On the Measure of Quantum Correlations
DOI:
https://doi.org/10.26713/cma.v14i1.1829Keywords:
Quantum correlations, C*-algebra, Decomposition theoryAbstract
In this paper, we present novel qualities of the measure of noncommutative (so quantum) correlations for general quantum systems. In other words, the fundamental difference between classical and non-commutative probability will be studied. In particular, we introduce the notion of coefficient of quantum correlations \(d(\omega, A)\). The main theorem says that there are quantum correlations if and only if \(d(\omega, A) > 0\). Our presentation is done within \(C^*\)-algebraic description of Quantum Theory.
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References
N. Bourbaki, Éléments de Mathématique, Intégration, Chapitres 1, 2, 3 et 4, Deuxiéme Edition Revue et Augmentée, Hermann Paris (1965), (in French) https://www.springer.com/series/7436.
O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics II: Equilibrium States Models in Quantum Statistical Mechanics, Theoretical and Mathematical Physics (TMP) series, Springer Berlin, Heidelberg, (1979), DOI: 10.1007/978-3-662-09089-3.
G. Choquet, Lectures on Analysis, Vol. I: Integration and Topological Vector Spaces, W.A. Benjamin Inc., New York/Amsterdam, xix + 360 pages (1969).
G. Choquet, Lectures on Analysis, Vol. II: Representation Theory, W.A. Benjamin Inc., New York/Amsterdam, xix + 315 pages (1969).
G. Choquet, Lectures on Analysis, Vol. III: Infinite Dimensional Measures and Problem Solution, New York/Amsterdam, xix + 320 pages (1969).
R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. II: Advanced Theory, Graduate Studies in Mathematics, Vol. 16, American Mathematical Society, USA, 676 pages (1997).
W. A. Majewski, On quantum correlations and positive maps, Letters in Mathematical Physics 67 (2004), 125 – 132, DOI: 10.1023/B:MATH.0000032702.55066.a6.
W. A. Majewski, On quantum statistical mechanics: A study guide, Advances in Mathematical Physics, Vol. 2017 (2017), Article ID 9343717, DOI: 10.1155/2017/9343717.
P. A. Meyer, Probability and Potentials, Blaisdell Publishing Company (1966).
R. R. Phelps, Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Mathematics, Vol. 1364, Springer, Berlin — Heidelberg (1989), DOI: 10.1007/978-3-662-21569-2.




