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arXiv:1512.02085 · Physical Review X

Quantum Processes Which Do Not Use Coherence

Benjamin Yadin, Jiajun Ma, Davide Girolami, Mile Gu, Vlatko Vedral

Published Nov 7, 2016• 141 citations
arXivHTMLPDF

Abstract

Coherence is a fundamental feature of quantum theory and promises to underpin many future quantum technologies. By studying processes where it is not a necessary resource, researchers sharpen the theory of coherence finding links with interferometry and quantum correlations.
DOI
10.1103/physrevx.6.041028

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Abstract Two primary facets of quantum technological advancement that hold great promise are quantum communication and quantum computation. For quantum communication, the canonical resource is entanglement. For quantum gate implementation, the resource is ‘magic’ in an auxiliary system. It has already been shown that quantum coherence is the fundamental resource for the creation of entanglement. We argue on the similar spirit that quantum coherence is the fundamental resource when it comes to the creation of ‘magic’. This unifies the two strands of modern development in quantum technology under the common underpinning of existence of quantum superposition, quantified by the coherence in quantum theory. We also obtain a coherence monotone from the discrete Wigner distribution. We further study the interplay between quantum coherence and ‘magic’ in a qutrit system and that between quantum entanglement and ‘magic’ in a qutrit-qubit setting.
One of the fundamental features that separates quantum physics from classical physics is the idea of quantum superposition, also known as coherence. This thesis concentrates on understanding quantum coherence in the mathematical framework of resource theories, viewing it both as a resource to be harnessed and as a way to quantitatively characterise quantum states in contrast to classical states. We first examine the type of coherence resource theory which has emerged recently to cope with general settings where the physical nature of the medium encoding information is not crucial, such as computation. We identify the set of quantum processes in which coherence is neither created nor used, and use these to provide a physically motivated resource theory pictured in terms of interferometry. Using the same concepts, we then find connections between coherence and discord, a type of quantum correlation. In particular, we show how coherence can be used to generate discord, and explore basis-dependent discord as an intermediate quantity. The second part of the thesis applies the resource theory framework to quantify quantum macroscopicity, taken here to mean the extent to which coherence exists in a system on a macroscopic scale. We find the appropriate type of resource theory for this purpose, giving criteria for good measures of macroscopic coherence. We use these criteria to evaluate some previously proposed measures and highlight the role of the quantum Fisher information. Next, we build up measures based on the concept of macroscopic distinguishability and use them to show that macroscopic quantum states are fragile to noise induced by interaction with an environment. Finally, we apply measures based on the Fisher information to a range of experiments involving mechanical degrees of freedom, in order to compare their macroscopicity.
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.