The classical-quantum boundary for correlations: Discord and related measures

By Kavan Modi, Aharon Brodutch, H. Cable, Tomasz Paterek, Vlatko Vedral. 2011

1,372 citations recorded by the source corpus.

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1de3d1784cca4dc5dd2b0afb7050b4dd4c03e9ab

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Citations in the corpus

Quantum Fluctuation Theorems for Arbitrary Environments: Adiabatic and Nonadiabatic Entropy Production (2017, background): “[76, 77], we maximize I(ρSE) over {P∗ m,Qμ}, then the inclusive entropy production is equal to the (symmetric) quantum discord [64, 78] of the state ρSE .”
Dynamics of non-Markovian open quantum systems (2015, background): “In addition, was proven by Rodriguez-Rosario et al. (2008) that initial states with zero discord (Modi et al., 2012a; Ollivier and Zurek, 2001), such as (31), i.e. fulfilling the property [ρs(0) ⊗ 11B , ρtot(0)] = 0, lead to completely positive reduced dynamics.”
Quantum-enhanced measurements without entanglement (2017, background): “…nonzero discord (from the point of view of A) if and only if it is altered by all possible local measurements performed on subsystem A: disturbance by measurement is a genuine quantum feature which is captured by the concept of discord, see (Adesso et al., 2016; Modi et al., 2012) for more details.”
Colloquium: Non-Markovian dynamics in open quantum systems (2015, background): “The above strategy can even be used in order to locally detect a specific type of quantum correlations, i.e. system-environment states with nonzero quantum discord (Modi et al., 2012).”
Quantum coherence and geometric quantum discord (2017, methodology): “…the starting point for the resource theoretic characterization of a quantum character, e.g., quantum entanglement (Horodecki et al., 2009) and QD (Modi et al., 2012), is the identification of free states which can be created at no cost and free operations which transform any free state into free…”
Quantum resource theories (2018, background): “…(Bartlett et al., 2007), quantum thermodynamics (Goold et al., 2016; Gour et al., 2015b), coherence (Streltsov et al., 2016), nonlocality (Brunner et al., 2014), non-Gaussianity (Weedbrook et al., 2012a), non-Markovianity (Rivas et al., 2014), and quantum correlations (Modi et al., 2012)).”
Quantum processes which do not use coherence (2015, background): “[21] Kavan Modi, Aharon Brodutch, Hugo Cable, Tomasz”
Daemonic ergotropy: enhanced work extraction from quantum correlations (2016, methodology): “More precisely, we demonstrate that if system and ancilla share no quantum quantum discord, 24 – 26 then the information gathered through the measurements performed on the state of the ancilla cannot help in catalyzing the extraction of work from the system.”