Sudden change of local quantum uncertainty and geometry for arbitrary two-qubit X-states
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Sudden change of local quantum uncertainty and geometry for arbitrary two-qubit X-states You-neng Guo1
· Hu-ping Peng1 · Ke Zeng1 · Guo-you Wang2
Received: 18 May 2020 / Accepted: 28 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Local quantum uncertainty (LQU) as a reliable measure of nonclassical correlations has been recently proposed by Girolami et al. (Phys Rev Lett 110:240402, 2013). In this paper, we have derived an explicit analytical expression of LQU and presented the level surfaces of constant LQU for a class of two-qubit X-states beyond Belldiagonal states. The dynamical behavior of quantum correlations via the LQU under decoherence environment is studied, and the phenomenon of a sudden change of LQU is demonstrated. Our results are illustrated through the action of different noisy environments individually on a single qubit of quantum system where there is a necessary condition for the occurrence of sudden change of LQU. Keywords Local quantum uncertainty · Nonclassical correlations · Decoherence channels
1 Introduction Quantum correlations (or nonclassical correlations) are invaluable resource in quantum communication and quantum computation in comparison with their classical analogues [1,2]. It is widely accepted that quantum entanglement, as a familiar and special type of quantum correlations, plays a key ingredient role in quantum information science [3,4]. However, quantum correlations are not only limited to quantum entanglement, it has been shown that some separable quantum states have nonclassical correlations that may arise without entanglement and that are also very useful in prac-
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Ke Zeng [email protected] Guo-you Wang [email protected]
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School of Electronic Information and Electrical Engineering, Changsha University, Changsha 410022, Hunan, People’s Republic of China
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College of Science, Hunan University of Technology, Zhuzhou 412007, Hunan, China 0123456789().: V,-vol
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tical quantum information processing [5–7]. In this sense, how to classify and quantify quantum correlations are of fundamental importance in the emerging field of quantum information. Up to now, various measures of nonclassical correlations such as quantum discord [8,9], quantum deficit [10,11], measurement-induced disturbance [12,13] and dissonance [14] have recently been proposed and extensively studied. Local quantum uncertainty (LQU) as a measure of quantum correlations has recently been introduced by Girolami et al. [15]. This measure is based on the notion of Wigner–Yanase skew information introduced by Wigner–Yanase to determine uncertainty in the measurement of an observable [16,17], has attracted much attention. Similar to other quantum correlations quantifier, LQU satisfies the physical requirements of a measure of quantum correlations, for instance, it vanishes for classically correlated states and is invariant under local unitary operations [15]. Due to its importance as a quantum correlations quantifier, LQU has been
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