Margolus-Levitin quantum speed limit for an arbitrary fidelity

• URL: http://arxiv.org/abs/2301.10063v3
• Date: Wed, 13 Dec 2023 07:51:44 GMT
• Title: Margolus-Levitin quantum speed limit for an arbitrary fidelity
• Authors: Niklas H\"ornedal, Ole S\"onnerborn
• Abstract summary: We derive the extended Margolus-Levitin quantum speed limit analytically and describe the systems that saturate the limit in detail. We also provide the limit with a symplectic-geometric interpretation, which indicates that it is of a different character than most existing quantum speed limits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Mandelstam-Tamm and Margolus-Levitin quantum speed limits are two well-known evolution time estimates for isolated quantum systems. These bounds are usually formulated for fully distinguishable initial and final states, but both have tight extensions to systems that evolve between states with an arbitrary fidelity. However, the foundations of these extensions differ in some essential respects. The extended Mandelstam-Tamm quantum speed limit has been proven analytically and has a clear geometric interpretation. Furthermore, which systems saturate the limit is known. The derivation of the extended Margolus-Levitin quantum speed limit, on the other hand, is based on numerical estimates. Moreover, the limit lacks a geometric interpretation, and no complete characterization of the systems reaching it exists. In this paper, we derive the extended Margolus-Levitin quantum speed limit analytically and describe the systems that saturate the limit in detail. We also provide the limit with a symplectic-geometric interpretation, which indicates that it is of a different character than most existing quantum speed limits. At the end of the paper, we analyze the maximum of the extended Mandelstam-Tamm and Margolus-Levitin quantum speed limits and derive a dual version of the extended Margolus-Levitin quantum speed limit. The maximum limit is tight regardless of the fidelity of the initial and final states. However, the conditions under which the maximum limit is saturated differ depending on whether or not the initial state and the final state are fully distinguishable. The dual limit is also tight and follows from a time reversal argument. We describe the systems that saturate the dual quantum speed limit.

Related papers

• Observing super-quantum correlations across the exceptional point in a single, two-level trapped ion [48.7576911714538]
  In two-level quantum systems - qubits - unitary dynamics theoretically limit these quantum correlations to $2qrt2$ or 1.5 respectively. Here, using a dissipative, trapped $40$Ca$+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics.
  arXiv  Detail & Related papers  (2023-04-24T19:44:41Z)
• Closed systems refuting quantum-speed-limit hypotheses [0.0]
  We show that the Margolus-Levitin quantum speed limit does not extend to closed systems in an obvious way. We also show that for isolated systems, the Mandelstam-Tamm quantum speed limit and a slightly weakened version of this limit that we call the Bhatia-Davies quantum speed limit always saturate simultaneously.
  arXiv  Detail & Related papers  (2023-03-16T15:55:13Z)
• 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)
• Growth of entanglement of generic states under dual-unitary dynamics [77.34726150561087]
  Dual-unitary circuits are a class of locally-interacting quantum many-body systems. In particular, they admit a class of solvable" initial states for which, in the thermodynamic limit, one can access the full non-equilibrium dynamics. We show that in this case the entanglement increment during a time step is sub-maximal for finite times, however, it approaches the maximal value in the infinite-time limit.
  arXiv  Detail & Related papers  (2022-07-29T18:20:09Z)
• Emergence of Fermi's Golden Rule [55.73970798291771]
  Fermi's Golden Rule (FGR) applies in the limit where an initial quantum state is weakly coupled to a continuum of other final states overlapping its energy. Here we investigate what happens away from this limit, where the set of final states is discrete, with a nonzero mean level spacing.
  arXiv  Detail & Related papers  (2022-06-01T18:35:21Z)
• 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)
• Observing crossover between quantum speed limits [0.0]
  Two well-known quantum speed limits are the Mandelstam-Tamm and the Margolus-Levitin bounds. Here, we test concurrently both limits in a multi-level system by following the motion of a single atom in an optical trap. Our data reveal two different regimes: one where the Mandelstam-Tamm limit constrains the evolution at all times, and a second where a crossover to the Margolus-Levitin limit is manifested at longer times.
  arXiv  Detail & Related papers  (2021-04-12T17:01:47Z)
• 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)
• Operational definition of a quantum speed limit [8.987823293206912]
  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.
  arXiv  Detail & Related papers  (2020-02-25T12:32:07Z)

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.