Entanglement fidelity and measure of entanglement
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Entanglement fidelity and measure of entanglement Vahid Azimi Mousolou1,2,3 Received: 6 April 2020 / Accepted: 11 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Entanglement fidelity · Measure of entanglement · Entanglement of formation · Concurrence · Negativity
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Vahid Azimi Mousolou [email protected]
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Department of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics, University of Isfahan, Box 81745-163, Isfahan, Iran
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School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
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Department of Physics and Astronomy, Uppsala University, 751 20 Box 516, Uppsala, Sweden 0123456789().: V,-vol
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V. Azimi Mousolou
1 Introduction Entanglement as one of the main notions of quantum source of information has been always at the centre of attention in quantum sciences and technologies. The fundamental roles of quantum entanglement in quantum cryptography, superdense coding, quantum teleportation, quantum error correction, efficient quantum computation and many other applied and basic quantum sciences [2,6,10,13] have turned the study of entanglement into a major area of research. Concerning the concept of quantum entanglement, the two relevant questions that naturally arise are: how to quantify and compare entanglement in quantum states? and how well entanglement of a quantum state is maintained and preserved through quantum channels during a quantum information processing? Although these questions have been addressed extensively in many research works, there are still much that remain to be explored. For the first question, we encounter a concept known as measure of entanglemen
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