Usage of an euler angle parameterization of SU(N) and U(N) for entanglement calculations on a two-qubit system

Journal of the Physical Society of Japan

Volumn 72, Issue SUPPL.C, 2003, Pages 181-184

  Tilma, Todd ^a   Sudarshan, E C G ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Entanglement; Group parameterizations; Group volumes; Qubit

Indexed keywords

EID: 26944485093     PISSN: 00319015     EISSN: 13474073     Source Type: Journal    
DOI: 10.1143/JPSJS.72SC.181     Document Type: Conference Paper

References (16)

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10. Remember that any 4 by 4 matrix with one element along the diagonal equal to unity and the rest equal to zero will be invariant under a U(3) subgroup of SU(4) and would therefore represent a pure state. The representation given in eq. (8) however is ideally suited for the following calculations based on the group parameters rafter evaluating the coset SU(4)/U(3) (see Tilma et al.2) for more details) since it is those r6 parameters [equally split between three λ3 phases and three ?(i?1)2+1 (i = 2, 3, 4) rotations] that are explicitly contained in the pure state volume measure2) which parameterizes the space CP3 via the corresponding Fubini-Study metric which directly acts upon the ρ1,1 element. This pure state representation is also consistent with the generalized ρd, given previously.1, 6)
11. The general form of the Bell states refers to the density matrices given in Appendix B with the addition of an overall phase.
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