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:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/1431703
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact