Relative purity, speed of fluctuations, and bounds on equilibration times
arXiv:2108.05936 · doi:10.1103/PhysRevA.104.052223
Abstract
We discuss the local equilibration of closed systems using the relative purity, a paradigmatic information-theoretic distinguishability measure that finds applications ranging from quantum metrology to quantum speed limits. First we obtain an upper bound on the average size of the fluctuations on the relative purity: it depends on the effective dimension resembling the bound obtained with the trace distance. Second, we investigate the dynamics of relative purity and its rate of change as a probe of the speed of fluctuations around the equilibrium. In turn, such speed captures the notion of how fast some nonequilibrium state approaches the steady state under the local nonunitary dynamics, somehow giving the information of the quantum speed limit towards the equilibration. We show that the size of fluctuations depends on the quantum coherences of the initial state with respect to the eigenbasis of the Hamiltonian, also addressing the role played by the correlations between system and reservoir into the averaged speed. Finally, we have derived a family of lower bounds on the time of evolution between these states, thus obtaining an estimate for the equilibration time at the local level. These results could be of interest to the subjects of equilibration, quantum speed limits, and also quantum metrology.
14 pages, 5 figures. Close to published version
References in corpus (14)
- Observable measure of quantum coherence in finite dimensional systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Quantum speed limit for physical processes
- Quantum speed limits in open system dynamics
- Strong and weak thermalization of infinite non-integrable quantum systems
- Geometric lower bound for a quantum coherence measure
- Alternative fidelity measure for quantum states
- Unifying Quantum and Classical Speed Limits on Observables
- Remainder Terms for Some Quantum Entropy Inequalities
- General relaxation time of the fidelity for isolated quantum thermodynamic systems
- Witnesses of coherence and dimension from multiphoton indistinguishability tests
- Geometric approach to quantum statistical inference
- Pure State Quantum Statistical Mechanics
- How to detect a possible correlation from the information of a sub-system in quantum mechanical systems