Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optical Fiber Communication Conference

Dynamical Accessibility in the Control of Quantum Systems

Walter F. Buell, B. A. Shadwick

Published Jan 1, 2001• 0 citations
Publisher

Abstract

We discuss the general question of dynamical accessibility among mixed quantum states from the perspective of conservation of kinematic invariants of the Liouville-von Neumann equation and invariants associated with dynamical symmetries of the evolution Hamiltonian.
DOI
10.1364/icqi.2001.pa28

Related papers

Restricted Controllability for Quantum Systems with Dynamical Symmetries

Walter F. Buell, B. A. Shadwick

APS•May 1, 2002•0 citations

On the Liouville–von Neumann Equation for Unbounded Hamiltonians

Davide Lonigro, Alexander Hahn, Daniel Klaus Burgarth

The evolution of mixed states of a closed quantum system is described by a group of evolution superoperators whose infinitesimal generator (the quantum Liouville superoperator, or Liouvillian) determines the mixed-state counterpart of the Schrödinger equation: the Liouville–von Neumann equation. When the state space of the system is infinite-dimensional, the Liouville superoperator is unbounded whenever the corresponding Hamiltonian is. In this paper, we provide a rigorous, pedagogically-oriented, and self-contained introduction to the quantum Liouville formalism in the presence of unbounded operators. We present and discuss a characterization of the domain of the Liouville superoperator originally due to M. Courbage; starting from that, we develop some simpler characterizations of the domain of the Liouvillian and its square. We also provide, with explicit proofs, some domains of essential selfadjointness (cores) of the Liouvillian.

arXiv:2408.04980•Open Systems & Information Dynamics•Dec 1, 2024•5 citations

On Invariant Subspace In Quantum Control Systems and Some Concepts of Integrable Quantum Systems

Andrzej Jamiołkowski, Takeo Kamizawa, Grzegorz Pastuszak

International Journal of Theoretical Physics•Jan 11, 2015•10 citations

Limits of control for quantum systems: Kinematical bounds on the optimization of observables and the question of dynamical realizability

S. G. Schirmer, J. V. Leahy

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for nondissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitrary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group $U(N)$ and the results of a few control computations are discussed briefly.

arXiv:quant-ph/0010032•Physical Review A•Jan 11, 2001•23 citations

Nonlinear quantum evolution with maximal entropy production

S. Gheorghiu-Svirschevski

We derive a well-behaved nonlinear extension of the nonrelativistic Liouville--von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure-state limit reduces to the usual Schr\"odinger evolution, while mixtures evolve toward maximum entropy equilibrium states with canonical-like probability distributions on energy eigenstates. The linear, near-equilibrium limit is found to amount to an essentially exponential relaxation to thermal equilibrium; a few elementary examples are given. In addition, the modified dynamics is invariant under the time-independent symmetry group of the Hamiltonian, and also invariant under the special Galilei group provided the conservation of total momentum is accounted for as well. Similar extensions can be generated for, e.g., nonextensive systems better described by a Tsallis q entropy.

arXiv:quant-ph/0007111•Physical Review A•Jan 12, 2001•49 citations

Evolution speed of open quantum dynamics

Dorje C. Brody, Bradley Longstaff

The authors present a theory to address the evolution speed for open-system dynamics and show that time-optimal control of quantum state hinges on understanding the interplay between the environmental influences, that may be beyond control, and the internal ``unitary'' dynamics.

arXiv:1906.04766•Physical Review Research•Nov 25, 2019•32 citations
The evolution of mixed states of a closed quantum system is described by a group of evolution superoperators whose infinitesimal generator (the quantum Liouville superoperator, or Liouvillian) determines the mixed-state counterpart of the Schrödinger equation: the Liouville–von Neumann equation. When the state space of the system is infinite-dimensional, the Liouville superoperator is unbounded whenever the corresponding Hamiltonian is. In this paper, we provide a rigorous, pedagogically-oriented, and self-contained introduction to the quantum Liouville formalism in the presence of unbounded operators. We present and discuss a characterization of the domain of the Liouville superoperator originally due to M. Courbage; starting from that, we develop some simpler characterizations of the domain of the Liouvillian and its square. We also provide, with explicit proofs, some domains of essential selfadjointness (cores) of the Liouvillian.
In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for nondissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitrary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group U(N)U(N)U(N) and the results of a few control computations are discussed briefly.
We derive a well-behaved nonlinear extension of the nonrelativistic Liouville--von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure-state limit reduces to the usual Schr\"odinger evolution, while mixtures evolve toward maximum entropy equilibrium states with canonical-like probability distributions on energy eigenstates. The linear, near-equilibrium limit is found to amount to an essentially exponential relaxation to thermal equilibrium; a few elementary examples are given. In addition, the modified dynamics is invariant under the time-independent symmetry group of the Hamiltonian, and also invariant under the special Galilei group provided the conservation of total momentum is accounted for as well. Similar extensions can be generated for, e.g., nonextensive systems better described by a Tsallis q entropy.