Generalized sequential state discrimination for multiparty QKD and its optical implementation

Abstract

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.

Conclusive discrimination by $N$ sequential receivers between $r\geq2$ arbitrary quantum states

“…Representations ( 9) and ( 17) imply that if, for a state instrument M, there exists a statistical realization Ξ where a state σ = |b b| is pure while the values of a projectionvalued measure P have the form P(ω) = |ξ ω ξ ω |, where {|ξ ω , ω ∈ Ω} is an orthonormal basis of H, then, for this state instrument M, there is representation (9) where the Kraus operators are labeled only by an outcome ω ∈ Ω and are defined via the relations (see Lemma 1 in Section 3.2 of Ref. [18]):…”

“…A. Bergou [3] firstly devised the sequential unambiguous state discrimination where a receiver discriminates a sender's quantum state and a further receiver discriminates posterior states from the previous receiver. However, in [3], every receiver performs the so called sequential unambiguous state discrimination where each receiver's conclusive result is always confident, even though this receiver can obtain the inconclusive result with a non-zero probability, and until now there have been numerous theoretical and experimental developments [4,5,6,7,8,9,10,11] on only this type of sequential state discrimination.…”

Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States

“…In the MED, a general solution exists for two quantum states [ 3 ] but a general solution to more than two quantum states does not exist. Nevertheless, state discrimination is used in wide application of quantum information processing [ 28 , 29 , 30 , 31 , 32 , 33 , 34 ].…”

Two-sequential Conclusive Discrimination between Binary Coherent States via Indirect Measurements

“…Beyond a standard quantum state discrimination between a sender and a receiver, the sequential unambiguous state discrimination scenario between a sender and N receivers was presented [10] in 2013, and experimental schemes for implementation of this scenario of a state discrimination have been theoretically proposed [11,12]. For example, when a sender prepares one of two polarized single photon states, then N receivers can build their quantum measurements by using the Sagnac-like interferometers [13,14].…”