Instantaneous Measurement of Nonlocal Variables

It is shown, under the assumption of the possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously, except for a finite time required for bringing to one location the classical records from these sites which yield the result of the measurement. It is a verification measurement: it yields reliably the eigenvalues of the nonlocal variables, but it does not prepare the eigenstates of the system.

Figure 1

The scheme of the measurement of a nonlocal variable of a two-part system. In the example shown, the results of the Bell measurement in Bob’s site were $n,M,1$. Thus, the nonlocal measurement has been essentially completed after three teleportation rounds.