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Geometry of quantum state space and quantum correlations

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Abstract

Quantum state space is endowed with a metric structure, and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical considerations on the quantum state space. In this article, considering the quantum state space being spanned by \(2\times 2\) density matrices, we determine a particular Riemannian metric for a state \(\rho \) and show that if \(\rho \) gets entangled with another quantum state, the negativity of the generated entangled state is, upto a constant factor, equal to square root of that particular Riemannian metric . Our result clearly relates a geometric quantity to a measure of entanglement. Moreover, the result establishes the possibility of understanding quantum correlations through geometric approach.

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Acknowledgments

The author would like to acknowledge DST, Govt of India, for the financial support through INSPIRE Fellowship.

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  1. Department of Physics and Center for Astroparticle Physics and Space Science, Bose Institute, Bidhan Nagar, Kolkata, 700091, India

    Prasenjit Deb

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  1. Prasenjit Deb
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Deb, P. Geometry of quantum state space and quantum correlations. Quantum Inf Process 15, 1629–1638 (2016). https://doi.org/10.1007/s11128-015-1227-2

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