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

Abstract

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.

Indirect Measurement for Optimal Quantum Communication Enhanced by Binary Non-standard Coherent States

“…is the projective measurement performed on H. and U is the unitary operator defined on a composite Hilbert space H ⊗ H. Fig. 1 illustrates the indirect measurement consist of σ, P on H and U on H ⊗ H. For a pure state |ψ ∈ H, U satisfies the following relation [53,54]…”

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

“…In this section, we specify for the case of two receivers a general scenario for an Nsequential conclusive state discrimination which we have introduced in [18]. Let Alice prepare one of two quantum states ρ 1 , ρ 2 with prior probabilities q 1 , q 2 , and let M l (l = 1, 2) be a state instrument [19] describing a conclusive quantum measurement with outcomes j ∈ {1, 2} of each l-th sequential receiver.…”

“…Let Alice prepare one of two quantum states ρ 1 , ρ 2 with prior probabilities q 1 , q 2 , and let M l (l = 1, 2) be a state instrument [19] describing a conclusive quantum measurement with outcomes j ∈ {1, 2} of each l-th sequential receiver. Then the consecutive measurement by two receivers is described by the state instrument [18]:…”

“…Recently, a general framework for the N -sequential conclusive state discrimination has been presented in [18], which can be applied both for discrimination of pure or mixed quantum states and also for any number N receivers. For this new scenario of a sequential conclusive state discrimination, experimental schemes should be theoretically developed.…”

“…The present article is organized as follows. In Section 2, we specify a general scenario for an N -sequential conclusive state discrimination which we have introduced in [18] for the case of two receivers and receivers' indirect measurement described in the frame of the Jaynes-Cummings interaction model. In Section 3, we derive the expression for the success probability of the two-sequential conclusive discrimination between two coherent states via indirect measurements within the Jaynes-Cummings model and numerically investigate the optimal case.…”