Data Processing Inequality for The Quantum Guesswork

TL;DR

This paper extends classical data processing inequalities to quantum guesswork, providing new bounds and properties for distinguishing non-orthogonal quantum states in quantum information processing.

Contribution

It generalizes classical data processing inequalities to the quantum guesswork setting and derives refined lower bounds on quantum guesswork.

Findings

Established pre and post data processing inequalities for quantum guesswork

Derived a more refined lower bound on quantum guesswork

Extended classical properties to the quantum state discrimination context

Abstract

Non-orthogonal quantum states pose a fundamental challenge in quantum information processing, as they cannot be distinguished with absolute certainty. Conventionally, the focus has been on minimizing error probability in quantum state discrimination tasks. However, another criterion known as quantum guesswork has emerged as a crucial measure in assessing the distinguishability of non-orthogonal quantum states, when we are allowed to query a sequence of states. In this paper, we generalize well known properties in the classical setting that are relevant for the guessing problem. Specifically, we establish the pre and post Data Processing Inequalities. We also derive a more refined lower bound on quantum guesswork.