Postselection-induced entanglement swapping from a vacuum-excitation entangled state to separate quantum systems

We show that a single particle in a superposition of different paths can entangle two objects located on each path. The entanglement has its maximum visibility for intermediate coupling strengths. In particular, when the two quantum systems with which the particle interacts are detectors that measure its presence and its polarization, a peculiar situation of entanglement in two separated systems that have never mutually interacted is realized.

Figure 1

Setup of a variant of the Mach-Zehnder interferometer. The source $S1$ emits a polarized particle that enters a beam splitter $BS1$ and exits in a coherent superposition of spatially separated states. In a sense, the particle is simultaneously in the left and in the right arm, as it can induce entanglement between two quantum systems $A$ and $B$, as can be evinced by measuring the cross moment between two observables $X$ and $Y$. The entanglement can be observed conditionally on the postselection, made by a judicious combination of a second beam splitter and of polarization-sensitive detectors $D_j$. The local unitary operators $V_j$ allow one to arbitrarily set the preparation $\Psi$ and the postselection $\Phi$.