Unified entropies and quantum speed limits for nonunitary dynamics

Abstract

We discuss a class of quantum speed limits (QSLs) based on unified quantum ($\alpha ,\mu$)-entropy for nonunitary physical processes. The bounds depend on both the Schatten speed and the smallest eigenvalue of the evolved state, and the two-parametric unified entropy. We specialize these results to quantum channels and non-Hermitian evolutions. In the first case, the QSL depends on the Kraus operators related to the quantum channel, while in the second case the speed limit is recast in terms of the non-Hermitian Hamiltonian. To illustrate these findings, we consider a single-qubit state evolving under the (i) amplitude damping channel, and (ii) the nonunitary dynamics generated by a parity-time-reversal symmetric non-Hermitian Hamiltonian. The QSL is nonzero at earlier times, while it becomes loose as the smallest eigenvalue of the evolved state approaches zero. Furthermore, we investigate the interplay between unified entropies and speed limits for the reduced dynamics of quantum many-body systems. The unified entropy is upper bounded by the quantum fluctuations of the Hamiltonian of the system, while the QSL is nonzero when entanglement is created by the nonunitary evolution. Finally, we apply these results to the XXZ model and verify that the QSL asymptotically decreases as the system size increases. Our results find applications to nonequilibrium thermodynamics, quantum metrology, and equilibration of many-body systems.

15 pages, 5 figures. Close to published version

References in corpus (19)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum metrology from a quantum information science perspective
• Quantum speed limit for physical processes
• Quantum speed limits in open system dynamics
• Topological phase transition in non-Hermitian quasicrystals
• Mixed state sensitivity of several quantum information benchmarks
• Quantum speed limits and the maximal rate of information production
• Some general properties of unified entropies
• Unified entropy, entanglement measures and monogamy of multi-party entanglement
• Quantum correlations and distinguishability of quantum states
• Action quantum speed limits
• Distance Bounds on Quantum Dynamics
• Information and entropy in quantum Brownian motion: Thermodynamic entropy versus von Neumann entropy
• Coherence and entanglement measures based on Rényi relative entropies
• Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity
• Prethermalisation and Thermalisation in the Entanglement Dynamics
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Quantum speed limit helps interpret geometric measure of entanglement
• Tighter constraints of multiqubit entanglement in terms of unified entropy

Cited by in corpus (1)

• Mixedness timescale in non-Hermitian quantum systems