Extracting information from a qubit by multiple observers: Toward a theory of sequential state discrimination

TL;DR

This paper investigates sequential unambiguous state discrimination on a single qubit by multiple observers, aiming to maximize the probability that each observer correctly identifies the state without errors, advancing the understanding of nondestructive quantum measurements.

Contribution

It introduces a framework for maximizing success probabilities in sequential unambiguous state discrimination, a step toward nondestructive quantum measurement theory.

Findings

Both Bob and Charlie can successfully identify the state with nonzero probability.

The success probability for Charlie depends on the residual information after Bob's measurement.

The residual information is quantified by the overlap between the post-measurement states.

Abstract

We discuss sequential unambiguous state-discrimination measurements performed on the same qubit. Alice prepares a qubit in one of two possible states. The qubit is first sent to Bob, who measures it, and then on to Charlie, who also measures it. The object in both cases is to determine which state Alice sent. In an unambiguous state discrimination measurement, we never make a mistake, i.e. misidentify the state, but the measurement may fail, in which case we gain no information about which state was sent. We find that there is a nonzero probability for both Bob and Charlie to identify the state, and we maximize this probability. The probability that Charlie's measurement succeeds depends on how much information about the state Alice sent is left in the qubit after Bob's measurement, and this information can be quantified by the overlap between the two possible states in which Bob's measurement leaves the qubit. This paper is a first step toward developing a theory of nondestructive sequential quantum measurements, which could be useful in quantum communication schemes.