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Randomized Entangled Mixed States from Phase States

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Abstract

We construct randomized entangled mixed states by using the formalism of phase states for d-dimensional systems (qudits). The randomized entangled mixed states are a special kind of mixed states that exhibit genuine multipartite correlation. Such states are obtained by the application of randomized entangling operators to an arbitrary pair of qudits of a multiqudit system. The study of the entanglement of randomized mixed states is of great importance in quantum computation since any experimental implementation of entangled states in a realistic environment can be made by imperfect entangling gates. We give a brief review of some necessary background about unitary phase operators and phase states of a multi-qudit system. Evolved density matrices arise when qudits of the multi-qudit system interact via a Hamiltonian of Heisenberg type. The randomized entangled states associated with evolved density matrices are derived via the action of an entangling operator on a pair of two qudits {i, j} of the multi-qudit system with some probability p. The randomized entangled mixed states for bipartite, tripartite and multipartite systems are explicitly expressed and their Kraus decomposition properties are discussed.

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Authors and Affiliations

  1. Department of Physics, Polydisciplinary Faculty, University Sultan Moulay Slimane, Beni Mellal, Morocco

    M. Mansour & Z. Dahbi

  2. Department of Physics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco

    M. Daoud

  3. LPHE-MS, FS Rabat, Morocco

    Z. Dahbi

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  1. M. Mansour
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  2. M. Daoud
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  3. Z. Dahbi
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Correspondence to M. Mansour.

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Mansour, M., Daoud, M. & Dahbi, Z. Randomized Entangled Mixed States from Phase States. Int J Theor Phys 59, 895–907 (2020). https://doi.org/10.1007/s10773-019-04375-2

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