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arXiv:1804.01600 · New Journal of Physics

Quantum speed limits under continuous quantum measurements

Luis Pedro García-Pintos, Adolfo del Campo

Published Feb 22, 2019• 46 citations
arXivHTMLPDF

Abstract

The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. We consider the speed of evolution for quantum systems undergoing stochastic dynamics due to continuous measurements. It is shown that that there are trajectories for which standard QSL are violated, and we provide estimates for the range of velocities in an ensemble of realizations of continuous measurement records. We determine the dispersion of the speed of evolution and characterize the full statistics of single trajectories. By characterizing the dispersion of the Bures angle, we further show that continuous quantum measurements induce Brownian dynamics in Hilbert space.

DOI
10.1088/1367-2630/ab099e

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The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. We consider the speed of evolution for quantum systems undergoing stochastic dynamics due to continuous measurements. It is shown that that there are trajectories for which standard QSL are violated, and we provide estimates for the range of velocities in an ensemble of realizations of continuous measurement records. We determine the dispersion of the speed of evolution and characterize the full statistics of single trajectories. By characterizing the dispersion of the Bures angle, we further show that continuous quantum measurements induce Brownian dynamics in Hilbert space.
Quantum speed limits (QSLs) provide an upper bound for the speed of evolution of quantum states in any physical process. Based on the Stratonovich-Weyl correspondence, we derive a universal QSL bound in arbitrary phase spaces that is applicable for both continuous variable systems and finite-dimensional discrete quantum systems. This QSL bound allows the determination of speed limit bounds in specific phase spaces that are tighter than those in Wigner phase space or Hilbert space under the same metric, as illustrated by several typical examples, e.g., a single-mode free field and NNN-level quantum systems in phase spaces. This QSL bound also provides an experimentally realizable way to examine the speed limit in phase spaces relevant to applications in quantum information and quantum optics.
Abstract We present a new quantum speed limit (QSL) for open quantum systems governed by Markovian dynamics. Our approach is based on analyzing the time derivative of the Bures angle between the initial pure state and its time-evolved state, leading to an analytically computable upper bound on the evolution speed. This bound naturally decomposes into three distinct physical contributions: a unitary term, a dissipative deformation term, and a fluctuation term. Building on this structure, we establish a general inequality that connects the QSL to the quantum Fisher information (QFI) in the short-time regime. This reveals a fundamental trade-off between evolution speed and estimation precision, and clarifies how decoherence can both accelerate and constrain information acquisition in open quantum systems.
Abstract The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e. the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.
Quantum speed limits (QSLs) rule the minimum time for a quantum state to evolve into a distinguishable state in an arbitrary physical process. These fundamental results constrain a notion of distance traveled by the quantum state, known as the Bures angle, in terms of the speed of evolution set by nonadiabatic energy fluctuations. I theoretically propose how to measure QSLs in an ultracold quantum gas confined in a time-dependent harmonic trap. In this highly-dimensional system of continuous variables, quantum tomography is prohibited. Yet, QSLs can be probed whenever the dynamics is self-similar by measuring as a function of time the cloud size of the ultracold gas. This makes it possible to determine the Bures angle and energy fluctuations, as I discuss for various ultracold atomic systems.
Abstract The time required for a given quantum system to evolve is known as the quantum speed limit (QSL), which can be used to characterize the speed of evolution of a quantum system. We study QSL time for Markovian and non-Markovian dynamics. Investigating the effect of QSL under non-unitary evolution is of fundamental interest. In this work, we derive QSL time for maximally entangled state and apply its results under various noise channels. We discuss measure of QSL, how correlations affect the rate of QSL. Further, we carried an investigation on connection between non-Markovianity and QSL. We show that the non Markovian evolution can speed up quantum evolution, therefore lead to smaller QSL time. We have established the connections between correlated channels, information loss and non-Markovianity. This theory may suggest some further connections to retrieve back information from surrounding and preserves decoherence.
Abstract Given the initial and final states of a quantum system, the speed of transportation of state vector in the projective Hilbert space governs the quantum speed limit. Here, we ask the question: what happens to the quantum speed limit under continuous measurement process? We model the continuous measurement process by a non-Hermitian Hamiltonian which keeps the evolution of the system Schrödinger-like even under the process of measurement. Using this specific measurement model, we prove that under continuous measurement, the speed of transportation of a quantum system tends to zero. Interestingly, we also find that for small time scale, there is an enhancement of quantum speed even if the measurement strength is finite. Our findings can have applications in quantum computing and quantum control where dynamics is governed by both unitary and measurement processes.