Quantum Resource Theories beyond Convexity

Understand

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.