24,079 research outputs found
Hermitian Tensor Product Approximation of Complex Matrices and Separability
The approximation of matrices to the sum of tensor products of Hermitian
matrices is studied. A minimum decomposition of matrices on tensor space
in terms of the sum of tensor products of Hermitian matrices
on and is presented. From this construction the separability of
quantum states is discussed.Comment: 16 page
Hermitian and skew hermitian forms over local rings
We study the classification problem of possibly degenerate hermitian and skew
hermitian bilinear forms over local rings where 2 is a unit
On the meaning and interpretation of Tomography in abstract Hilbert spaces
The mechanism of describing quantum states by standard probability
(tomographic one) instead of wave function or density matrix is elucidated.
Quantum tomography is formulated in an abstract Hilbert space framework, by
means of the identity decompositions in the Hilbert space of hermitian linear
operators, with trace formula as scalar product of operators. Decompositions of
identity are considered with respect to over-complete families of projectors
labeled by extra parameters and containing a measure, depending on these
parameters. It plays the role of a Gram-Schmidt orthonormalization kernel. When
the measure is equal to one, the decomposition of identity coincides with a
positive operator valued measure (POVM) decomposition. Examples of spin
tomography, photon number tomography and symplectic tomography are reconsidered
in this new framework.Comment: Submitted to Phys. Lett.
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