Quantum evolution with a large number of negative decoherence rates

Katarzyna Siudzińska,Dariusz Chruściński

doi:10.1088/1751-8121/aba7f2

Abstract

We analyze the evolution of open quantum systems governed by time-local master equations beyond the Markovian semigroup. Non-Markovian effects are usually attributed to the negativity of some decoherence rates in the time-dependent generator. For the qubit dynamics, it is well known that there can be one permanently negative rate in the so-called eternally non-Markovian evolution. We show that for qudits one can have (d − 1)2 out of the total d 2 − 1 rates that are always negative, and the evolution is still physically legitimate—that is, represented by a completely positive, trace-preserving dynamical map.

Highlights

In quantum mechanics, it is impossible to completely isolate a physical system from the influence of environment
Quantum processes that describe the evolution of open quantum systems are represented by time-parametrized collections of quantum channels Λ(t), which are completely positive, trace-preserving (CPTP) maps [3]
Even though a mixture of Markovian dynamical maps is sometimes generated with negative decoherence rates, the evolution can be simulated with a classical Markov process [9]

Summary

INTRODUCTION

It is impossible to completely isolate a physical system from the influence of environment. L(t)L(τ ) = L(τ )L(t) for any pair t and τ , we can drop the chronological operator T from eq (3) In this case, a sufficient condition for L(t) to generate a CP-. Since one of the rates is permanently negative, the authors called this evolution eternally non-Markovian. For√any pair of qubit density operators ρ1, ρ2 ( X 1 = Tr XX† denotes the trace norm of X) This property is considered an alternative concept of Markovianity [8]. We consider the mixture of legitimate qubit dynamical maps generated by time-local generators This evolution is generalized even further to the qudit dynamics described by the generalized Pauli channels [10]. We find that all the rates cam be temporarily negative and the evolution is still given by a legitimate dynamical map

PAULI CHANNELS

GENERALIZED PAULI CHANNELS

CONVEX COMBINATION OF MARKOVIAN SEMIGROUPS

CLASSICAL MARKOV PROCESS

MARKOVIANITY AND NON-MARKOVIANITY REGIONS

CONCLUSIONS