Quantum entanglement

Physics

Operator (biology)

Mathematics

Quantum operation

Transcription factor

Gene

Algorithm

Data mining

Statistics

Conic section

Quantum state

Open quantum system

Repressor

POVM

Chemistry

Geometry

Measure (data warehouse)

Coherence (philosophical gambling strategy)

Computer science

Quantum mechanics

Theoretical computer science

Biochemistry

Robustness (evolution)

Quantum

Physical Review Letters

Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g., joint measurability, positive operator valued measures simulable by projective measurements, and state assemblages preparable with a given Schmidt number.

Quantifying Quantum Resources with Conic Programming