The laws of physics do not prohibit counterfactual communication

Counterfactual communication, the deterministic transmission of information without the exchange of physical carriers, has been a subject of debate. Early theoretical proposals and experimental demonstrations sparked skepticism, particularly regarding the nature of reality and the apparent violation of physical intuition. Questions arose about the mechanism of information transfer and the apparent discontinuous appearance of quantum bits. Griffiths' Consistent Histories criterion and Vaidman's weak trace criterion were used to assess the counterfactuality of proposed schemes. While a modified protocol by Aharonov and Vaidman satisfied Vaidman's criterion, it failed to meet Griffiths' criterion. This paper aims to present a scheme that unequivocally satisfies both criteria.

The paper reviews previous work on counterfactual communication, highlighting the Salih et al. 2013 protocol and its subsequent modifications. It discusses the contrasting viewpoints of Griffiths and Vaidman regarding the criteria for counterfactuality—Consistent Histories and weak trace, respectively. The authors note that while Aharonov and Vaidman proposed a modified protocol satisfying the weak trace criterion, it lacked fulfillment of the Consistent Histories criterion. This sets the stage for their proposed improved scheme.

The authors propose a protocol that aims for high accuracy in Alice determining Bob's bit choice while demonstrably ensuring that Alice's post-selected photons have not interacted with Bob. Their setup utilizes interaction-free measurement and the quantum Zeno effect. A schematic diagram (Fig. 1) illustrates the sequential steps, including polarization rotators, polarizing beam splitters (PBSs), and detectors. The probability of a photon taking different paths is analyzed, highlighting the importance of post-selection to filter out unwanted histories. The success of the protocol relies on the significantly higher probability of a photon reaching Alice's detector D7 when Bob does not block the channel. Accuracy can be tuned by adjusting the initial polarization rotation, with higher accuracy achieved at the cost of more photon loss. The authors emphasize that post-selection is passive and doesn't involve communication with Bob. The paper then uses consistent histories to analyze the paths of photons, demonstrating that histories where the photon interacts with Bob have zero probability in the relevant consistent families. The weak trace approach is employed by considering weak measurements, where the effect on the particle is negligible, yet the aggregate effect on many particles can provide information. Using the forward-evolving state formulation (TSVF), they show that the forward and backward evolving states do not overlap at Bob's location, resulting in zero weak values, confirming that the photons detected at Alice's detectors never interact with Bob. An experimental setup (Fig. 2) is described, using MEMS mirrors oscillating at different frequencies to enable weak measurements. The frequency analysis of the signals at various detectors (Fig. 3) confirms the absence of Bob's mirror frequencies at Alice's detectors, experimentally validating the counterfactual nature of the communication. The relationship between postselection success probability and accuracy is analyzed (Fig. 4), showing that the success probability can be made arbitrarily close to unity by adjusting the initial half-wave plate setting. The paper also directly addresses a counter example using the Aharonov–Vaidman protocol by showing it fails the consistent histories criterion through examination of specific histories (Fig. 5) and comparing the chain kets of those histories.

The key findings of the paper are: 1. A novel counterfactual communication protocol is proposed and experimentally demonstrated, where Alice's post-selected photons demonstrably never interact with Bob. 2. The protocol is shown to satisfy both the Consistent Histories criterion and the weak trace criterion for counterfactuality, addressing previous limitations of other schemes. 3. Experimental results using weak measurements confirm the absence of interaction between Alice's post-selected photons and Bob's apparatus. 4. The fidelity of Alice's learning of Bob's bit can be made arbitrarily close to unity by adjusting experimental parameters. 5. Analysis of the Aharonov-Vaidman modification of the Salih et al. protocol reveals that it does not satisfy the Consistent Histories criterion, despite meeting the weak trace criterion. These findings provide strong evidence against the assertion that counterfactual communication is impossible.

The results of this study strongly support the feasibility of counterfactual communication. The successful implementation of a protocol satisfying both the Consistent Histories and weak trace criteria demonstrates the counterfactual nature of the communication. The experimental verification using weak measurements adds further weight to this conclusion. The ability to achieve arbitrarily high fidelity enhances the practical implications of this finding. The analysis of the Aharonov-Vaidman protocol highlights the importance of considering both criteria for a complete assessment of counterfactuality. This research contributes significantly to our understanding of quantum mechanics and its implications for information processing and communication.

This paper presents a robust counterfactual communication protocol satisfying both major criteria for counterfactuality, experimentally verified via weak measurements. The high fidelity achievable demonstrates the practical potential of this approach. Future work could explore the application of this method in secure communication protocols or further investigate the fundamental implications for quantum mechanics.

While the experimental results strongly support the findings, potential limitations include experimental imperfections like noise and the leakage of light from Alice's path into D0. Furthermore, the protocol's efficiency, in terms of the number of photons required for successful communication, could be further optimized. The study focused on a specific setup; further investigation might be needed to determine the generality of these findings.