Quantum Information Processing

, Volume 15, Issue 4, pp 1629–1638 | Cite as

Geometry of quantum state space and quantum correlations

  • Prasenjit Deb


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.


Quantum correlations Negativity Entanglement Riemannian metrics 



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


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Physics and Center for Astroparticle Physics and Space ScienceBose InstituteKolkataIndia

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