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arXiv:1711.02323 · Physical Review A

Characterizing nonclassical correlations via local quantum Fisher information

Sunho Kim, Longsuo Li, Asutosh Kumar, Junde Wu

Published Mar 19, 2018• 102 citations
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Abstract

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys. Rev. A 86, 022342 (2012)], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord for pure quantum states.

DOI
10.1103/physreva.97.032326

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We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys. Rev. A 86, 022342 (2012)], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord for pure quantum states.
We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in \cite{Lu}, we show that the presence of a quantum correlations can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord in pure state.
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Recently, researchers have found that not only entanglement but also quantum discord and even classical correlation can enhance the precision of parameter estimation. Thus the correlation which contributes quantum metrology should be treated as a new type of resource. In this paper, we directly construct a measure of the resource named as the relative quantum Fisher information (rQFI). It quantifies the improvement of QFI caused by correlations naturally. Operationally, rQFI quantifies the improvement of optimal precision achieved by joint measurement on a composite system, instead of the local measurement on the subsystem. Furthermore, rQFI itself is an alternative type of total correlation which captures effects of quantum entanglement, quantum discord, and classical correlation. It reduces to an entanglement measure for pure states. A detailed study for general two-qubit states is presented. Additionally, an alternative generalized discord measure can be extracted out of the rQFI.
Nonclassical correlations beyond entanglement might provide a resource in quantum information tasks, such as quantum computation or quantum metrology. Quantum discord is a measure of nonclassical correlations to which entanglement belongs as a subset. Exploring the operational meaning of quantum discord as a resource in quantum information processing tasks, such as quantum metrology, is of essential importance to our understanding of nonclassical correlations. In our recent work [Phys. Rev. A 98, 012115 (2018)], we considered a protocol---which we call the greedy local thermometry protocol---for estimating the temperature of thermal equilibrium states from local measurements, elucidating the role of diagonal discord in enhancing the protocol sensitivity in the high-temperature limit. In this paper, we extend our results to a general greedy local parameter estimation scenario. In particular, we introduce a quantum discord---which we call discord for local metrology---to quantify the nonclassical correlations induced by the local optimal measurement on the subsystem. We demonstrate explicitly that discord for local metrology plays a role in sensitivity enhancement in the high-temperature limit by showing its relation to loss in quantum Fisher information. In particular, it coincides with diagonal discord for estimating a linear coupling parameter.
Abstract Inspired by previous studies on entanglement potentials as measures of nonclassicality for single-mode optical states, this work introduces two novel quantifiers based on local quantum uncertainty potential(LQUP) and local quantum Fisher information potential(LQFIP). These two related potentials are employed to characterize the nonclassical nature of single-mode optical fields beyond conventional entanglement-based measures and exhibit similar trends. In particular, the relationship between LQFIP and LQUP is revealed. The exact lower and upper bounds of LQFIP versus LQUP are obtained for a specific class of nonclassical states, and the respective states which saturate those bounds are also characterized. This allows us to establish a strong hierarchy of nonclassicality for single-qubit optical states, mapped directly from the hierarchy of two-qubit quantum correlations. Our findings not only provide new tools for quantifying nonclassicality but also deepen the understanding of quantum resources in optical systems, with potential applications in quantum metrology and information processing. PACS numbers: 03.65.Ta, 03.67.-a, 03.65.Yz
We have introduced a measure of Gaussian quantum correlations based on quantum Fisher information. For bipartite Gaussian states the minimum quantum Fisher information due to local unitary evolution on one of the parties reliably quantifies quantum correlation. In quantum metrology the proposed measure becomes the tool to investigate the role of quantum orrelation in setting metrological precision. In particular, a deeper insights can be gained on how quantum correlations are instrumental to enhance metrological precision. Our analysis demonstrates that not only entanglement but also quantum correlation plays an important role to enhance metrological precision. Clearly unraveling the underlaying mechanism we show that quantum correlations, even in the absence of entanglement, can be exploited as the resource to beat standard quantum limit and attain Heisenberg limit in quantum metrology.