  We propose a new protocol for the weak measurement of any observable with
remote pre and postselections. We show that if two parties share a pure
entangled state, then by using local operations and classical communication
they can preselect and postselect at distant locations leading to the weak
value of an observable as a shift in the pointer of the apparatus at one
location in the process of the weak measurement. This can be achieved with
either sharing of a pure maximally or non-maximally entangled state. We
generalize the protocol for realizing the weak value of any observable with
remote pre and postselection of mixed states. Finally, we show how the weak
value is modified in the remote pre and postselection setting if Alice and Bob
share a mixed entangled state.
