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Entanglement fidelity and measure of entanglement

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Abstract

The notion of entanglement fidelity is to measure entanglement preservation through quantum channels. Nevertheless, the amount of entanglement present in a state of a quantum system at any time is measured by quantities known as measures of entanglement. Since there are different types of measures of entanglement, one may expect an entanglement fidelity to associate with its own measure of entanglement counterpart. Here, we aim to investigate association between the so-called entanglement fidelity and some measures of entanglement, namely, entanglement of formation, concurrence and negativity. New entanglement fidelities based upon these measures of entanglement are introduced and statistically compared with the so-called previously introduced entanglement fidelity. It is shown that the entangling aspect of the so-called entanglement fidelity is neither of type entanglement of formation and concurrence nor of type negativity. The results, in addition, expose inability of the so-called entanglement fidelity for detecting, in a broad sense, entanglement preservation through quantum channels. Our analyses open up a new venue in the study of entanglement fidelity and measure of entanglement by demonstrating that each measure of entanglement solely defines its own entanglement fidelity.

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Notes

  1. Note that we here use the negativity defined in Ref. [8], which is twice the negativity introduced in Ref. [17].

  2. For two-qubit pure states, concurrence and negativity are the same [8].

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Acknowledgements

This research was supported by Department of Applied Mathematics and Computer Science at University of Isfahan (Iran) and in part by a grant from IPM through Grant No. 98810042.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics, University of Isfahan, Box 81745-163, Isfahan, Iran

    Vahid Azimi Mousolou

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran

    Vahid Azimi Mousolou

  3. Department of Physics and Astronomy, Uppsala University, 751 20, Box 516, Uppsala, Sweden

    Vahid Azimi Mousolou

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Correspondence to Vahid Azimi Mousolou.

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Azimi Mousolou, V. Entanglement fidelity and measure of entanglement. Quantum Inf Process 19, 329 (2020). https://doi.org/10.1007/s11128-020-02808-0

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