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Geometry of quantum state space and entanglement

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Abstract

Recently, an explicit relation between a measure of entanglement and a geometric entity has been reported in Deb (Quantum Inf Process 15:1629–1638, 2016). It has been shown that if a qubit gets entangled with another ancillary qubit, then negativity, up to a constant factor, is equal to the square root of a specific Riemannian metric defined on the metric space corresponding to the state space of the qubit. In this article, we consider different class of bipartite entangled states and show explicit relation between two measures of entanglement and Riemannian metric.

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Acknowledgements

The authors would like to acknowledge Scientific and Engineering Research Board, Govt. of India, for financial support. The authors also acknowledge Bose Institute for providing the research facilities.

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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 & Pratapaditya Bej

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  1. Prasenjit Deb
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  2. Pratapaditya Bej
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Correspondence to Prasenjit Deb.

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Deb, P., Bej, P. Geometry of quantum state space and entanglement. Quantum Inf Process 18, 72 (2019). https://doi.org/10.1007/s11128-019-2192-y

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