Abstract. The quantum variance of a self-adjoint operator depends on a density matrix whose particular example is a pure state (formulated by a projection). A general variance can be obtained from certain variances of pure states. This is very different from the probabilistic case.

AMS Subject Classification (1991): 81Q50, 40C05

Keyword(s): density matrix, pure state, projection, variance

Received November 3, 2011, and in revised form February 18, 2012. (Registered under 57/2011.)