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.

Recently, sequential state discrimination, as a quantum-key distribution protocol, has been proposed for multiple receivers. A previous study [J. A. Bergou et al., Phys. Rev. Lett. 111, 100501 (2013)] showed that every receiver could successfully perform a sequential state discrimination of two pure states with identical prior probabilities. In this study, we extend the sequential state discrimination to mixed states with arbitrary prior probability. First, we analytically obtain the condition of the receiver's optimal measurement. In addition, we show that the optimal probability for every receiver to share the mixed state prepared by the sender is not zero. Furthermore, we compare the sequential state discrimination to the strategies of quantum reproducing and quantum broadcasting. We find that there are cases in which, unlike that of the pure state, the sequential state discrimination of mixed states shows a better performance than the other strategies.

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum states when N receivers are separately located. In this report, we propose optical designs that can perform sequential state discrimination of two coherent states. For this purpose, we consider not only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior probabilities. Since our optical designs do not include electric feedback, they can be implemented without difficulty. Furthermore, we analyze our proposal for the case of photon loss. We also demonstrate that sequential state discrimination of two coherent states performs better than the probabilistic quantum cloning strategy. This proposal can facilitate multiparty QKD based on coherent states.

Sequential state discrimination is a strategy for N separated receivers. As sequential state discrimination can be applied to multiparty quantum key distribution (QKD), it has become one of the relevant research fields in quantum information theory. Up to now, the analysis of sequential state discrimination has been confined to special cases. In this report, we consider a generalization of sequential state discrimination. Here, we do not limit the prior probabilities and the number of quantum states and receivers. We show that the generalized sequential state discrimination can be expressed as an optimization problem. Moreover, we investigate a structure of generalized sequential state discrimination for two quantum states and apply it to multiparty QKD. We demonstrate that when the number of receivers is not too many, generalized sequential state discrimination for two pure states can be suitable for multiparty QKD. In addition, we show that generalized sequential state discrimination for two mixed states can be performed with high optimal success probability. This optimal success probability is even higher than those of quantum reproducing and quantum broadcasting strategy. Thus, generalized sequential state discrimination of mixed states is adequate for performing multiparty QKD. Furthermore, we prove that generalized sequential state discrimination can be implemented experimentally by using linear optics. Finally, we analyze the security of multiparty QKD provided by optimal sequential state discrimination. Our analysis shows that the multiparty QKD guarantees nonzero secret key rate even in low channel efficiency.

Quantum state discrimination of coherent states has been one of important problems in quantum information processing. Recently, R. Han et al. showed that minimum error discrimination of two coherent states can be nearly done by using Jaynes-Cummings Hamiltonian. In this paper, based on the result of R. Han et al., we propose the methods where minimum error discrimination of more than two weak coherent states can be nearly performed. Specially, we construct models which can do almost minimum error discrimination of three and four coherent states. Our result can be applied to quantum information processing of various coherent states.