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SUMMARY:G.G. Amosov
DTSTART:20240909T120000Z
DTEND:20240909T130000Z
DTSTAMP:20260423T005704Z
UID:QOART/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QOART/43/">O
 n a generalized approach to quantum tomography via projective unitary repr
 esentations of groups</a>\nby G.G. Amosov as part of Quantum Optics and Re
 lated Topics\n\n\nAbstract\nSuppose that $\\mathfrak {M}$ is a positive op
 erator-valued measure on a measurable space $X$ with values in the set of 
 all positive bounded operators\n$B(H)_+$ in a separable Hilbert space $H$.
  If $g\\to U_g$ is a projective unitary representation of a group $G$ in $
 H$ and one can define an action of $G$\non $X$ by the rule $x\\in X \\to g
 x\\in X\,\\ g\\in G$\, then $\\mathfrak M$ is said to be covariant with re
 spect to $\\mathcal {U}=\\{U_g\,\\ g\\in G\\}$ under the condition $U_g\\m
 athcal {M}(B)U_g^*=\\mathfrak {M}(gB)$ for all measurable subsets $B\\subs
 et X$ and $g\\in G$. In quantum tomography theory we use a set of function
 s instead of a density operator $\\rho $. Using a covariant POVM $\\mathfr
 ak M$ equipped with a projective unitary representation $\\mathcal U$ we c
 an determines two possible functions of this kind. One is $f_{\\rho}(g)=Tr
 (\\rho U_g)$ and the other is $F_{\\rho }(B)=Tr(\\rho \\mathfrak {M}(B))$.
  The first function can be named a characteristic function of $\\rho $\, w
 hile the second one is associated with a measurement of $\\rho $ by $\\mat
 hfrak {M}$. We attribute these two functions to homodyne and heterodyne me
 asurements and discuss the connection between them.\n
LOCATION:https://researchseminars.org/talk/QOART/43/
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