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.
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.
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.
The quantum key distribution for multiparty is one of the essential subjects of study. Especially, without using entangled states, performing the quantum key distribution for multiparty is a critical area of research. For this purpose, sequential state discrimination, which provides multiparty quantum communication and quantum key distribution for multiple receivers, has recently been introduced. Moreover, the sequential state discrimination is applicable for the security analysis against an eavesdropper's attack. In this work, we provide the security analysis of quantum key distribution by proposing a unified model of sequential state discrimination including an eavesdropper. In this model, the success probability of eavesdropping is used as a figure of merit for the security analysis. Moreover, we obtain a non-zero secret key rate between the sender and receiver, which implies that the sender and receiver can share a secret key despite the eavesdropper's scheme that optimizing the success probability of eavesdropping. Further, we propose an experimental methodology for the proposed model, which is implementable with linear optics. We observe that the secret key between the sender and receiver can be non-zero, even with imperfections.
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.
The quantum key distribution for multiparty is one of the essential subjects of study. Especially, without using entangled states, performing the quantum key distribution for multiparty is a critical area of research. For this purpose, sequential discrimination, which provides multiparty quantum communication and quantum key distribution for {multiple receivers}, has recently been introduced. However, since there is a possibility of eavesdropping on the measurement result of a receiver by an intruder using quantum entanglement, a security analysis for {quantum key distribution} should be performed. {However,} no one has provided the security analysis for {quantum key distribution in view of the sequential scheme} yet. In this work, by proposing a unified model of sequential discrimination including an eavesdropper, we provide the security analysis of {quantum key distribution based on the unified model of sequential discrimination strategy.} In this model, the success probability of eavesdropping and the secret key rate can be used as a figure of merit. Then, we obtain a non-zero secret key rate between the sender and receiver, which implies that the sender and receiver can share a secret key despite eavesdropping. Further, we propose a realistic quantum optical experiment for the proposed model. We observe that the secret key between the sender and receiver can be non-zero, even with imperfections. As opposed to common belief, we further observe that the success probability of eavesdropping is smaller in the case of colored noise than in the case of white noise.
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.
N-sequential Conclusive State Discrimination in a General Case
In the present article, we develop a general framework for the description of an N-sequential state discrimination, where each of N receivers always obtains a conclusive result. For this new state discrimination scenario, we derive two mutually equivalent general representations of the success probability and prove that if one of two states, pure or mixed, is prepared by a sender, then the optimal success probability is given by the Helstrom bound for any number N of sequential receivers. Furthermore, we specify receivers' indirect measurements resulting in the optimal N-sequential conclusive state discrimination protocol. The developed framework is true for any number N of sequential receivers, any number of arbitrary quantum states, pure or mixed, to be discriminated, and all types of receivers' quantum measurements. The new general results derived within the developed framework are important both from the theoretical point of view and for a successful multipartite quantum communication even in the presence of a quantum noise.