On the correspondence between classical and quantum measurements on a bosonic field

Details On the correspondence between classical and quantum measurements on a bosonic field On the correspondence between classical and quantum measurements on a bosonic field

1999-07-16

arxiv.org/abs/quant-ph/9907057v1

Int.J.Mod.Phys. B13 (1999) 3069-3086

Physics

Quantum Physics

RevTex. 17 pages. 1 eps figure. To appear on Mod. Phys. Lett. B

Scientific paper

10.1142/S0217979299002861

We study the correspondence between classical and quantum measurements on a harmonic oscillator that describes a one-mode bosonic field. We connect the quantum measurement of an observable of the field with the possibility of amplifying the observable ideally through a quantum amplifier. The ``classical'' measurement corresponds to the joint measurement of the position $q$ and momentum $p$ of the harmonic oscillator, with following evaluation of a function $f$ of the outcome $\alpha=q+ip$. For the electromagnetic field the joint measurement is achieved by a heterodyne detector. The quantum measurement of an observable $\hat O$ is obtained by preamplifying the heterodyne detector through an ideal amplifier of $\hat O$, and rescaling the outcome by the gain $g$. We give a general criterion which states when this preamplified heterodyne detection scheme approaches the ideal quantum measurement of $\hat O$ in the limit of infinite gain. We show that this criterion is satisfied and the ideal measurement is achieved for the case of the photon number operator and for the quadrature. For both operators the method is robust to nonunit quantum efficiency of the heterodyne detector. On the other hand, we show that the preamplified heterodyne detection scheme does not work for arbitrary observable of the field. As a counterexample, we prove that the simple quadratic function of the field $\hat K=i(a^{\dag 2}-a^2)/2$ has no corresponding polynomial function $f(\alpha,\bar \alpha)$---including the obvious choice $f=\hbox{Im}(\alpha^2)$---that allows the measurement of $\hat K$ through the preamplified heterodyne measurement scheme.

Affiliated with

Also associated with

No associations

Rating

On the correspondence between classical and quantum measurements on a bosonic field does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the correspondence between classical and quantum measurements on a bosonic field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the correspondence between classical and quantum measurements on a bosonic field will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-162974