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

Heisenberg's position-measurement-momentum-disturbance relation is derivabl e from the uncertainty relation sigma(q) sigma(p) greater than or equal to h/2 only Sol the case when the particle is initially in a momentum eigensta te. Here I derive a new measurement-disturbance relation which applies when the particle is prepared in a twin-slit slope, position and the measuremen t can determine iii I which Slit the particle is present. The relation is d x Delta p greater than or equal to 2h/pi, where d is the slit separation a nd 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.