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arXiv · 2007.00697

Canonical forms of two-qubit states under local operations

Sudha·H. S. Karthik·Rajarshi Pal·K. S. Akhilesh·Sibashish Ghosh·K. S. Mallesh·A. R. Usha Devi
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Abstract

Canonical forms of two-qubits under the action of stochastic local operations and classical communications (SLOCC) offer great insight for understanding non-locality and entanglement shared by them. They also enable geometric picture of two-qubit states within the Bloch ball. It has been shown (Verstraete et.al. {Phys. Rev. A, 64, 010101(R) (2001)) that an arbitrary two-qubit state gets transformed under SLOCC into one of the {\em two} different canonical forms. One of these happens to be the Bell diagonal form of two-qubit states and the other non-diagonal canonical form is obtained for a family of rank deficient two-qubit states. The method employed by Verstraete et.al. required highly non-trivial results on matrix decompositions in $n$ dimensional spaces with 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.

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Sudha, H. S. Karthik, Rajarshi Pal, K. S. Akhilesh, Sibashish Ghosh, K. S. Mallesh, A. R. Usha Devi. 2020-07-01. Canonical forms of two-qubit states under local operations. https://doi.org/10.1103/physreva.102.052419

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