The best approximation of an objective state with a given set of quantum states

• URL: http://arxiv.org/abs/2106.09359v1
• Date: Thu, 17 Jun 2021 10:25:15 GMT
• Title: The best approximation of an objective state with a given set of quantum states
• Authors: Li-qiang Zhang, Nan-nan Zhou, and Chang-shui Yu
• Abstract summary: Approximating a quantum state by the convex mixing of some given states has strong experimental significance. We find a closed form of the minimal distance in the sense of l norm between a given d-dimensional objective quantum state and the state convexly mixed by those restricted in any given (mixed-) state set.
• Score: 1.0249024223548817
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides potential applications in quantum resource theory. Here we find a closed form of the minimal distance in the sense of l_2 norm between a given d-dimensional objective quantum state and the state convexly mixed by those restricted in any given (mixed-) state set. In particular, we present the minimal number of the states in the given set to achieve the optimal distance. The validity of our closed solution is further verified numerically by several randomly generated quantum states.

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