Abstract
We introduce the concept of a “classical observable” as an operator with vanishingly small quantum fluctuations on a set of density matrices. Their study provides a natural starting point to analyse the quantum measurement problem. In particular, it allows to identify Schrödinger cats and the associated projection operators intrinsically, without the need to invoke an environment. We discuss how our new approach relates to the open system analysis of quantum measurements and to thermalization studies in closed quantum systems.
Highlights
We introduce the concept of a “classical observable” as an operator with vanishingly small quantum fluctuations on a set of density matrices
An experiment corresponds to ‘reading’ its expectation value. This procedure corresponds in all cases to experimental practice, where there is always a link between the quantum system and our ‘knowing it’, that is described in terms of an expectation value and not in terms of a projection operator
T 2π/|ω1 − ω2|, the two harmonic oscillator ladders are indistinguishable within the Heisenberg limited energy resolution and we find that X = X1 X2 is still a classical observable, with C(X) = 1 − 2/N
Summary
We introduce the concept of a “classical observable” as an operator with vanishingly small quantum fluctuations on a set of density matrices. For the density matrix of a pure state ρ = |ψ ψ|, the projection operator P = |ψ ψ| is classical. In order to find operators that do remain classical under time evolution, we maximize
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