Extending Heisenberg's measurement--disturbance relation to the twin-slit case

Abstract

Heisenberg's position-measurement--momentum-disturbance relation is derivable from the uncertainty relation $\sigma (q)\sigma (p)\ge \hslash /2$ only for the case when the particle is initially in a momentum eigenstate. Here I derive a new measurement--disturbance relation which applies when the particle is prepared in a twin-slit superposition and the measurement can determine at which slit the particle is present. The relation is $d\times \Delta p\ge 2\hslash /\pi$, where $d$ is the slit separation and $\Delta p=D_M(P_f,P_i)$ is the Monge distance between the initial $P_i(p)$ and final $P_f(p)$ momentum distributions.

10 pages, no figures. Begins by discussing Heisenberg's measurement-disturbance relation. Quotes from Heisenberg's works show that [contrary to the impression gained from the recent critique by M. Ozawa (quant-ph/0210044)] Heisenberg (at least in 1930) was careful in restricting the situation for which his measurement-disturbance relation could be derived from the uncertainty relation