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Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system

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Abstract

Detection and classification of entanglement properties of a multi-qubit system is a topic of great interest. This topic has been studied extensively, and thus we found different approaches for the detection and classification of multi-qubit entangled states. We have applied partial transposition operation on one of the qubits of the three-qubit system and then studied the entanglement properties of the three-qubit system, which is under investigation. Since the partial transposition operation is not a quantum operation, we have approximated partial transposition operation in such a way that it represents a completely positive map. The approximated partial transposition operation is also known as structural physical approximation of partial transposition (SPA-PT). We have studied in detail the application of SPA-PT on a three-qubit system and provided explicitly the matrix elements of the density matrix describing SPA-PT of a three-qubit system. Moreover, we propose a criterion to classify all possible stochastic local operations and classical communication inequivalent classes of a pure as well as mixed three-qubit state through SPA-PT map, which makes our criterion experimentally realizable. We have illustrated our criterion for detection and classification of three-qubit entangled states by considering few examples.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study and no experimental data.]

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Acknowledgements

A.K. would like to acknowledge the financial support from CSIR. This work is supported by CSIR File No. 08/133(0027)/2018-EMR-1.

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Authors and Affiliations

  1. Delhi Technological University, Delhi, 110042, India

    Anu Kumari & Satyabrata Adhikari

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  1. Anu Kumari
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  2. Satyabrata Adhikari
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Correspondence to Satyabrata Adhikari.

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Kumari, A., Adhikari, S. Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system. Eur. Phys. J. D 76, 73 (2022). https://doi.org/10.1140/epjd/s10053-022-00398-3

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