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A Note on the Measure of Discord [article]

George J. Klir, Behzad Parviz
2013 arXiv   pre-print
A new entropy-like measure as well as a new measure of total uncertainty pertaining to the Dempster-Shafer theory are introduced.  ...  It is argued that these measures are better justified than any of the previously proposed candidates.  ...  While it may be argued that subadditivity is not essential in this case, we have not been able to fmd any way to A Note on the Measure of Discord 139 justify this argument.  ... 
arXiv:1303.5409v1 fatcat:5blkj75r5zhs5kc42vw6zl2mym

Super Quantum Discord and Inferior "Geometric Discord" Based on Weak Measurement in Noninertial Frames

Maohuai Xiang, Jiliang Jing
2014 Journal of Quantum Information Science  
However, we note that the geometric discord based on the weak measurements becomes smaller, so we name it inferior "geometric discord".  ...  Instead of projective measurement, we use weak measurement to define quantum and geometric discords, and compare them with the normal quantum and geometric discords based on the projective measurement  ...  A A A w R P x R P x S R P x p x S p x S ρ ρ − = + − Similarly, we also can define the geometric discord by using the weak measurement to perform on the subsystem A of the state AR ρ .  ... 
doi:10.4236/jqis.2014.41005 fatcat:3brbwmuzdzhzjfk52m74htjjdq

Quantum discord protection from amplitude damping decoherence

Jiwon Yune, Kang-Hee Hong, Hyang-Tag Lim, Jong-Chan Lee, Osung Kwon, Sang-Wook Han, Yong-Su Kim, Sung Moon, Yoon-Ho Kim
2015 Optics Express  
In this paper, we study how quantum discord, or more specifically, the measures of entropic discord and geometric discord are affected by the influence of amplitude damping decoherence.  ...  However, it is now known that some quantum features may be acheived with quantum discord, a generalized measure of quantum correlation.  ...  Note that a symmetric discord has been proposed in order to ensure the symmetry [21] .  ... 
doi:10.1364/oe.23.026012 pmid:26480116 fatcat:nyjoe66mvbhwlgreniu7hhhk4q

Problem with geometric discord

M. Piani
2012 Physical Review A. Atomic, Molecular, and Optical Physics  
On the other hand it is known that the standard, mutual-information based discord does not suffer this problem; a simplified proof of such a fact is given.  ...  Lett. 105, 190502 (2010)] is not a good measure for the quantumness of correlations, as it can increase even under trivial local reversible operations of the party whose classicality/non-classicality is  ...  This note was completed during a visit to the National Quantum Information Centre (KCIK) in Gdańsk, whose hospitality is gratefully acknowledged. This work has been supported by CIFAR and NSERC.  ... 
doi:10.1103/physreva.86.034101 fatcat:54hkxdf6rza2nakutv35vaqliq

Diagonal quantum discord

Zi-Wen Liu, Ryuji Takagi, Seth Lloyd
2019 Journal of Physics A: Mathematical and Theoretical  
This paper analyzes the properties of diagonal discord, a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to  ...  Quantum discord measures quantum correlation by comparing the quantum mutual information with the maximal amount of mutual information accessible to a quantum measurement.  ...  Sampling symmetric X-states In section 6, we intend to compare the values of diagonal discord and ordinary (optimized) discord of some generic class of states.  ... 
doi:10.1088/1751-8121/ab0774 fatcat:qs6ozfihmvdrbgdb47yzfkrqvi

No energy transport without discord [article]

Seth Lloyd, Zi-Wen Liu, Stefano Pirandola, Vazrik Chiloyan, Yongjie Hu, Samuel Huberman, Gang Chen
2017 arXiv   pre-print
We report the results of a measurement of the increase in discord due to nanoscale heat flow across an aluminum-sapphire interface and find it to be 4.28 × 10^24 bits m^-2 K^-1 s^-1.  ...  We show that the rate of heat transfer between two quantum systems at different temperatures is directly proportional to the instantaneous rate of increase of diagonal/energetic discord between the systems  ...  Note that the experiment is not a test of a theoretical prediction, but instead a direct measurement of discord based on the theory.  ... 
arXiv:1510.05035v2 fatcat:7dxhhxlczrenhpemmb7k34wiwi

Linking Quantum Discord to Entanglement in a Measurement

Alexander Streltsov, Hermann Kampermann, Dagmar Bruß
2011 Physical Review Letters  
We generalize the results to multipartite measurements on a part of the system and on the total system.  ...  We show that a von Neumann measurement on a part of a composite quantum system unavoidably creates distillable entanglement between the measurement apparatus and the system if the state has nonzero quantum  ...  If we consider bipartite quantum states ρ AB , and von Neumann measurements on A with a complete set of orthogonal rank one projectors Π A i = |i A i A |, i Π A i = 1 1 A , then the quantum discord is  ... 
doi:10.1103/physrevlett.106.160401 pmid:21599342 fatcat:cdtyrynwx5ejjabzufihuywgn4

Minimum disturbance rewards with maximum possible classical correlations

Varad R. Pande, Anil Shaji
2017 Physics Letters A  
Weak measurements done on a subsystem of a bipartite system having both classical and nonClassical correlations between its components can potentially reveal information about the other subsystem with  ...  We use weak quantum discord and the fidelity between the initial bipartite state and the state after measurement to construct a cost function that accounts for both the amount of information revealed about  ...  behaviour of discord and discord-like measures when the measurements on one or both subsystems were restricted to weak quantum measurements [9, 10] .  ... 
doi:10.1016/j.physleta.2017.04.036 fatcat:uexs23dc25gxhbjjnnuzmzpd44

Weak measurements and nonClassical correlations [article]

Lekshmi S, N Shaji, Anil Shaji
2015 arXiv   pre-print
We extend the definition of quantum discord as a quantifier of nonClassical correlations in a quantum state to the case where weak measurements are performed on subsystem A of a bipartite system AB.  ...  Weak quantum discord reduces to discord in the appropriate limits as well. We also discuss the implications of these observations on the interpretations of quantum discord.  ...  Apart from noting that the values of D w are more sharply clustered around D for larger values of α we also note that on an average the weak quantum discord is lesser than the normal quantum discord by  ... 
arXiv:1511.09224v1 fatcat:w7tvd76sercuzme66pvtqew3ya

Witnessed entanglement and the geometric measure of quantum discord

Tiago Debarba, Thiago O. Maciel, Reinaldo O. Vianna
2012 Physical Review A. Atomic, Molecular, and Optical Physics  
In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which is slightly different from a previous conjectured one [Phys. Rev.  ...  A 84, 052110 (2011)].We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically.  ...  This notion of quantumness beyond entanglement is captured by the quantum discord, which is defined as all the correlations contained in a state but the classical ones [7] , or as a measure of disturbance  ... 
doi:10.1103/physreva.86.024302 fatcat:b6szy7xzsrdwzekairtr7cggxi

Quantum Correlations in Multipartite Quantum Systems [article]

Thiago R. de Oliveira
2017 arXiv   pre-print
We review some concepts and properties of quantum correlations, in particular multipartite measures, geometric measures and monogamy relations.  ...  We also discuss the relation between classical and total correlations  ...  Acknowledgment I would like to thanks Marcelo Sarandy for many discussion about discord and quantum correlation and Ernesto Galvão for carefully reading the first draft.  ... 
arXiv:1706.03101v1 fatcat:nlhoklkhmvbnbp2wfhxw3zqtpu

Analytical progress on symmetric geometric discord: Measurement-based upper bounds

Adam Miranowicz, Paweł Horodecki, Ravindra W. Chhajlany, Jan Tuziemski, Jan Sperling
2012 Physical Review A. Atomic, Molecular, and Optical Physics  
We analyze a geometric measure of symmetric discord defined as the Hilbert-Schmidt distance of a given state to the closest classical-classical (CC) correlated state.  ...  In particular, a geometric measure of asymmetric discord [Dakic et al., Phys. Rev.  ...  Geometric measures of the discord of a state are also similarly completely determined by optimal measurements on it, as noted by Luo and Fu [11] and elucidated in the review by Modi et al. [4] .  ... 
doi:10.1103/physreva.86.042123 fatcat:svlnuvdzovbq7dkvoxmzcxc3vu

Non-commutativity measure of quantum discord

Yu Guo
2016 Scientific Reports  
It is shown by several examples that these measures can reflect the amount of the original quantum discord. two measures: the trace norm measure and the Hilbert-Schmidt norm one.  ...  Quantum discord is a manifestation of quantum correlations due to non-commutativity rather than entanglement.  ...  Acknowledgements This work is supported by the National Natural Science Foundation of China under Grant No. 11301312. Additional Information  ... 
doi:10.1038/srep25241 pmid:27122226 pmcid:PMC4848517 fatcat:hmf3ufdxfrhebba5ddo3ahzopm

Witnessing the quantum discord of all the unknown states [article]

Sixia Yu, Chengjie Zhang, Qing Chen, C.H.Oh
2011 arXiv   pre-print
A quantum circuit is designed to measure the quantum discord witness by using only local qubit-measurements.  ...  Unlike entanglement, whose detection is extremely difficult, the quantum discord of an arbitrary bipartite state allows itself to be detected perfectly by a single observable, the quantum discord witness  ...  Also we note that the expectation values of an observable on multi copies of a state is naturally nonlinear.  ... 
arXiv:1102.4710v1 fatcat:nqffzwgmzzazvb6jmr6pjxvv6a

Witnessing quantum discord in2×Nsystems

Bogna Bylicka, Dariusz Chruściński
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
Therefore, we provide a natural witness for a quantum discord: if a 2 x N state is not SPPT it must contain nonclassical correlations measured by quantum discord.  ...  It is an analog of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be entangled.  ...  This work was partially supported by the Polish Ministry of Science and Higher Education Grant No 3004/B/H03/2007/33.  ... 
doi:10.1103/physreva.81.062102 fatcat:nu7pnbmysvfqvoqn6owj4dbwdi
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