Eigenvalues, Peres' separability condition and entanglement
Abstract
The general expression with the physical significance and positive definite condition of the eigenvalues of $4\times 4$ Hermitian and traceone 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2000
 arXiv:
 arXiv:quantph/0002073
 Bibcode:
 2000quant.ph..2073W
 Keywords:

 Quantum Physics
 EPrint:
 12 pages (Revtex)