From Discord to Entanglement

  • Shunlong LuoEmail author
Part of the Quantum Science and Technology book series (QST)


Two prominent and widely studied notions of quantum correlations are discord and entanglement, with the latter occupying a central place in quantum information theory, while the former being regarded of marginal significance and even being criticized by some researchers, although the deep relations between them have been revealed in recent years. Discord and entanglement, being indistinguishable for pure states, only differ for mixed states. The aim of this work is to subsume entanglement under discord by identifying entanglement as the minimal shadow of discord over extended systems. For this purpose, we first present a brief and concise review of some historical aspects of discord and entanglement, emphasizing the ideas leading to them and the intimate relations between them. Then by exploiting an intrinsic connection between classicality and separability of correlations, we derive entanglement from discord in terms of state extensions, and put discord in a more primitive place than entanglement in this context. We comment that the entanglement of pure states studied by EPR and Schrödinger can actually also be well understood as discord, only with the emergence of nonlocality characterized by the Bell inequalities involving mixed states rather than pure states, the LOCC paradigm for mixed-state entanglement becomes significant and attracts great interests. Discord and entanglement are different manifestations of the same global quantum substrate, with discord conceptually more ubiquitous in quantum information and more deeply rooted in quantum measurements.



This work was supported by the National Natural Science Foundation of China, Grant Nos. 11375259, 61134008, the National Center for Mathematics and Interdisciplinary Sciences, CAS, Grant No. Y029152K51.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingPeople’s Republic of China

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