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

• URL: http://arxiv.org/abs/2203.06862v1
• Date: Mon, 14 Mar 2022 05:20:50 GMT
• Title: Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system
• Authors: Anu Kumari, Satyabrata Adhikari
• Abstract summary: We find different approaches for the detection and classification of multi-qubit entangled states. We have applied partial transposition operation on one of the qubit of the three-qubit system. We have illustrated our criterion for detection and classification of three-qubit entangled states by considering few examples.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 qubit 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 so we have approximated partial transposition operation in such a way so that it represent 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 criterion to classify all possible stochastic local operations and classical communication(SLOCC) 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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