Tightening of quantum speed limit bound and tracing back information under non-Markoviandynamics

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