Quantum Resource Theories beyond Convexity

TL;DR

This paper introduces a new class of quantum resource theories based on non-convex sets, providing operational tools and demonstrating advantages in quantum discrimination, correlations, and non-Markovianity estimation.

Contribution

It develops non-convex star-shaped quantum resource theories, offering novel methods and witnesses that outperform traditional linear approaches in various quantum information tasks.

Findings

Non-convex resource theories capture quantum properties beyond convex frameworks.

Non-linear witnesses outperform linear ones in quantum discrimination and correlation tests.

Applications include quantum discord, non-Markovianity, and CP-symmetry violation.

Abstract

A class of quantum resource theories, based on non-convex star-shape sets, presented in this work captures the key quantum properties that cannot be studied by standard convex theories. We provide operational interpretations for a resource of this class and demonstrate its advantage to improve performance of correlated quantum discrimination tasks and testing of quantum combs. Proposed techniques provide useful tools to describe quantum discord, total correlations in composite quantum systems and to estimate the degree of non-Markovianity of an analyzed quantum dynamics. Other applications include the problem of unistochasticity of a given bistochastic matrix, with relevance for quantization of classical dynamics and studies of violation of CP-symmetry in high energy physics. In all these cases, the non-linear witnesses introduced here outperform the standard linear witnesses. Importance of our findings for quantum information theory is also emphasized.