Extending Heisenberg's Measurement-Disturbance Relation to the Twin-Slit Case

Heisenberg's position-measurement-momentum-disturbance relation is derivable from the uncertainty relation (q)(p) h/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 × p 2h/, where d is the slit separation and p = D_M(P_f, P_i) is the Monge distance between the initial P_i(p) and final P_f(p) momentum distributions.