Structure of Nondestructive Measurement for Discriminating Quantum States

Abstract

Quantum theory not only explains the physics of the microscopic world consistently but also provides excellent quantum information protocols, which show better performance than classical counterparts. Especially, quantum communication provides a secret key, which is more secured than classical communication. Since the scenario of quantum communication consists of state preparation by Alice and measurement by Bob, quantum communication can be described by using quantum state discrimination.

In quantum state discrimination, the purpose of Alice and Bob is to maximize the success probability that Bob correctly guesses Alice’s quantum state. If the structure of Alice’s quantum states is fixed, Bob should construct a measurement, which maximizes success probability. There are several strategies for quantum state discrimination, and in this thesis, we consider minimum error discrimination and unambiguous discrimination. If Bob performs minimum error discrimination, destructive measurement sometimes can be the optimal measurement. Here, destructive measurement destroys Alice’s initial quantum state. Someone may naively think that destructive measurement is sufficient for quantum state discrimination. However, destructive measurement is not always useful for every situation of quantum state discrimination. When coherent states are considered as Alice’s quantum states, destructive measurement, which theoretically performs minimum error discrimination, is difficult to be constructed using linear optics. Therefore, a nondestructive measurement can be more applicable than destructive measurement. Furthermore, nondestructive measurement does not destroys Alice’s initial quantum state. This means that nondestructive measurement can provide a new scenario of quantum state discrimination, which consists of more than one receiver. This scenario is so-called sequential state discrimination. It is well known that sequential state discrimination can provide quantum communication, where more than two parties can share a secret message.

This thesis investigates the structure of nondestructive measurement in quantum state discrimination. First, This thesis analyzes mathematical structure of nondestructive measurement. From this mathematical frame, in this thesis, we investigate an optimal strategy of sequential state discrimination. Also, we compare sequential state discrimination with quantum reproducing and broadcasting strategy. Also, we show that the optimal success probability of sequential state discrimination can be larger than that of the other two strategies. Second, This thesis proposes an experimental structure of nondestructive measurement. Here, a nondestructive measurement is experimentally designed using linear optics and light-atom interaction. Based on linear optics, we show that Banaszek model and Huttner-like model can provide optimal sequential state discrimination of binary coherent states. Also, considering reality, we analyze the case where noise affects Alice’s coherent state. Furthermore, we propose that sequential state discrimination of binary coherent states is more applicable for realistic multiparty QKD than probabilistic cloning scheme. Further, based on light-atom interaction, we propose a nondestructive measurement which discriminates N􀀀ary coherent states with almost minimum error probability. Also, we show that the nondestructive measurement, based on light-atom interaction, can perform coherent state discrimination, whose error probability is smaller than the destructive measurement, based on Dolinar-type scheme.