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arXiv:1711.10551 · Physical Review A

Entangling protocols due to non-Markovian dynamics

Nicolás Mirkin, Pablo M. Poggi, Diego A. Wisniacki

Published Feb 7, 2019• 26 citations
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Abstract

It is widely spread in the literature that non-Markovianity (NM) may be regarded as a resource in quantum mechanics. However, it is still unclear how and when this alleged resource may be exploited. Here, we study the relationship between NM and quantum optimal control under the objective of generating entanglement within $M$ noninteracting subsystems, each one coupled to the same non-Markovian environment. Thus, we design a variety of entangling protocols that are only achievable due to the existence of the environment. We show that NM plays a crucial role in all the entangling protocols considered, revealing that the degree of NM completely determines the success of the entangling operation performed by the control. This is a demonstration of the virtues of NM and the way that it can be exploited in a general entangling setup.

DOI
10.1103/physreva.99.020301

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•Jun 23, 2015•29 citations
It is widely spread in the literature that non-Markovianity (NM) may be regarded as a resource in quantum mechanics. However, it is still unclear how and when this alleged resource may be exploited. Here, we study the relationship between NM and quantum optimal control under the objective of generating entanglement within MMM noninteracting subsystems, each one coupled to the same non-Markovian environment. Thus, we design a variety of entangling protocols that are only achievable due to the existence of the environment. We show that NM plays a crucial role in all the entangling protocols considered, revealing that the degree of NM completely determines the success of the entangling operation performed by the control. This is a demonstration of the virtues of NM and the way that it can be exploited in a general entangling setup.
The issue of whether non-Markovianity (NM) could be considered as a resource in quantum information has been a subject of intense debate in recent years. Recently, a simple mechanism was proposed in which one of the main features of NM, the backflow of information from the environment to the system, represents a fundamental and quantifiable resource for generating entanglement within an open quantum system coupled to a finite and small environment [N. Mirkin, P. Poggi, and D. Wisniacki, Phys. Rev. A 99, 020301(R) (2019)]. In this work, we extend the validity of this resource mechanism by studying a completely different and more general scheme where the system is coupled to an infinite structured reservoir. Under both setups, we show that the degree of NM univocally determines the optimal degree of entanglement reachable by controlling the open system. This result strongly suggests the universality of a quantitative relation between entanglement and NM by using quantum optimal control.
Non-Markovian quantum dynamics, characterized by information backflow from the environment to the system, has emerged as a potential resource for quantum technologies. A key challenge is therefore to control and enhance such memory effects. In this work, we investigate the use of reinforcement learning (RL) to maximize non-Markovianity in a driven two-level system coupled to a structured reservoir. We compare RL-based control strategies with standard optimal control theory (OCT). We show that OCT produces localized but relatively weak revivalsin the instantaneous non-Markovianity rate, whereas RL policies generate significantly stronger and better-timed information backflow by synchronizing the system dynamics with favorable memory intervals of the environment. This enhanced exploitation of memory effects leads to a higher total integrated non-Markovianity for RL than for OCT, with SAC achieving the largest overall enhancement and PPO delivering slightly lower but still strongly improved performance with smoother, experimentally attractive pulses. Our results contribute to the emerging view of non-Markovianity as an operational resource and illustrate how RL can serve as a flexible, model-free tool for non-Markovian quantum control.
We study optimal control strategies to optimize the relaxation rate towards the fixed point of a quantum system in the presence of a non-Markovian (NM) dissipative bath. Contrary to naive expectations that suggest that memory effects might be exploited to improve optimal control effectiveness, NM effects influence the optimal strategy in a non trivial way: we present a necessary condition to be satisfied so that the effectiveness of optimal control is enhanced by NM subject to suitable unitary controls. For illustration, we specialize our findings for the case of the dynamics of single qubit amplitude damping channels. The optimal control strategy presented here can be used to implement optimal cooling processes in quantum technologies and may have implications in quantum thermodynamics when assessing the efficiency of thermal micro-machines.
Quantum technology, exploiting entanglement and the wave nature of matter, relies on the ability to accurately control quantum systems. Quantum control is often compromised by the interaction of the system with its environment since this causes loss of amplitude and phase. However, when the dynamics of the open quantum system is non-Markovian, amplitude and phase flow not only from the system into the environment but also back. Interaction with the environment is then not necessarily detrimental. We show that the back-flow of amplitude and phase can be exploited to carry out quantum control tasks that could not be realized if the system was isolated. The control is facilitated by a few strongly coupled, sufficiently isolated environmental modes. Our paradigmatic example considers a weakly anharmonic ladder with resonant amplitude control only, restricting realizable operations to SO(N). The coupling to the environment, when harnessed with optimization techniques, allows for full SU(N) controllability.
Quantum thermodynamics studies how quantum systems and operations may be exploited as sources of work to perform useful thermodynamic tasks. In real-world conditions, the evolution of open quantum systems typically displays memory effects, resulting in a non-Markovian dynamics. The associated information backflow has been observed to provide advantage in certain thermodynamic tasks. However, a general operational connection between non-Markovianity and thermodynamics in the quantum regime has remained elusive. Here, we analyze the role of non-Markovianity in the central task of extracting work via thermal operations from general multitime quantum processes, as described by process tensors. By defining a hierarchy of four classes of extraction protocols, expressed as quantum combs, we reveal three different physical mechanisms (work investment, multitime correlations, and system-environment correlations) through which non-Markovianity increases the work distillable from the process. The advantages arising from these mechanisms are linked precisely to a quantifier of the non-Markovianity of the process. These results show in very general terms how non-Markovianity of any given quantum process is a fundamental resource that unlocks an enhanced performance in thermodynamics.
Abstract We study optimal control strategies to optimize the relaxation rate towards the fixed point of a quantum system in the presence of a non-Markovian (NM) dissipative bath. Contrary to naive expectations that suggest that memory effects might be exploited to improve optimal control effectiveness, NM effects influence the optimal strategy in a non trivial way: we present a necessary condition to be satisfied so that the effectiveness of optimal control is enhanced by NM subject to suitable unitary controls. For illustration, we specialize our findings for the case of the dynamics of single qubit amplitude damping channels. The optimal control strategy presented here can be used to implement optimal cooling processes in quantum technologies and may have implications in quantum thermodynamics when assessing the efficiency of thermal micro-machines.