Sequential state discrimination and requirement of quantum dissonance

Abstract

We study the procedure for sequential unambiguous state discrimination. A qubit is prepared in one of two possible states, and measured by two observers Bob and Charlie sequentially. A necessary condition for the state to be unambiguously discriminated by Charlie is the absence of entanglement between the principal qubit, prepared by Alice, and Bob's auxiliary system. In general, the procedure for both Bob and Charlie to recognize between two nonorthogonal states conclusively relies on the availability of quantum discord which is precisely the quantum dissonance when the entanglement is absent. In Bob's measurement, the left discord is positively correlated with the information extracted by Bob, and the right discord enhances the information left to Charlie. When their product achieves its maximum the probability for both Bob and Charlie to identify the state achieves its optimal value.

Sequential state discrimination with quantum correlation

“…That is, even for the probabilities P 1 = P 2 = 1/2, it is required to ignore one of the states in the optimal solution. The phenomenon is a symmetry breaking due to the lack of quantum information in qubit A as pointed out in [8]. In Fig.…”

“…After Bob's discrimination, the qubit A is sent to the second observer Charlie, who knows Bob's protocol and performs a similar unambiguous discrimination. A necessary condition for Charlie's discrimination is that the states he receive are linearly independent [8,18]. In Eq.…”

“…It is one of the theories to extract information from a quantum system by multiple observers [22,23,24]. The results in [8] demonstrate that the entanglement is not only unnecessary for Bob's recognition, but also an obstacle for the next observer Charlie. The left discord of the state in Bob's hands corresponds to the information he extracts, and the right one to the information he left to Charlie.…”

“…The work [8] goes even further, studying the quantum correlations in sequential state discrimination (SSD) presented in [22]. In the protocol of SSD, another observer Charlie will also perform an unambiguous discrimination measurement on the same qubit after Bob's measurement.…”

“…However, both the researches [8] and [22] have been limited to the special case with equal prior probabilities. There are some critical reasons for solving the general problem with arbitrary priors.…”