13,603 research outputs found
Faithful teleportation with arbitrary pure or mixed resource states
We study faithful teleportation systematically with arbitrary entangled
states as resources. The necessary conditions of mixed states to complete
perfect teleportation are proved. Based on these results, the necessary and
sufficient conditions of faithful teleportation of an unknown state |\phi> in
C^d with an entangled resource {\rho} in C^m \otimes C^d and C^d \otimes C^n
are derived. It is shown that for {\rho} in C^m\otimesC^d, {\rho} must be a
maximally entangled state, while for {\rho} in C^d \otimes C^n, {\rho} must be
a puremaximally entangled state. Moreover, we show that the sender's
measurements must be all projectors of maximally entangled pure states. The
relations between the entanglement of the formation of the resource states and
faithful teleportation are also discussed.Comment: 9 page
A note on the growth factor in Gaussian elimination for generalized Higham matrices
The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C
are real, symmetric and positive definite and is the
imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth
factor in Gaussian elimination is less than 3. In this paper, based on the
previous results, a new bound of the growth factor is obtained by using the
maximum of the condition numbers of matrixes B and C for the generalized Higham
matrix A, which strengthens this bound to 2 and proves the Higham's conjecture.Comment: 8 pages, 2 figures; Submitted to MOC on Dec. 22 201
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