The effect of quantum memory on quantum speed limit time

Abstract

Quantum speed limit time defines the limit on the minimum time required for a quantum system to evolve between two states. Investigation of bounds on speed limit time of quantum system under non-unitary evolution is of fundamental interest, as it reveals interesting connections to quantum (non-)Markovianity. Here, we discuss the characteristics of quantum speed limit time as a function of quantum memory, quantified as the deviation from temporal self-similarity of quantum dynamical maps for CP-divisible as well as indivisible maps. This provides an operational meaning to CPdivisible (non-)Markovianity.I.

Quantum speed limit time: role of coherence as a dynamical witness to distinguish multi-qubit entangled states

“…The quantum system dynamics in the non-Markovian regime is an active area of research for multiple reasons [3,[7][8][9][10][11]. It's known that quantum correlations are lesser susceptible to noise in non-Markovian [12] realms, and quantum memory speeds up the evolution of quantum states [13]. These cases bring out the need for detailed investigations of quantum systems in non-Markovian environments.…”

Phase covariant channel: Quantum speed limit of evolution

“…where Λ(t) = e −lt/2 (cosh(zt/2) + l z sinh(zt/2)) [28] is the decoherence function. The decoherence rate then becomes…”

“…Even though there exists no direct connection between non-Markovianity, a class of which is identified by information backflow and quantum speed limit time (τ QSL ) [26], it's been shown that τ QSL could be realized as a witness of the decay-revival mechanism of quantum correlations [27] for a certain class of quantum noises. In [21,28], it has been seen that quantum non-Markovianity speeds up the evolution of quantum states, which gives an operational definition to the CP-(in) divisible non-Markovian quantum channels. From the practical point of view, τ QSL finds a lot of applications in a wide range of fields [29].…”

Quantum speed limit for the creation and decay of quantum correlations

“…Similarly, in [4] QSL time for achieving a target fidelity for driven quantum systems has been derived. The fact that the impact of the bath on a quantum system is not always detrimental in nature has sped up the research work unraveling the characteristics of open quantum systems [5], and naturally the investigation of speed of evolution under non-unitary dynamics has become an active research topic [6][7][8][9][10]. Quantum speed limit for open quantum system based on different measures has been proposed [11][12][13].…”

“…Quantum speed limit for open quantum system based on different measures has been proposed [11][12][13]. The investigation of QSL time realizes wide range of applications in the field of quantum information processing and technology as it reflects the nature of the physical process the quantum system undergoes [8]. Thus for example, the memory effects on the dynamics of quantum systems originating from the coupling between the system and bath results in the decay-revival mechanism of quantum correlations, which is very well captured by the quantum speed limit time for certain physical processes [7].…”