Entropy Production of Doubly Stochastic Quantum Channels

Abstract

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly-stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.

24 pages

References in corpus (3)

• Hypercontractivity of quasi-free quantum semigroups
• Relative Entropy Convergence for Depolarizing Channels
• Entropy production rates of bistochastic strictly contractive quantum channels on a matrix algebra

Cited by in corpus (19)

• Quantum Error Mitigation
• Universal Sampling Lower Bounds for Quantum Error Mitigation
• Fundamental limits on quantum dynamics based on entropy change
• Complete entropic inequalities for quantum Markov chains
• Quantum conditional relative entropy and quasi-factorization of the relative entropy
• Multiplicative Properties of Quantum Channels
• Sandwiched Rényi Convergence for Quantum Evolutions
• Stability of logarithmic Sobolev inequalities under a noncommutative change of measure
• Eventually entanglement breaking Markovian dynamics: structure and characteristic times
• Exponential Decay of Matrix $\Phi$-Entropies on Markov Semigroups with Applications to Dynamical Evolutions of Quantum Ensembles
• Rapid thermalization of dissipative many-body dynamics of commuting Hamiltonians
• Quantum computational advantage with constant-temperature Gibbs sampling
• A game of quantum advantage: linking verification and simulation
• Contractivity properties of a quantum diffusion semigroup
• Matrix Poincaré, Φ-Sobolev inequalities, and quantum ensembles
• Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance
• Improved Quantum Hypercontractivity Inequality for the Qubit Depolarizing Channel
• Potential output purity of completely positive maps
• Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains