On average output entropy of a quantum channel

• URL: http://arxiv.org/abs/2404.07978v1
• Date: Thu, 11 Apr 2024 17:57:20 GMT
• Title: On average output entropy of a quantum channel
• Authors: M. E. Shirokov,
• Abstract summary: A new useful metric on the set of generalized ensembles is proposed and explored. The concept of passive energy of an ensemble introduced here plays an important role in the article.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe analytical properties of the average output entropy of a quantum channel as a function of a pair (channel, input ensemble). In particular, tight semicontinuity bounds for this function with the rank/energy constraints are obtained by using the modified semicontinuity bounds for the quantum conditional entropy of quantum-classical states and a special approximation technique. Several applications are considered. New semicontinuity and continuity bounds for the output Holevo information of a channel as a function of a pair (channel, input ensemble) are obtained. The semicontinuity bound for the entanglement of formation with the rank constraint obtained in [1] is improved. In the preliminary part, some results concerning ensembles of quantum states are presented. In particular, a new useful metric on the set of generalized ensembles is proposed and explored. The concept of passive energy of an ensemble introduced here plays an important role in the article.

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