Optimal approximations of available states and a triple uncertainty relation

Abstract

We investigate the optimal convex approximation of the quantum state with respect to a set of available states. By isometric transformation, we have presented the general mathematical model and its solutions together with a triple uncertainty equality relation. Meanwhile, we show a concise inequality criterion for decomposing qubit mixed states. The new results include previous ones as special cases. Our model and method may be applied to solve similar problems in high-dimensional and multipartite scenarios

comments are welcome

References in corpus (7)

• Measuring Quantum Coherence with Entanglement
• Frozen Quantum Coherence
• The Fidelity and Trace Norm Distances for Quantifying Coherence
• Heisenberg Uncertainty Relation for Three Canonical Observables
• Complete characterization of qubit masking
• Convex approximations of quantum channels
• Comment on "Optimal convex approximations of quantum states"

Cited by in corpus (2)

• The optimal approximation of qubit states with limited quantum states
• The best approximation of a given qubit state with the limited pure-state set