Quantumness and entanglement witnesses

Facchi, Paolo; Pascazio, Saverio; Vedral, Vlatko; Yuasa, Kazuya

doi:10.1088/1751-8113/45/10/105302

Cited by 15 publications

(28 citation statements)

References 20 publications

(29 reference statements)

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“…[ρ a , ρ b ] = 0 =⇒ ρ a and ρ b are quantum states. (6) Indeed, according to the definition (3), in order to prove that a state ρ is quantum, we need to show that there exist observables A, B such that Tr(ρ [A, B]) = 0. Note that to each state we can associate an observable in A having the density matrix as a matrix representation.…”

Section: Witnessing and Quantifying Quantumnessmentioning

confidence: 99%

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Measuring quantumness: from theory to observability in interferometric setups

et al. 2018

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We investigate the notion of quantumness based on the non-commutativity of the algebra of observables and introduce a measure of quantumness based on the mutual incompatibility of quantum states. We show that such a quantity can be experimentally measured with an interferometric setup and that, when an arbitrary bipartition of a given composite system is introduced, it detects the one-way quantum correlations restricted to one of the two subsystems. We finally show that, by combining only two projective measurements and carrying out the interference procedure, our measure becomes an efficient universal witness of quantum discord and non-classical correlations.

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Section: Witnessing and Quantifying Quantumnessmentioning

confidence: 99%

“…Equations (7) and (8) imply that Q is a proper witness of the quantum nature of the states ρ a and ρ b . An assertion equivalent to (6) is that if ρ a is classical…”

Section: Witnessing and Quantifying Quantumnessmentioning

confidence: 99%

Measuring quantumness: from theory to observability in interferometric setups

et al. 2018

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“…Following Ref. [6] we will freely use this identification in the finite-dimensional case and will commit the sin of not distinguishing between states and density matrices.…”

Section: Characterization Of Classical Statesmentioning

confidence: 99%

“…Therefore, if the symmetrized product (2) of two positive observables can take negative values, the algebra A is non-Abelian and the system is quantum. A state ρ of a quantum (or classical) system is defined to be classical [6] if…”

Section: Introduction and Motivationsmentioning

confidence: 99%

Defining quantumness via the Jordan product

Facchi¹,

Ferro²,

Marmo³

et al. 2013

J. Phys. A: Math. Theor.

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We propose alternative definitions of classical states and quantumness witnesses by focusing on the algebra of observables of the system. A central role will be assumed by the anticommutator of the observables, namely the Jordan product. This approach turns out to be suitable for generalizations to infinite dimensional systems. We then show that the whole algebra of observables can be generated by three elements by repeated application of the Jordan product.

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“…Here, we shall show that with the QW (1) as the starting point, one is able to construct the the Clauser-Horne-Shimony-Holt-type (CHSH-type) noncontextual inequality [6] and the Svetlichny inequality [3,4]. Therefore, the violation of the inequalities clearly implies the Alicki-Van Ryn quantumness [1,7,8]. That is, quantum contextuality and * Electronic address: hysu@mail.nankai.edu.cn † Electronic address: chenjl@nankai.edu.cn genuine multipartite nonlocality both belong to the Alicki-Van Ryn quantumness.…”

Section: Introductionmentioning

confidence: 99%