Indirect Measurements of a Harmonic Oscillator

Abstract

The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model describing both system and apparatus and consisting of a harmonic oscillator coupled to a field. The equation of motion is a quantum stochastic differential equation. By solving it we establish the conditions ensuring that the two perspectives are compatible, in that the apparatus indeed measures the observable it is ideally supposed to.

On Entropy Production of Repeated Quantum Measurements I. General Theory

“…Such an instantaneous direct measurement is, of course, an idealization, most real measurements are indirect and require some finite time to complete (see[FGH19] for a concrete study).4 See [vN55, Section V.3]. In modern parlance, this follows from the operator-convexity of the function x → x log x, see, e.g.,[Car10].…”