Canonical forms of two-qubit states under local operations
- URL: http://arxiv.org/abs/2007.00697v2
- Date: Sat, 7 Nov 2020 03:26:11 GMT
- Title: Canonical forms of two-qubit states under local operations
- Authors: Sudha, H. S. Karthik, Rajarshi Pal, K. S. Akhilesh, Sibashish Ghosh,
K. S. Mallesh and A. R. Usha Devi
- Abstract summary: We show how canonical forms of two-qubit states can be identified in classical polarization optics.
Our approach results in a simple geometric visualization of two-qubit states in terms of their SLOCC canonical forms.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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