Quantum Doeblin coefficients: A simple upper bound on contraction coefficients

• URL: http://arxiv.org/abs/2405.00105v2
• Date: Thu, 23 May 2024 13:03:23 GMT
• Title: Quantum Doeblin coefficients: A simple upper bound on contraction coefficients
• Authors: Christoph Hirche,
• Abstract summary: Contraction coefficients give a quantitative strengthening of the data processing inequality. It is often challenging to calculate these coefficients. We discuss a quantum generalization of Doeblin coefficients.
• Score: 3.2634122554914002
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Contraction coefficients give a quantitative strengthening of the data processing inequality. As such, they have many natural applications whenever closer analysis of information processing is required. However, it is often challenging to calculate these coefficients. As a remedy we discuss a quantum generalization of Doeblin coefficients. These give an efficiently computable upper bound on many contraction coefficients. We prove several properties and discuss generalizations and applications. In particular, we give additional stronger bounds. One especially for PPT channels and one for general channels based on a constraint relaxation. Additionally, we introduce reverse Doeblin coefficients that bound certain expansion coefficients.

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