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arXiv:1301.2152 · Physical Review A

Probing an untouchable environment for its identification and control

Masaki Owari, Koji Maruyama, Takeji Takui, Go Kato

Published Jan 30, 2015• 6 citations
arXivHTMLPDF

Abstract

When manipulating a quantum system $S$, its surrounding system, or environment, $E$ induces unwanted effects. It is mainly due to its vastness and the lack of knowledge about the Hamiltonian ${H}_{SE}$ that governs the dynamics inside $E$ and the interaction with $S$. The detail of ${H}_{SE}$ is usually extremely hard to identify, since $E$ can hardly be measured or controlled directly. Nevertheless, here we show that it is possible to probe and control a part of, if not all, the dynamics involving $E$, within the time scale in which its effective dimension can be seen to be finite. That is, we may be able to let a noisy environment work in our favor as a part of quantum computer.

DOI
10.1103/physreva.91.012343

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When manipulating a quantum system SSS, its surrounding system, or environment, EEE induces unwanted effects. It is mainly due to its vastness and the lack of knowledge about the Hamiltonian HSE{H}_{SE}HSE​ that governs the dynamics inside EEE and the interaction with SSS. The detail of HSE{H}_{SE}HSE​ is usually extremely hard to identify, since EEE can hardly be measured or controlled directly. Nevertheless, here we show that it is possible to probe and control a part of, if not all, the dynamics involving EEE, within the time scale in which its effective dimension can be seen to be finite. That is, we may be able to let a noisy environment work in our favor as a part of quantum computer.
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations. In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors. In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness- enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.
From computers to medicine, miniaturization approaches the atomic scale, where device operation can be dominated by quantum effects that are strongly coupled to the local environment. These influences may be seen not as a nuisance, but rather a nearly untapped source of information about physical or biochemical processes playing out nearby. How can one extract maximum information from such fluctuations with an atomic probe, under typical experimental constraints? The authors use quantum estimation theory to outline a general strategy for dynamical measurement of a broad class of environmental processes.
In this thesis, common features from the theories of open quantum systems, estimation of state dynamics and statistical mechanics have been integrated in a comprehensive framework, with the aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of specic control tasks, since it can be responsible for uncontrolled time-dependent (and even discontinuous) changes \nof the system. However, if the effects of the random interaction with a noisy environment are properly modeled by the introduction of a given stochasticity within the dynamics of the system, then even noise contributions might be seen as control knobs. As a matter of fact, even a partial knowledge of the environment can allow to set the system in a dynamical condition in which the response is optimized by the presence of noise sources. In particular, we have investigated what kind of measurement devices can work better in \nnoisy dynamical regimes and studied how to maximize the resultant information via the adoption of estimation algorithms. Moreover, we have shown the optimal interplay between quantum dynamics, environmental noise and complex network topology in maximizing the energy transport efficiency. Then, foundational scientic aspects, such as the occurrence of an ergodic property for the system-environment interaction modes of a randomly perturbed quantum system or the characterization of the stochastic quantum Zeno phenomena, have been analyzed by using the predictions of the large deviation theory. Finally, the energy cost in maintaining the system in the non-equilibrium regime due to the presence of the environment is evaluated by reconstructing the corresponding thermodynamics entropy production. In conclusion, the present thesis can constitute the basis for an effective \nresource theory of noise, which is given by properly engineering the interaction between a dynamical (quantum or classical) system and its external environment.
The identification of time-varying parameters (e.g., directly inaccessible in situ signals in vacuum and low-temperature environments) is prevalent for characterizing the dynamics of quantum processes. Under certain circumstances, they can be identified from time-resolved measurements via Ramsey interferometry experiments, but only with specially designed probe systems can the parameters be explicitly read out, and a rigorous identifiability analysis is lacking, i.e., whether the measurement data are sufficient for unambiguous identification. In this paper we formulate this problem as the invertibility of the input-output mapping associated with the quantum system for which an algebraic identifiability criterion is derived based on the system's relative degree. The invertibility analysis also leads to an inversion-based algorithm for numerically identifying the parameters, which is computationally much more efficient than nonlinear regression methods. The effectiveness of the criterion are demonstrated by numerical examples.