the overall entanglement cost. Our results highlight the operational significance of multipartite entanglement and provide practical protocols for the local discrimination of orthogonal state sets exhibiting quantum nonlocality.
State discrimination is one of the key steps in quantum information tasks. This paper introduces the assisted quantum entanglement to achieve this step. For this purpose, the paper introduces some preliminary knowledge to help enter the research topic, such as the matrix rank, Kronecker product, quantum states and the calculation method of Schmidt decomposition and rank. The latter involves the Singular value decomposition in matrix factorization theory. The method of distinguishing orthogonal states in single and many-body systems is also introduced, by using the so-called positive operator-valued measurements. Then the paper proves the fact that single or multipartite system non-orthogonal states are indistinguishable regardless of whether there are auxiliary resources, which may be either separable or entangled states. The paper further illustrates the feasibility of maximum entangled states acting on two-body systems and gives corresponding examples. At the same time, the feasibility of auxiliary resources for smaller entanglement is also investigated.
Discrimination of Bell states plays an important role in a number of quantum computational protocols such as teleportation and secret sharing. However, most of the protocols dealing with Bell state discrimination in the literature either involve performing correlated measurements or destroying the entanglement of the system. Here, we demonstrate an NMR-based experimental realization of a protocol for Bell state discrimination, following a scheme proposed by Gupta et al (quant-ph/0504183v1, 23 April 2005), which does not destroy the Bell state under consideration. Using the proposed protocol, one can deterministically distinguish the Bell states, without performing a measurement using the entangled basis. State discrimination is performed through two independent measurements on one ancilla qubit, which leaves the Bell states unchanged.
Quantum state discrimination underlies various applications in quantum information processing tasks. It essentially describes the distinguishability of quantum systems in different states, and the general process of extracting classical information from quantum systems. It is also useful in quantum information applications, such as the characterization of mutual information in cryptographic protocols, or as a technique for deriving fundamental theorems on quantum foundations. It has deep connections to physical principles such as relativistic causality. Quantum state discrimination traces a long history of several decades, starting with the early attempts to formalize information processing of physical systems such as optical communication with photons. Nevertheless, in most cases, the problems of finding optimal strategies of quantum state discrimination remain unsolved, and related applications are valid in some limited cases only. The present review aims to provide an overview on quantum state discrimination, covering some recent progress, and addressing applications in some selected areas. This review serves to strengthen the link between results in quantum state discrimination and quantum information applications, by showing the ways in which the fundamental results are exploited in applications and vice versa.
Teleporting an unknown qubit state is a paradigmatic quantum information processing task revealing the advantage of quantum communication protocols over their classical counterpart. For a teleportation protocol using a Bell state as quantum channel, the resource has been identified to be the concurrence. However, for mixed multipartite states the lack of computable entanglement measures has made the identification of the quantum resource responsible for this advantage more challenging. Here, by building on previous results showing that localizable concurrence is the necessary resource for controlled quantum teleportation, we show that any teleportation protocol using an arbitrary multipartite state, that includes a Bell measurement, requires a nonvanishing localizable concurrence between two of its parties to perform better than the classical protocol. By first analyzing Greenberger–Horne–Zeilinger (GHZ) channel and GHZ measurement teleportation protocol, in the presence of GHZ-symmetric-preserving noise, we compare different multipartite entanglement measures with the fidelity of teleportation, and we find that the protocol performs better than the classical protocol when all multipartite entanglement measures vanish, except for the localizable concurrence. Finally, we extend our proof to an arbitrary teleportation protocol with an arbitrary multipartite entangled channel.