Characterization of entanglement transformation via group representation theory

Abstract

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary composite system, is realized in the four-dimensional complex space in terms of a set of novel bases that are pseudo orthonormalized. The two-to-one homomorphism is then established for the group $SL(2,C)\otimes SL(2,C)$ onto the $SO(4,C)$. It is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system.

5 pages, no figures

References in corpus (3)

• The Uniqueness Theorem for Entanglement Measures
• Local filtering operations on two qubits
• Local transformation of mixed states of two qubits to Bell diagonal states

Cited by in corpus (2)

• Geometrical aspects of entanglement
• Spatial Reflection and Associated String Order in Quantum Spin Chains