Discrimination Among Quantum States

Shengyu Zhang, Mingsheng Ying

We introduce a notion of set discrimination, which is an interesting extension of quantum state discrimination. A state is secretly chosen from a number of quantum states, which are partitioned into some disjoint sets. A set discrimination is required to identify which set the given state belongs to. Several essential problems are addressed in this paper, including the condition of perfect set discrimination, unambiguous set discrimination, and in the latter case, the efficiency of the discrimination. This generalizes some important results on quantum state discrimination in the literature. A combination of state and set discrimination and the efficiency are also studied.

Ulrike Futschik

Min Namkung, Younghun Kwon

Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.

真弓 八野, Fumiaki Shibata

Michael R. Frey, Jaclyn D. Szymonifka

A Gaussian statistic, or discriminator, is proposed for conclusively discriminating between two pure quantum states. The discriminator is based on registrations from a limit of an increasing number of weak measurements on a single system. The average error of the discriminator is near that of the optimal conclusive Helstrom discriminator and, in fact, the Gaussian discriminator is the limit point of a class of conclusive discriminators which includes the Helstrom discriminator. The Gaussian discriminator always leaves some post-measurement state (PMS) separation; by contrast, the PMS separation with the Helstrom discriminator is always zero. Simple, closed-form expressions are given for the distribution and error performance of the Gaussian discriminator.

Chuanwei Zhang, Chuan-Feng Li, Guang-Can Guo