Quantum Covariance, Quantum Fisher Information, and the Uncertainty Relations

Gibilisco, Paolo; Hiai, Fumio; Petz, Dénes

doi:10.1109/tit.2008.2008142

Cited by 57 publications

(91 citation statements)

References 29 publications

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“…In this paper we instead introduce an infinite family of quantifiers of quantum correlations beyond entanglement which vanish on both classical-quantum and quantum-classical states and thus properly capture the quantum correlations with respect to both subsystems. More precisely, the 'quantum f −correlations' are here defined as the maximum metric-adjusted f −correlations between pairs of local observables with the same fixed equispaced spectrum and are in one-toone correspondence with the family of metric-adjusted skew informations [55][56][57][58][59][60][61]. While similar ideas were explored earlier in [62,63] to quantify entanglement, here we show that our quantifiers only reduce to entanglement monotones when restricted to pure states.…”

Section: Introductionmentioning

confidence: 67%

Characterising Two-Sided Quantum Correlations Beyond Entanglement via Metric-Adjusted f–Correlations

Cianciaruso

Frérot

Tufarelli

et al. 2018

Information Geometry and Its Applications

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We introduce an infinite family of quantifiers of quantum correlations beyond entanglement which vanish on both classical-quantum and quantum-classical states and are in one-to-one correspondence with the metric-adjusted skew informations. The 'quantum f −correlations' are defined as the maximum metric-adjusted f −correlations between pairs of local observables with the same fixed equispaced spectrum. We show that these quantifiers are entanglement monotones when restricted to pure states of qubit-qudit systems. We also evaluate the quantum f −correlations in closed form for two-qubit systems and discuss their behaviour under local commutativity preserving channels. We finally provide a physical interpretation for the quantifier corresponding to the average of the Wigner-Yanase-Dyson skew informations.

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Section: Introductionmentioning

confidence: 67%

Characterising Two-Sided Quantum Correlations Beyond Entanglement via Metric-Adjusted f–Correlations

Cianciaruso

Frérot

Tufarelli

et al. 2018

Information Geometry and Its Applications

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“…This meaning has interesting applications in refining the Heisenberg uncertainty relations [28][29][30][31][32] and in characterizing the Bell inequalities [33].…”

Section: Introductionmentioning

confidence: 99%

Quantifying correlations via the Wigner-Yanase skew information

Luo

2012

Phys. Rev. A

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In order to quantify the information content of quantum states in the presence of conserved quantities, Wigner and Yanase introduced the notion of skew information [Proc. Natl. Acad. Sci. USA 49, 910, (1963)], which was later identified as a paradigmatic version of quantum Fisher information. The skew information is quite different from, yet deeply connected with, the ubiquitous quantum entropies and has important applications in quantum theory. In this paper, pursuing further the original idea of Wigner and Yanase, we propose a measure for correlations in terms of the skew information, investigate its fundamental properties, and elucidate its characteristics. An appealing feature of this measure for correlations is that its evaluation does not involve any optimization, in sharp contrast to the entanglement and discord measures, and can be straightforwardly calculated. In particular, the algorithm and explicit formulas for general bipartite states are prescribed, and simple analytical expressions for some special states, including arbitrary bipartite pure states, the Bell-diagonal states, and some highly symmetric states such as the Werner states and the isotropic states, are obtained.

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“…Because of the finite spacing between angles, these projections miss in-between details of the system and contain in toto less order than did the signal specimen. Coarse graining even demarks the transition from a quantum to classical universe [2–4]. Thus, in [1] the concept of coarse graining provides the physical grounds we sought for defining the concept of order on its own (i.e., independent of disorder).…”

Section: Introductionmentioning

confidence: 99%

Order in a multidimensional system

Frieden

Gatenby

2011

Phys. Rev. E

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We show that any convex K-dimensional system has a level of order R that is proportional to its level of Fisher information I. The proportionality constant is 1/8 the square of the longest chord connecting two surface points of the system. This result follows solely from the requirement that R decrease under small perturbations caused by a coarse graining of the system. The form for R is generally unitless, allowing the order for different phenomena, or different representations (e.g., using time vs frequency) of a given phenomenom, to be compared objectively. Order R is also invariant to uniform magnification of the system. The monotonic contraction properties of R and I define an arrow of time and imply that they are entropies, in addition to their usual status as informations. This also removes the need for data, and therefore an observer, in derivations of nonparticipatory phenomena that utilize I. Simple graphical examples of the new order measure show that it measures as well the level of “complexity” in the system. Finally, an application to cell growth during enforced distortion shows that a single hydrocarbon chain can be distorted into a membrane having equal order or complexity. Such membranes are prime constituents of living cells.

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Quantum Covariance, Quantum Fisher Information, and the Uncertainty Relations

Cited by 57 publications

References 29 publications

Characterising Two-Sided Quantum Correlations Beyond Entanglement via Metric-Adjusted f–Correlations

Characterising Two-Sided Quantum Correlations Beyond Entanglement via Metric-Adjusted f–Correlations

Quantifying correlations via the Wigner-Yanase skew information

Order in a multidimensional system

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