Sequential measurements on qubits by multiple observers: Joint best guess strategy

TL;DR

This paper investigates a sequential measurement strategy on a single qubit by multiple observers aiming to maximize their joint success probability in guessing the initial state, highlighting a method for nondestructive quantum measurements.

Contribution

It introduces the joint best guess strategy for sequential state discrimination, allowing multiple observers to probabilistically and optimally identify the initial qubit state.

Findings

Maximized joint success probability for multiple observers.

Demonstrated probabilistic bypass of collapse postulate and no-broadcasting theorem.

Applicable to multiparty quantum communication with single qubits.

Abstract

We study sequential state discrimination measurements performed on the same qubit by subsequent observers. Specifically, we focus on the case when the observers perform a kind of a minimum-error type state discriminating measurement where the goal of the observers is to maximize their joint probability of successfully guessing the state that the qubit was initially prepared in. We call this the joint best guess strategy. In this scheme, 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, and so on to altogether N consecutive receivers who all perform measurements on it. The goal for all observers is to determine which state Alice sent. In the joint best guess strategy, every time a system is received the observer is required to make a guess, aided by the measurement, about its state. The price to pay for this requirement is that errors must be permitted, the guess can be correct or in error. There is a nonzero probability for all the receivers to successfully identify the initially prepared state, and we maximize this joint probability of success. This work is a step toward developing a theory of nondestructive sequential quantum measurements and could be useful in multiparty quantum communication schemes based on communicating with single qubits, particularly in schemes employing continuous variable states. It also represents a case where subsequent observers can probabilistically and optimally get around both the collapse postulate and the no-broadcasting theorem.