Partial Trace and Invariant Integration
In the case of finite dimensional Hilbert spaces, there is a useful way of looking at partial trace involving integration with respect to a suitably normalized Haar measure μ over the unitary group U(W) of W. Suitably normalized means that μ is taken to be a measure with total mass dim(W).
Theorem. Suppose V, W are finite dimensional Hilbert spaces. Then
commutes with all operators of the form and hence is uniquely of the form . The operator R is the partial trace of T.
Read more about this topic: Partial Trace
Famous quotes containing the words partial, trace and/or integration:
“It is characteristic of the epistemological tradition to present us with partial scenarios and then to demand whole or categorical answers as it were.”
—Avrum Stroll (b. 1921)
““In your company a man could die,” I said, “a man could die and you wouldn’t even notice, there’s no trace of friendship, a man could die in your company.””
—Max Frisch (1911–1991)
“The only phenomenon with which writing has always been concomitant is the creation of cities and empires, that is the integration of large numbers of individuals into a political system, and their grading into castes or classes.... It seems to have favored the exploitation of human beings rather than their enlightenment.”
—Claude Lévi-Strauss (b. 1908)