Postselection and counterfactual communication

A recently proposed quantum protocol for counterfactual communication [Y. Aharonov and L. Vaidman, Phys. Rev. A 99, 010103(R) (2019)] relies on postselection to eliminate the weak trace in the transmission channel. We show that the postselection in this protocol additionally eliminates the flow of Fisher information from transmitter to receiver. However, we also show that a classical communication protocol with postselection can be counterfactual. Hence, we argue that postselection should not be allowed in genuine quantum counterfactual communication. In the proposed quantum protocol, the probability of discarding an event by postselection tends to zero with an increasing number of ideal optical components. But the counterfactual violation strength tends to infinity at a faster rate. Consequently, the quantum protocol is not counterfactual proper.

Figure 1

The doubly nested Mach-Zehnder interferometer as used in the reduced CFC protocol of Ref. [17]. Solid and open rectangles represent mirrors and beam splitters, respectively. Bob can insert mirrors (0-bit process) or detectors (1-bit process) in his laboratory. Vanishingly weak polarization rotations have been inserted at both locations where Alice's photon can enter Bob's laboratory. The detectors detect single photons and their polarization.