Canonical forms of two-qubit states under local operations

Sudha Shenoy, . and Karthik, H. S. and Pal, Rajarshi and Akhilesh, K. S. and Ghosh, Sibasish and Mallesh, K. S. and Usha Devi, A. R. (2020) Canonical forms of two-qubit states under local operations. Physical Review A, 102 (5). ISSN 2469-9934

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Canonical forms of two-qubits under the action of stochastic local operations and classical communications (SLOCC) offer great insight for understanding nonlocality and entanglement shared by them. They also enable geometric picture of two-qubit states within the Bloch ball. It has been shown Phys. Rev. A 64, 010101(R) (2001)] that an arbitrary two-qubit state gets transformed under SLOCC into one of the two different canonical forms. One of these happens to be the Bell diagonal form of two-qubit states and the other a nondiagonal canonical form is obtained for a family of rank deficient two-qubit states. The method employed by Verstraete et al. Phys. Rev. A 64, 010101(R) (2001)] required highly nontrivial results on matrix decompositions in n-dimensional spaces with an indefinite metric. Here we employ an entirely different approach-inspired by the methods developed by Rao et al. J. Mod. Opt. 45, 955 (1998)] in classical polarization optics-which leads naturally towards the identification of two inequivalent SLOCC invariant canonical forms for two-qubit states. In addition, our approach results in a simple geometric visualization of two-qubit states in terms of their SLOCC canonical forms.

Item Type: Article
Subjects: D Physical Science > Physics
Divisions: Department of > Physics
Depositing User: Mr Umendra uom
Date Deposited: 01 Apr 2021 05:32
Last Modified: 25 Jul 2022 06:27

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