• Open Access

Quantum Processes Which Do Not Use Coherence

Benjamin Yadin, Jiajun Ma, Davide Girolami, Mile Gu, and Vlatko Vedral
Phys. Rev. X 6, 041028 – Published 7 November 2016

Abstract

A major signature of quantum mechanics beyond classical physics is coherence, the existence of superposition states. The recently developed resource theory of quantum coherence allows the formalization of incoherent operations—those operations which cannot create coherence. We identify the set of operations which additionally do not use coherence. These are such that coherence cannot be exploited by a classical observer, who measures incoherent properties of the system, to go beyond classical dynamics. We give a physical interpretation in terms of interferometry and prove a dilation theorem, showing how these operations can always be constructed by the system interacting, in an incoherent way, with an ancilla. Such a physical justification is not known for the incoherent operations; thus, our results lead to a physically well-motivated resource theory of coherence. Next, we investigate the implications for coherence in multipartite systems. We show that quantum correlations can be defined naturally with respect to a fixed basis, providing a link between coherence and quantum discord. We demonstrate the interplay between these two quantities in the operations that we study and suggest implications for the theory of quantum discord by relating these operations to those which cannot create discord.

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  • Received 4 April 2016

DOI:https://doi.org/10.1103/PhysRevX.6.041028

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Benjamin Yadin1,*, Jiajun Ma2, Davide Girolami1,†, Mile Gu3,4,5,‡, and Vlatko Vedral1,2,5,6

  • 1Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom
  • 2Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084 Beijing, China
  • 3School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639673, Republic of Singapore
  • 4Complexity Institute, Nanyang Technological University, 60 Nanyang View, Singapore 639673, Republic of Singapore
  • 5Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
  • 6Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117551, Singapore

  • *benjamin.yadin@physics.ox.ac.uk
  • davegirolami@gmail.com
  • ceptryn@gmail.com

Popular Summary

One of the core tenets of quantum theory is that systems can exist in superpositions of different states, now often termed “coherence.” However, only recently have scientists formulated a rigorous mathematical characterization of this property, work that has paved the way for many studies of coherence as a fundamental quantity. A crucial part of quantum theory is the identification of operations under which coherence can never increase, so-called incoherent operations. Here, we study a new set with a much-needed physical interpretation and discuss the implications of coherence in multipartite systems.

We choose to focus on operations that cannot create coherence and, in a precise sense, cannot exploit coherence to outperform classical processes. We show that these strictly incoherent operations have a physical interpretation in terms of interferometry, and we give a prescription for their implementation by interacting the system of interest with a coherent ancilla. In doing so, we transcend abstract mathematical maps and instead work with basic gates and measurements. We argue that our set is the appropriate one for defining measures of coherence. Beyond single systems, we show that these operations have strong implications for the understanding of quantum correlations. We additionally find a fundamental link between coherence and discord-type correlations by giving conditions for the conversion between these resources.

We expect that our results will inform research on coherence and further our understanding of the general connection between coherence and quantum correlations.

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Vol. 6, Iss. 4 — October - December 2016

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