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arXiv:2309.00869 · Physical Review A

Nondestructive discrimination of Bell states between distant parties

Bohdan Bilash, Youngrong Lim, Hyukjoon Kwon, Yosep Kim, Hyang‐Tag Lim, Wooyeong Song, Yong‐Su Kim

Published Oct 9, 2024• 1 citation
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Abstract

Identifying Bell states without destroying them is frequently dealt with in quantum technologies nowadays, such as in quantum communication and quantum computing. In practice, quantum entangled states are often distributed among distant parties, and it might be required to determine them separately at each location, without inline communication between parties. We present a scheme for discriminating an arbitrary Bell state distributed to two distant parties without destroying them. The scheme requires two entangled states that are preshared between the parties and we show that, without these ancillary resources, the probability of nondestructively discriminating the Bell state is bounded by 1/4, which is the same as random guessing. Furthermore, we demonstrate a proof-of-principle experiment through an IonQ quantum computer that our scheme can surpass classical bounds when applied to a practical quantum processor.

DOI
10.1103/physreva.110.042407

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Identifying Bell states without destroying them is frequently dealt with in quantum technologies nowadays, such as in quantum communication and quantum computing. In practice, quantum entangled states are often distributed among distant parties, and it might be required to determine them separately at each location, without inline communication between parties. We present a scheme for discriminating an arbitrary Bell state distributed to two distant parties without destroying them. The scheme requires two entangled states that are preshared between the parties and we show that, without these ancillary resources, the probability of nondestructively discriminating the Bell state is bounded by 1/4, which is the same as random guessing. Furthermore, we demonstrate a proof-of-principle experiment through an IonQ quantum computer that our scheme can surpass classical bounds when applied to a practical quantum processor.
In this paper, the following scenario is considered: there are two qubits possessed by two parties at different locations. Qubits have been prepared in one of a maximum of four, mutually-orthogonal, entangled states and the parties wish to distinguish between the states by using local operations and classical communication. Although in general it is not possible to distinguish between four arbitrary states, the parties can spend some preshared entanglement to achieve perfect discrimination between four qubit states and can also preserve the entanglement of the states after discrimination. This is shown by employing the theory of majorization and the connections between entanglement transformations and state discrimination protocols.
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Entangled states can help in quantum-state discrimination by local operations and classical communication (LOCC). For example, a Bell state is necessary (and sufficient) to perfectly discriminate a set of either three or four Bell states by LOCC. In this paper, we consider the task of LOCC discrimination of the states of noisy Bell ensembles, where a given ensemble consists of the states obtained by mixing the Bell states with an arbitrary two-qubit state with nonzero probabilities. It is proved that a Bell state is required for optimal discrimination by LOCC, even though the ensembles do not contain, in general, any maximally entangled state and, in specific instances, any entangled state.