Modification of counterfactual communication protocols that eliminates weak particle traces

The possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, has been known for quarter of a century. The protocols of full communication, including transmitting unknown quantum states, were proposed only a few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace being larger than the trace left by a single particle passing through the channel. This made the claim of counterfactuality of these protocols at best controversial. However, a simple modification of these recent protocols eliminates the trace in the transmission channel, making all these protocols counterfactual.

Figure 1

Counterfactual detection of the presence of the shutter. (a) The interferometer is tuned in such a way that detector $D$ never clicks if the paths are free. (b) Alice knows that Bob chose bit 1 (blocked the path) when she observes the click in $D$. The gray thick line shows the trace left by the photon. The trace is not present in the transmission channel. (c) Forward (dashed green line) and backward (red pointed line) evolving wave functions of the photon.

Figure 2

Counterfactual detection of the absence of the shutter. (a) The inner interferometer is tuned to destructive interference toward the continuation in the large interferometer. (b) The whole interferometer is tuned such that when arm $B$ is blocked, detector $D$ cannot click. (c) There is a trace in arm $C$ and inside the inner interferometer. In particular, there is a trace in the transmission channel which contradicts counterfactuality of the protocol. (d) The overlap of the forward and the backward evolving waves explains the weak trace in the interferometer.

Figure 3

Modified bit 0 counterfactual communication. (a), (b) describe the tuning of the interferometer: (a) the forward evolving wave function when there are no shutters and (b) with the shutters; the whole interferometer is tuned such that when arms $B$ and $B^{\prime }$ are blocked, detector $D$ cannot click. (c) Forward and backward evolving states. (d) Trace of the photon.

Figure 4

(a), (b) One element of the chain of interferometers according to the old proposal for counterfactual communication. (a) Forward and backward evolving states. (b) The weak trace. (c), (d) The same for the modified element of the chain of the counterfactual protocol. There is no trace in the communication channel.