Eigenvalues, Peres' separability condition and entanglement

Details Eigenvalues, Peres' separability condition and entanglement Eigenvalues, Peres' separability condition and entanglement

2000-02-25

arxiv.org/abs/quant-ph/0002073v2

Comm. Theor. Phys. Vol.42, p206 (2004) [a little revision]

Physics

Quantum Physics

12 pages (Revtex); Revised Version; The example of transfer of entanglement is rewritten

Scientific paper

The general expression with the physical significance and positive definite condition of the eigenvalues of $4\times 4$ Hermitian and trace-one matrix are obtained. This implies that the eigenvalue problem of the $4\times 4$ density matrix is generally solved. The obvious expression of Peres' separability condition for an arbitrary state of two qubits is then given out and it is very easy to use. Furthermore, we discuss some applications to the calculation of the entanglement, the upper bound of the entanglement, and a model of the transfer of entanglement in a qubit chain through a noisy channel.

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