Quantum speed of evolution in a Markovian bosonic environment

• URL: http://arxiv.org/abs/2107.01075v1
• Date: Fri, 2 Jul 2021 13:30:02 GMT
• Title: Quantum speed of evolution in a Markovian bosonic environment
• Authors: Paulina Marian and Tudor A. Marian
• Abstract summary: We present explicit evaluations of quantum speed limit times pertinent to the Markovian dynamics of an open continuous-variable system. We employ two indicators of how different the initial and evolved states are, namely, the fidelity of evolution and the Hilbert-Schmidt distance of evolution.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present explicit evaluations of quantum speed limit times pertinent to the Markovian dynamics of an open continuous-variable system. Specifically, we consider the standard setting of a cavity mode of the quantum radiation field weakly coupled to a thermal bosonic reservoir. The evolution of the field state is ruled by the quantum optical master equation, which is known to have an exact analytic solution. Starting from a pure input state, we employ two indicators of how different the initial and evolved states are, namely, the fidelity of evolution and the Hilbert-Schmidt distance of evolution. The former was introduced by del Campo {\em et al.} who derived a time-independent speed limit for the evolution of a Markovian open system. We evaluate it for this field-reservoir setting, with an arbitrary input pure state of the field mode. The resultant formula is then specialized to the coherent and Fock states. On the other hand, we exploit an alternative approach that employs both indicators of evolution mentioned above. Their rates of change have the same upper bound, and consequently provide a unique time-dependent quantum speed limit. It turns out that the associate quantum speed limit time built with the Hilbert-Schmidt metric is tighter than the fidelity-based one. As apposite applications, we investigate the damping of the coherent and Fock states by using the characteristic functions of the corresponding evolved states. General expressions of both the fidelity and the Hilbert-Schmidt distance of evolution are obtained and analyzed for these two classes of input states. In the case of a coherent state, we derive accurate formulas for their common speed limit and the pair of associate limit times.

Related papers

• Quantum speed limit of a single atom in a squeezed optical cavity mode [0.0937465283958018]
  We study the quantum speed limit of a single atom trapped in a Fabry-Perot microresonator. The analytical expression of evolved atom state can be obtained by using the non-Hermitian Schr"odinger equation.
  arXiv  Detail & Related papers  (2023-10-24T06:52:27Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• Quantum Speed Limit for Change of Basis [55.500409696028626]
  We extend the notion of quantum speed limits to collections of quantum states. For two-qubit systems, we show that the fastest transformation implements two Hadamards and a swap of the qubits simultaneously. For qutrit systems the evolution time depends on the particular type of the unbiased basis.
  arXiv  Detail & Related papers  (2022-12-23T14:10:13Z)
• Optimal bounds on the speed of subspace evolution [77.34726150561087]
  In contrast to the basic Mandelstam-Tamm inequality, we are concerned with a subspace subject to the Schroedinger evolution. By using the concept of maximal angle between subspaces we derive optimal bounds on the speed of such a subspace evolution. These bounds may be viewed as further generalizations of the Mandelstam-Tamm inequality.
  arXiv  Detail & Related papers  (2021-11-10T13:32:15Z)
• Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation [3.9111580372138834]
  An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced. It yields efficient representations of ground states for interacting Hamiltonians on near-term quantum computers.
  arXiv  Detail & Related papers  (2021-02-02T15:17:03Z)
• The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
  It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
  arXiv  Detail & Related papers  (2021-01-04T16:09:10Z)
• Quantum speed limit time for topological qubit influenced by fermionic and bosonic environment [0.0]
  Quantum speed limit time can be used to determine the rate of quantum evolution for closed and open quantum systems. We consider the topological qubit influenced by fermionic and bosonic environment. It is observed that with increasing magnitude of magnetic field, the quantum speed limit time decreases.
  arXiv  Detail & Related papers  (2020-11-28T19:10:51Z)
• Time-optimal quantum transformations with bounded bandwidth [0.0]
  We derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state. In a final section, we use the quantum speed limits to obtain upper bounds on the power with which energy can be extracted from quantum batteries.
  arXiv  Detail & Related papers  (2020-11-24T08:42:08Z)
• Quantum speed limits for time evolution of a system subspace [77.34726150561087]
  In the present work, we are concerned not with a single state but with a whole (possibly infinite-dimensional) subspace of the system states that are subject to the Schroedinger evolution. We derive an optimal estimate on the speed of such a subspace evolution that may be viewed as a natural generalization of the Fleming bound.
  arXiv  Detail & Related papers  (2020-11-05T12:13:18Z)
• Jumptime unraveling of Markovian open quantum systems [68.8204255655161]
  We introduce jumptime unraveling as a distinct description of open quantum systems. quantum jump trajectories emerge, physically, from continuous quantum measurements. We demonstrate that quantum trajectories can also be ensemble-averaged at specific jump counts.
  arXiv  Detail & Related papers  (2020-01-24T09:35:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.