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arXiv:hep-th/9402062 · Journal of Modern Optics

Some Remarks on Quantum Coherence

Andreas Albrecht

Published Dec 1, 1994• 27 citations
arXivHTMLPDF

Abstract

There are many striking phenomena which are attributed to ‘quantum coherence’. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical applications. A useful starting point for such discussions is a definition of ‘quantum coherence’. In this article I give a definition of quantum coherence and use a number of illustrations to explore the implications of this definition. I point to topics of current interest in the fields of cosmology and quantum computation where questions of quantum coherence arise, and I emphasize the impact that interactions with the environment can have on quantum coherence.

DOI
10.1080/09500349414552311

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There are many striking phenomena which are attributed to ‘quantum coherence’. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical applications. A useful starting point for such discussions is a definition of ‘quantum coherence’. In this article I give a definition of quantum coherence and use a number of illustrations to explore the implications of this definition. I point to topics of current interest in the fields of cosmology and quantum computation where questions of quantum coherence arise, and I emphasize the impact that interactions with the environment can have on quantum coherence.
There are many striking phenomena which are attributed to "quantum coherence". It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical applications. A useful starting point for such discussions is a definition of "quantum coherence". In this article I give a definition of quantum coherence and use a number of illustrations to explore the implications of this definition. I point to topics of current interest in the fields of cosmology and quantum computation where questions of quantum coherence arise, and I emphasize the impact that interactions with the environment can have on quantum coherence.
This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions. 1. Overview Ever since the discovery of quantum mechanics people have been puzzled by the counter-intuitive character of the laws of nature. Over time we have learned to accept more and more effects that are unimaginable in a classical Newtonian world. Modern technology exploits quantum effects both to our benefit and detriment—among the memorable examples we should cite laser technology and not omit the atomic bomb. In recent years interest in quantum information theory has been generated by the prospect of employing its laws to design devices of surprising power [1]. New ideas include quantum cryptography [2, 3] and quantum computation. In 1994 Shor [4] discovered a quantum algorithm to factor numbers efficiently (that is in time that grows only polynomically with the length of the number to be factored). This has unleashed a wave of activity across a broad range of disciplines: physics, computer science, mathematics and engineering. This fruitful axis of research has uncovered many new effects that are strikingly different from their classical counterparts, both from the physical point of view as well as from a computer science and communication theory perspective. Over time these communities have gained a greater understanding of the concepts and notions of the other. The idea that information cannot be separated from
Quantum computing, with its transformative potential in solving complex problems, faces a critical challenge: coupling with the environment and the consequent decoherence of quantum systems. This article examines the state of the art on the subject, providing a theoretical basis for understanding how environmental interactions impact quantum algorithms. Quantum coherence, a fundamental element of quantum mechanics, allows quantum states to exist in superposition. However, interaction with the environment triggers decoherence, resulting in the loss of this coherence and affecting the accuracy of the results of quantum algorithms. The study investigates the mechanisms of environmental coupling, such as interactions with photons, fluctuations in magnetic fields, and other external factors. Additionally, the impact of decoherence on notable algorithms, such as Shor's algorithm, is explored, analyzing its implications for the efficiency in determining results. Contemporary mitigation strategies, including quantum error correction techniques applied to this algorithm, are also discussed. The results highlight that decoherence represents a significant obstacle to the practical application of quantum computing in scientific, organizational and social problems. In parallel, a promising set of tools to mitigate or avoid the effects of decoherence is being developed, advancing the viability of quantum computers as applicable technologies.