Quantum-communication protocol employing weak measurements

We propose a communication protocol exploiting correlations between two events with a definite time ordering: (a) the outcome of a weak measurement on a spin, and (b) the outcome of a subsequent ordinary measurement on the spin. In our protocol, Alice first generates a “code” by performing weak measurements on a sample of N spins. The sample is sent to Bob, who later performs a postselection by measuring the spin along either of two certain directions. The results of the postselection define the “key", which he then broadcasts publicly. Using both her previously generated code and this key, Alice is able to infer the direction chosen by Bob in the postselection. Alternatively, if Alice broadcasts publicly her code, Bob is able to infer from the code and the key the direction chosen by Alice for her weak measurement. Two possible experimental realizations of the protocols are briefly mentioned.