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

arXiv commentcomments are welcome

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Cited by in corpus (5)

• Probabilistic state synthesis based on optimal convex approximation
• The optimal approximation of qubit states with limited quantum states
• The best approximation of a given qubit state with the limited pure-state set
• The best approximation of an objective state with a given set of quantum states
• Identifying the $3$-qubit $W$ state with quantum uncertainty relation