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

Scientific Reports. 2018. Vol. 8. No. 1. P. 6515-1–6515-13.

Min Namkung, Younghun K.

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.

Keywords: quantum information theory, Квантовая теория информации