Operational definition of a quantum speed limit
- URL: http://arxiv.org/abs/2002.10822v2
- Date: Mon, 8 Jun 2020 15:20:21 GMT
- Title: Operational definition of a quantum speed limit
- Authors: Yanyan Shao, Bo Liu, Mao Zhang, Haidong Yuan, Jing Liu
- Abstract summary: The quantum speed limit is a fundamental concept in quantum mechanics, which aims at finding the minimum time scale or the maximum dynamical speed for some fixed targets.
Here we provide an operational approach for the definition of the quantum speed limit, which utilizes the set of states that can fulfill the target to define the speed limit.
- Score: 8.987823293206912
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: The quantum speed limit is a fundamental concept in quantum mechanics, which
aims at finding the minimum time scale or the maximum dynamical speed for some
fixed targets. In a large number of studies in this field, the construction of
valid bounds for the evolution time is always the core mission, yet the physics
behind it and some fundamental questions like which states can really fulfill
the target, are ignored. Understanding the physics behind the bounds is at
least as important as constructing attainable bounds. Here we provide an
operational approach for the definition of the quantum speed limit, which
utilizes the set of states that can fulfill the target to define the speed
limit. Its performances in various scenarios have been investigated. For
time-independent Hamiltonians, it is inverse-proportional to the difference
between the highest and lowest energies. The fact that its attainability does
not require a zero ground-state energy suggests it can be used as an indicator
of quantum phase transitions. For time-dependent Hamiltonians, it is shown that
contrary to the results given by existing bounds, the true speed limit should
be independent of the time. Moreover, in the case of spontaneous emission, we
find a counterintuitive phenomenon that a lousy purity can benefit the
reduction of the quantum speed limit.
Related papers
- Concurrence speed limit and its connection with bounds in many body physics [0.0]
We derive a speed limit bound for a quantum correlation named the concurrence for the generally mixed quantum states of two qubits.
We discuss the connection of the findings of this article in the interdisciplinary area of the condensed matter physics or the many body physics and quantum information science.
arXiv Detail & Related papers (2024-11-07T18:09:58Z) - Quantum highway: Observation of minimal and maximal speed limits for few and many-body states [19.181412608418608]
Inspired by the energy-time uncertainty principle, bounds have been demonstrated on the maximal speed at which a quantum state can change.
We show that one can test the known quantum speed limits and that modifying a single Hamiltonian parameter allows the observation of the crossover of the different bounds on the dynamics.
arXiv Detail & Related papers (2024-08-21T18:00:07Z) - Squeezing the quantum noise of a gravitational-wave detector below the standard quantum limit [21.757974626255706]
We show how the LIGO A+ upgrade reduced the detectors' quantum noise below the Standard Quantum Limit by up to 3 dB while achieving a broadband sensitivity improvement.
The Heisenberg uncertainty principle dictates that the position and momentum of an object cannot both be precisely measured.
arXiv Detail & Related papers (2024-04-22T20:32:18Z) - 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) - Quantum Speed Limit From Tighter Uncertainty Relation [0.0]
We prove a new quantum speed limit using the tighter uncertainty relations for pure quantum systems undergoing arbitrary unitary evolution.
We show that the MT bound is a special case of the tighter quantum speed limit derived here.
We illustrate the tighter speed limit for pure states with examples using random Hamiltonians and show that the new quantum speed limit outperforms the MT bound.
arXiv Detail & Related papers (2022-11-26T13:14:58Z) - Speed limits on correlations in bipartite quantum systems [1.3854111346209868]
We derive speed limits on correlations such as entanglement, Bell-CHSH correlation, and quantum mutual information of quantum systems evolving under dynamical processes.
Some of the speed limits we derived are actually attainable and hence these bounds can be considered to be tight.
arXiv Detail & Related papers (2022-07-12T16:23:28Z) - A shortcut to adiabaticity in a cavity with a moving mirror [58.720142291102135]
We describe for the first time how to implement shortcuts to adiabaticity in quantum field theory.
The shortcuts take place whenever there is no dynamical Casimir effect.
We obtain a fundamental limit for the efficiency of an Otto cycle with the quantum field as a working system.
arXiv Detail & Related papers (2022-02-01T20:40:57Z) - 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) - Speed Limits for Macroscopic Transitions [0.0]
We show for the first time that the speed of the expectation value of an observable defined on an arbitrary graph is bounded by the "gradient" of the observable.
Unlike previous bounds, the speed limit decreases when the expectation value of the transition Hamiltonian increases.
arXiv Detail & Related papers (2021-10-19T03:39:51Z) - 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) - Quantum speed limit for thermal states [0.0]
Quantum speed limits are rigorous estimates on how fast a state of a quantum system can depart from the initial state in the course of quantum evolution.
Most known quantum speed limits, including the celebrated Mandelstam-Tamm and Margolus-Levitin ones, are general bounds applicable to arbitrary initial states.
Here we derive a quantum speed limit for a closed system initially prepared in a thermal state and evolving under a time-dependent Hamiltonian.
arXiv Detail & Related papers (2020-05-13T16:42:28Z)
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.