We formulate and provide a solution to an approximation problem that occurs in various settings: Finding an optimal additive decomposition of a given Hermitian Hilbert–Schmidt operator, in a term commuting with a second Hermitian compact operator and a term as small as possible in the trace norm sense. In the finite-dimensional case, we show how to interpret our result through a Sylvester equation. An application to a quantum information problem and an interpretation in quantum probability are also sketched.
Optimal commuting approximation of Hermitian operators
TICOZZI, FRANCESCO
2005
Abstract
We formulate and provide a solution to an approximation problem that occurs in various settings: Finding an optimal additive decomposition of a given Hermitian Hilbert–Schmidt operator, in a term commuting with a second Hermitian compact operator and a term as small as possible in the trace norm sense. In the finite-dimensional case, we show how to interpret our result through a Sylvester equation. An application to a quantum information problem and an interpretation in quantum probability are also sketched.File in questo prodotto:
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