Geometry of quantum state space and quantum correlations |
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Authors: | Prasenjit Deb |
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Affiliation: | 1.Department of Physics and Center for Astroparticle Physics and Space Science,Bose Institute,Kolkata,India |
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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 (2times 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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