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

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.

Sequential state discrimination of coherent states

“…This condition is an important constraint on sequential state discrimination. In this process, a receiver-Bob, should use non-optimal unambiguous discrimination on Alice’s quantum state 28 , 30 . When Bob obtains a conclusive result, he sends his post-measurement state to another receiver Charlie.…”

“…If the two prior probabilities q 1 and q 2 are not equal, it is difficult to analytically determine the optimally success probabilty. However, When Bob and Charlie discriminate only one of the two pure states of Alice, the success probability is expressed by 30 …”

“…The dashed line shows the optimal success probability when Bob and Charlie discriminate only one of two coherent states of Alice. In that case, the optimal success probability for different prior probabilities is expressed by 27 , 28 , 30 …”

“…The derivation can be found in the result of M. Namkung et al . 28 , 30 . Since exists on the tangential point between a plane and a surface , can be obtained from the following condition as: …”

“…Also, M. Hillery and J. Mimih 29 produced the success probability of sequential state discrimination for N symmetric pure states. In 2018, the structure of sequential state discrimination for arbitrary N pure states with general prior probability was investigated 30 . In fact, sequential state discrimination provides the answer to the question “Can we obtain information about a before-measurement quantum state, from a post-measurement state?” 31 .…”