  Nonlocal measurement, or instantaneous measurement of nonlocal observables,
is a considerably difficult task even for a simple form of product observable
since relativistic causality prohibits interaction between spacelike separate
subsystems. Following a recent proposal for effectively creating the von
Neumann measurement Hamiltonian of nonlocal observables [Brodutch and Cohen,
Phys. Rev. Lett. 116, 070404 (2016)], here we report a proof-of-principle
demonstration of nonlocally measuring a product observable using linear optics
without the violation of relativistic causality. Our scheme provides a feasible
approach to perform nonlocal measurements via quantum erasure with linear
optics.
