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AIJR Proceedings

Variation of Quantum Speed Limit with Correlated Channels

Natasha Awasthi, Surbhi Sachdev

Published Aug 8, 2020• 1 citation
Publisher

Abstract

There is a bound on the speed of evolution of quantum system. Out of many bounds few bounds have been studied. In this article we study the effect of quantum speed limit in correlated noisy channel. Our model serves as a platform for a detail study of the effect of quantum speed limit on correlated noise channel. It has found that how the quantum speed limit varies by increasing the correlation between consecutive uses of noisy channels.

DOI
10.21467/proceedings.100.16

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There is a bound on the speed of evolution of quantum system. Out of many bounds few bounds have been studied. In this article we study the effect of quantum speed limit in correlated noisy channel. Our model serves as a platform for a detail study of the effect of quantum speed limit on correlated noise channel. It has found that how the quantum speed limit varies by increasing the correlation between consecutive uses of noisy channels.
Abstract Quantum theory sets a fundamental bound for the minimal time evolution between initial and final state of a system . This bound is called quantum speed limit time , which is used to quantify the speed of evolution of a quantum system. If quantum speed limit time decreases, the evolution keeps on increasing. In this paper, we study the effect of quantum speed limit time in terms of correlated and uncorrelated noise channels like amplitude damping and phase damping channel. We use maximally entangled mixed state as our initial state. We observe the behavior of quantum speed limit time under Markovian and non-Markovian dynamics. We prove that for the special class of our inital state and for the dynamical evolution of a system, there exist a link between quantum speed limit time and non-Markovianity. However, an interesting results were also observed regarding the tightness of bound in Markovian region. Our results shed light on the information back-flow between system and environment in terms of quantum evolution which is useful as a resource in quantum information processing task.
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.
The laws of quantum physics place a limit on the speed of computation, in particular the evolution time of a system cannot be arbitrarily fast. Bounds on the speed of evolution for unitary dynamics have been long studied. A few bounds on the speed of evolution for noisy dynamics have also been obtained recently, these bounds, however, are in general not tight. In this article we present a new framework for quantum speed limit of noisy dynamics. With this framework we obtain the exact maximal angle that a noisy dynamics can achieve at any given time, this then provides tight bounds on the evolution time for noisy dynamics. The obtained bound reveals that noisy dynamics are generically different from unitary dynamics, in particular we show that the 'orthogonalization' time, which is the minimum time needed to evolve any state to its orthogonal states, is in general not applicable to noisy dynamics.
The maximal evolution speed of a quantum system can be represented by quantum speed limit time (QSLT). We investigate the QSLT of a two-qubit system passing through a correlated channel (amplitude damping, phase damping, and depolarizing). By adjusting the correlation parameter of the channel and the initial entanglement, a method to accelerate the evolution speed of the system for some specific channels is proposed. It is shown that, in the amplitude damping channel and the depolarizing channel, QSLT may be shortened in some cases by increasing the correlation parameter of the channel and the initial entanglement, which are in sharp contrast to the phase damping channel. In particular, under depolarizing channels, the transition from no-speedup evolution to speedup evolution for the system can be realized by changing the correlation strength of the channel.
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.