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arXiv:1902.00909 · Quanta

An Invitation to Quantum Channels

Vinayak Jagadish, Francesco Petruccione

Published Jul 26, 2018• 39 citations
arXivHTMLPDF

Abstract

Open quantum systems have become an active area of research, owing to its potential applications in many different fields ranging from computation to biology. Here, we review the formalism of dynamical maps used to represent the time evolution of open quantum systems and discuss the various representations and properties of the same, with many examples. Quanta 2018; 7: 54–67.

DOI
10.12743/quanta.v7i1.77

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Open quantum systems have become an active area of research, owing to its potential applications in many different fields ranging from computation to biology. Here, we review the formalism of dynamical maps used to represent the time evolution of open quantum systems and discuss the various representations and properties of the same, with many examples. Quanta 2018; 7: 54–67.
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Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction of static and dynamic molecular properties. In recent years, quantum algorithms have been leveraged for the computation of open quantum systems as the predicted quantum advantage of quantum devices over classical ones may allow previously inaccessible applications. Accomplishing this goal will require input and expertise from different research perspectives, as well as the training of a diverse quantum workforce, making a compilation of current quantum methods for treating open quantum systems both useful and timely. In this Review, we first provide a succinct summary of the fundamental theory of open quantum systems and then delve into a discussion on recent quantum algorithms. We conclude with a discussion of pertinent applications, demonstrating the applicability of this field to realistic chemical, biological, and material systems.
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and methods traditionally employed by different communities. We present in some detail the mathematical structure and the general properties of the dynamical maps underlying open system dynamics. We also discuss the microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions.
This review gives a summary of the many techniques that are used in the analysis of open quantum systems. Emphasis is on those cases where it is unsuitable to use a memoryless or Markovian point of view, generally because there is no large separation of time scales between system and environment dynamics. The approaches reviewed include master equations, Heisenberg equations of motion, chain mapping representations, and various stochastic methods such as path integral Monte Carlo and stochastic equations. Guidance is given on how to evaluate the suitability of each of these methods for application in different physical problems.
The study of the physical properties of open quantum systems is at the heart of many investigations, which aim to describe their dynamical evolution on theoretical ground and through physical realizations. Here, we develop a presentation of different aspects, which characterize these systems and confront different physical situations that can be realized leading to systems, which experience Markovian, non-Markovian, divisible or non-divisible interactions with the environments to which they are dynamically coupled. We aim to show how different approaches describe the evolution of quantum systems subject to different types of interactions with their environments. Quanta 2021; 10: 42–54.
The description of the evolution of open quantum systems is a topic of great interest both for its wide range of technological applications and for the understanding of fundamental aspects of quantum theory. In this context, the quantum dynamical mappings formalism is a widely used tool for generally characterizing open systems dynamics. Nonetheless, for this formalism there is no agreement on how to define Markovianity, which is an extremely important concept for most informational analysis of quantum systems. In this undergraduate thesis we compare the quantum dynamical mappings framework with the stochastic processes theory, which has a precise definition of Markovianity, and show that there is a fundamental difference between them that prevents us from properly defining Markovianity in the quantum case. In the end, we briefly present an alternative approach, the process tensor framework, in which is possible to consistently define quantum Markovianity. We then argue that, for this reason, the process tensor framework might be more adequate than quantum dynamical mappings for generally describing the evolution of open quantum systems