Multicopy quantum state discrimination

In this paper, we study the problem of multicopy quantum two-state discrimination. By exploring the quantum hypothesis testing, i.e., the probabilistic quantum cloning, we derive the upper bounds of the minimal error discrimination (MED) and the optimal unambiguous discrimination (OUD), which coincides with the Helstrom theorem and the JS limit. Furthermore, when prior probabilities are unknown, we derive the minimax MED and the minimax OUD. Based on the optimal N→M probabilistic quantum cloning, we present the optimal strategies of collective measurements of the MED and the OUD. When the number of the copies is infinite, regardless of whether prior probabilities are known or not, the success probabilities of the MED and the OUD go to 100%, in accordance with the quantum measurement hypothesis that unknown quantum state can be determined if and only if infinite identical quantum state copies are given.

In this paper, we study the problem of multicopy quantum two-state discrimination. By exploring the quantum hypothesis testing, i.e., the probabilisfic quantum cloning, we derive the upper bounds of the minimal error discrimination （MED） and the optimal unambiguous discrimination （OUD）, which coincides with the Helstrom theorem and the JS limit. Furthermore, when prior probabilities are unknown, we derive the minimax MED and the minimax OUD. Based on the optimal NM probabilistic quantum cloning, we present the optimal strategies of collective measurements of the MED and the OUD. When the number of the copies is infinite, regardless of whether prior probabilities are known or not, the success probabilities of the MED and the OUD go to 100%, in accordance with the quantum measurement hypothesis that unknown quantum state can be determined if and only if infinite identical quantum state copies are given.