Constraints on SU(2) Circled-Times SU(2) invariant polynomials for a pair of entangled qubits
Journal Article
·
· Physics of Atomic Nuclei
- Joint Institute for Nuclear Research, Laboratory of Information Technologies (Russian Federation)
We discuss the entanglement properties of two qubits in terms of polynomial invariants of the adjoint action of SU(2) Circled-Plus SU(2) group on the space of density matrices P{sub +}. Since elements of P{sub +} are Hermitian, non-negative fourth-order matrices with unit trace, the space of density matrices represents a semi-algebraic subset, P{sub +} is an element of R{sup 15}. We define P{sub +} explicitly with the aid of polynomial inequalities in the Casimir operators of the enveloping algebra of SU(4) group. Using this result the optimal integrity basis for polynomial SU(2) Circled-Plus SU(2) invariants is proposed and the well-known Peres-Horodecki separability criterion for 2-qubit density matrices is given in the form of polynomial inequalities in three SU(4) Casimir invariants and two SU(2) Circled-Plus SU(2) scalars; namely, determinants of the so-called correlation and the Schlienz-Mahler entanglement matrices.
- OSTI ID:
- 22043905
- Journal Information:
- Physics of Atomic Nuclei, Journal Name: Physics of Atomic Nuclei Journal Issue: 6 Vol. 74; ISSN 1063-7788; ISSN PANUEO
- Country of Publication:
- United States
- Language:
- English
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