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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Quantum Speed Limit for Physical Processes

Márcio M. Taddei, Bruno M. Escher, L. Davidovich, R. L. de Matos Filho

Published Jan 1, 2013• 91 citations
Publisher

Abstract

We present an attainable upper bound on the quantum speed limit of general physical processes based on the quantum Fisher information. This result allows one to tackle experimentally more realistic open-system dynamics.
DOI
10.1364/qim.2013.w6.32

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The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed for unitary dynamics. Here we show that it is possible to extend this concept to nonunitary processes, using an attainable lower bound that is connected to the quantum Fisher information for time estimation. This result is used to delimit the minimal evolution time for typical noisy channels.
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in the literature on this area, for only unitary evolutions -- closed quantum systems -- had been considered. On this Ph.D. thesis, such limitation is overcome: our main result is a bound for quantum-system evolutions in general, whether unitary or not, and correctly recovers the known bounds in the unitary case. Applications of this bound to several concrete cases of interest are herein presented. This bound is also used to extend to the non-unitary case the discussion of the role of entanglement in fast evolutions, leading to nontrivial results. For the derivation of the results, a geometric approach has been employed, which allows a clear interpretation of the bounds and a discussion of the criteria for their saturation. No previous knowledge of quantum-state geometry by the reader has been assumed.
Quantum mechanics imposes fundamental constraints known as quantum speed limits (QSLs) on the information processing speed of all quantum systems. Every QSL known to date comes from the restriction imposed on the evolution time between two quantum states through the value of a single system observable such as the mean energy relative to its ground state. So far these restrictions only place upper bounds on the information processing speed of a quantum system. Here I report QSLs each with permissible information processing speeds separated by forbidden speed intervals. They are found by a systematic and efficient procedure that takes the values of several compatible system observables into account simultaneously. This procedure generalizes almost all existing QSL proofs; the QSLs show a novel first-order phase transition in the minimum evolution time.
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.