2025/05/21 by I. M. George, Marco Tomamichel, George, Ian +1 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Correlation #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Markov chain #Quantum #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum channel #Quantum correlation #Quantum operation #Quantum state #Quantum system #Spectroscopy and Quantum Chemical Studies #State (computer science)
paper · pdf · doi:10.48550/arxiv.2505.15281
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/08/05
The maximal correlation coefficient measures the linear correlation in a bipartite distribution and contraction coefficients measure how much information is lost under a noisy channel. Remarkably, Raginsky established a close relation between these two concepts by showing that the χ2 contraction coefficient equals the maximal correlation coefficient of the joint input/output distribution of the channel. In quantum theory, several generalizations of these concepts have been proposed, but none recover all the classical properties. Here we construct a framework in which the classical theory extends to the quantum setting. We introduce families of quantum maximal correlation coefficients and show that many impose limits on converting quantum states under local operations. We establish a family of quantum contraction coefficients are efficiently computable, yielding a generic efficient algorithm for mixing times of quantum channels with a full rank fixed point. Furthermore, we establish a quantum analogue of Raginsky's classical correspondence that relates these two families of quantities. To do this, we develop the operator-theoretic approach to Petz's family of non-commutative L2(p) spaces that extend the data processing inequality for variance to quantum theory.