Extracting unambiguous information from a single qubit by sequential observers

TL;DR

This paper generalizes a scheme for sequentially extracting unambiguous information from a single qubit, analyzing success and failure probabilities, mutual information, and the conditions for effective information transmission.

Contribution

It introduces generalized schemes for unambiguous qubit information extraction with arbitrary priors, optimizing success and failure probabilities, and analyzing information transfer.

Findings

Maximum joint success probability does not always imply information transfer.

Optimal schemes depend on balancing success and failure probabilities.

Certain parameter regions yield no information despite high success probabilities.

Abstract

In a recent paper [Phys. Rev. Lett. 111, 100501 (2013)], a scheme was proposed where subsequent observers can extract unambiguous information about the initial state of a qubit, with finite joint probability of success. Here, we generalize the problem for arbitrary preparation probabilities (arbitrary priors). We discuss two different schemes: one where only the joint probability of success is maximized and another where, in addition, the joint probability of failure is also minimized. We also derive the mutual information for these schemes and show that there are some parameter regions for the scheme without minimizing the joint failure probability where, even though the joint success probability is maximum, no information is actually transmitted by Alice.