Analysis of Optimal Sequential State Discrimination for Linearly Independent Pure Quantum States

Min Namkung,Younghun Kwon

doi:10.1038/s41598-018-24575-w

Abstract

Recently, J. A. Bergou et al. proposed sequential state discrimination as a new quantum state discrimination scheme. In the scheme, by the successful sequential discrimination of a qubit state, receivers Bob and Charlie can share the information of the qubit prepared by a sender Alice. A merit of the scheme is that a quantum channel is established between Bob and Charlie, but a classical communication is not allowed. In this report, we present a method for extending the original sequential state discrimination of two qubit states to a scheme of N linearly independent pure quantum states. Specifically, we obtain the conditions for the sequential state discrimination of N = 3 pure quantum states. We can analytically provide conditions when there is a special symmetry among N = 3 linearly independent pure quantum states. Additionally, we show that the scenario proposed in this study can be applied to quantum key distribution. Furthermore, we show that the sequential state discrimination of three qutrit states performs better than the strategy of probabilistic quantum cloning.

Highlights

Bergou et al.[21] proposed sequential state discrimination(SSD), a new strategy for quantum state discrimination, that contains multi-receivers
We study the structure of the convex set of linearly independent N pure states for sequential state discrimination, mainly dealing with the convex set of N = 331–33
We need to formulate the sequential state discrimination for N linearly independent pure quantum states, which can be considered as a optimization problem based on the conditions of POVM of receivers Bob and Charlie

Summary

Introduction

Bergou et al.[21] proposed sequential state discrimination(SSD), a new strategy for quantum state discrimination, that contains multi-receivers. Charlie performs an optimal unambiguous discrimination on Bob’s post-measurement state. Because Bob performs an nonoptimal unambiguous discrimination, the real vector corresponding to Bob’s POVM exists inside the convex set. Charlie performs the optimal unambiguous discrimination, and the real vector corresponding to Charlie’s POVM exists on the surface of the convex set. When Bob uses an optimal unambiguous discrimination, the Charlie’s convex set element is only a zero vector. When Bob performs a nonoptimal unambiguous discrimination, the Charlie’s convex set contains other elements, except for the zero vector. This implies that Charlie can obtain some information from the post-measurement states of Bob

Methods

Results

Conclusion