Canonical forms of two-qubit states under local operations

Sudha and Karthik, H. S. and Pal, Rajarshi and Akhilesh, K. S. and Ghosh, Sibasish and Mallesh, K. S. and Devi, A. R. Usha (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: 01 Apr 2021 05:32

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