Evolution speed of open quantum dynamics
arXiv:1906.04766 · doi:10.1103/PhysRevResearch.1.033127
Abstract
The space of density matrices is embedded in a Euclidean space to deduce the dynamical equation satisfied by the state of an open quantum system. The Euclidean norm is used to obtain an explicit expression for the speed of the evolution of the state. The unitary contribution to the evolution speed is given by the modified skew information of the Hamiltonian, while the radial component of the evolution speed, connected to the rate at which the purity of the state changes, is shown to be determined by the modified skew information of the Lindblad operators. An open-system analogue of the quantum navigation problem is posed, and a perturbative analysis is presented to identify the amount of change on the speed. Properties of the evolution speed are examined further through example systems, showing that the evolution speed need not be a decreasing function of time.
5 pages
References in corpus (18)
- Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Quantum speed limit for physical processes
- Quantum speed limit for non-Markovian dynamics
- Quantum speed limits in open system dynamics
- Bloch vectors for qudits
- Quantum Metrology in Open Systems: Dissipative Cramér-Rao Bound
- Mixed-state evolution in the presence of gain and loss
- Tightening Quantum Speed Limits for Almost All States
- Speed limit for open quantum systems
- Speeding up and slowing down the relaxation of a qubit by optimal control
- Tight, robust, and feasible quantum speed limits for open dynamics
- Quantum Speed Limit For Mixed States Using Experimentally Realizable Metric
- Analysis of quantum semigroups with GKS-Lindblad generators I. Simple generators
- Time-optimal navigation through quantum wind
- Speed limits in Liouville space for open quantum systems
- Information geometry of density matrices and state estimation
- Complex extension of Wigner's theorem
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- Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions
- Qubit Geodesics on the Bloch Sphere from Optimal-Speed Hamiltonian Evolutions
- Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds
- Fundamental speed limits on entanglement dynamics of bipartite quantum systems
- Purity Speed Limit of Open Quantum Systems from Magic Subspaces
- Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
- Optimal quantum speed for mixed states
- Quantum speed limit for the maximum coherent state under squeezed environment
- Open quantum dynamics for plant motions
- Lindblad dynamics of open multi-mode bosonic systems: Algebra of bilinear superoperators, exceptional points and speed of evolution
- Biological efficiency in processing information
- Quantum speed limit for the OTOC from an open systems perspective
- Effect of measurements on quantum speed limit
- Nonlinear speed-ups in ultracold quantum gases