The laws of physics do not prohibit counterfactual communication

The work addresses whether deterministic communication can occur without any physical carriers (e.g., photons) traversing the communication channel to the receiver, a notion known as counterfactual communication. Prior skepticism arose over what carries information across space and whether such schemes truly avoid particles entering the channel, especially in quantum versions like the Salih et al. 2013 protocol. The paper targets two main goals: (i) enabling Alice to infer Bob’s bit with arbitrarily high accuracy, and (ii) demonstrating unambiguously that the photons Alice post-selects to learn Bob’s message were never at Bob’s location. The authors frame the debate using two criteria for counterfactuality: Vaidman’s weak trace (zero first-order weak signal at the receiver’s site) and Griffiths’ Consistent Histories (CH) criterion (no nonzero chain-ket histories placing the photon at Bob in any consistent family compatible with the post-selection). They aim to satisfy both simultaneously, countering claims that counterfactual communication is impossible even with post-selection.

Early proposals and demonstrations of interaction-free and counterfactual communication leveraged interaction-free measurement and the quantum Zeno effect. Critiques include Griffiths’ CH-based argument against counterfactuality and Vaidman’s weak-trace-based argument that a particle ‘was’ wherever weak values are nonzero. Aharonov and Vaidman proposed a modification of the 2013 Salih protocol to satisfy the weak-trace criterion, suggesting counterfactuality is attainable; however, the present authors argue that modification fails the CH criterion due to non-orthogonal chain kets in relevant histories. Thus, existing literature provided partial satisfaction of criteria, motivating a scheme meeting both.

Protocol setup: The authors implement a single (outer) cycle of the 2013 Salih et al. counterfactual communication protocol arranged sequentially in time. The scheme employs polarization optics: a source emits H-polarized single photons; HWP1 sets the initial H/V amplitudes; PBS transmits H along arm A and reflects V along arm B; additional HWPs and PBSs implement an inner interferometer chain akin to a quantum Zeno effect region near Bob. Detectors D0, D1, D2, D3, etc., register outputs. Bob encodes a bit by either blocking the transmission channel (bit corresponding to ‘block’) or leaving it open (not blocking). The protocol uses passive post-selection: Alice accepts only runs where her detectors D0 or D1 click (no communication with Bob during post-selection). By tuning HWP1 to make the initial state closer to V, accuracy approaches unity at the cost of a lower survival (post-selection) probability and increased photon loss to Bob’s blocker when he blocks. Consistent Histories analysis: The authors define families of histories with projectors onto spatial arms (A, B, C, etc.) and polarization (H, V) at successive times t0, t1, t2, t3, followed by a final projector onto the post-selected output arm/polarization (e.g., F, H). They compute chain kets for all histories compatible with detection at Alice’s chosen post-selection port. For the relevant consistent family (mutually orthogonal nonzero chain kets), all histories that include projectors corresponding to paths reaching Bob (e.g., Cj) have zero weights due to the final state projector onto F,H and the unitary evolution of the inner interferometer chain. Therefore, conditioned on successful post-selection at Alice, the photon was never at Bob with probability 1 in CH terms. They contrast this with the Aharonov–Vaidman modification, where they exhibit non-orthogonal, nonzero chain kets (e.g., a path including C2, B3) demonstrating inconsistency of the histories family and thus failure of CH-based counterfactuality in that variant. Weak-trace experiment: To test the weak-trace criterion, they implement a tabletop optical setup with polarizing beamsplitters (Thorlabs PBS251), half-wave plates (Thorlabs AHWP05-600), a 635 nm CW diode laser (Nanosystems LD635) acting as a heralded-like source for low-power beams, and MEMS mirrors (MikroSysteme A13227037) that introduce weak, distinct-frequency tilts: Alice’s mirror Ma oscillates at one frequency, and Bob’s mirrors M1 and M2 at two distinct frequencies. Position-sensitive quadrant detectors (Thorlabs PQ200B) at D0, D1, D2 sample at 25 kHz (LeCroy Versafire 452). A Fast Fourier transform of the beam position signals reveals the presence or absence of the mirrors’ oscillation frequencies. The forward- and backward-evolving states (TSVF reasoning) do not overlap at Bob for the relevant pre- and post-selection, predicting zero weak value at Bob. Beyond first-order, any disturbance from Bob’s vibrating mirrors would redirect light away from the post-selected detector (towards other detectors), ensuring that the post-selected signal at D0 (or D1) contains no imprint of Bob’s frequencies. Experimentally, spectra at D0 show Alice’s frequency but not Bob’s, consistent with zero weak trace at Bob for photons contributing to the post-selected outcome. Performance characterization: The scheme’s behavior is parameterized by P, the probability the photon enters the inner interferometer chain (set by HWP1). For an idealized infinite inner-cycle limit: if Bob blocks, detection probabilities are D0: 1−P, D1: P, D3 (loss): 0; if Bob does not block, D0: 1−P, D1: 0, D3 (loss): P. With an initial example (photon in arm A with probability 1/3 and in arm B with probability 2/3, many inner cycles to suppress loss), D1 achieves 100% accuracy when it clicks, while D0’s accuracy is 75%, with about half the photons lost on average. By choosing HWP1 to bias closer to V (smaller P of entering Bob’s side), the fidelity of Alice’s inference can be made arbitrarily close to unity, at the cost of reduced post-selection survival probability.

• Counterfactuality under Consistent Histories: For the authors’ scheme and post-selected detections at Alice, all histories that would place the photon at Bob have zero weight in consistent families, implying the post-selected photons have never been to Bob (probability 1 under CH).
• Weak-trace criterion satisfied: Weak measurements implemented via vibrating mirrors show that post-selected detections at Alice’s detector carry no frequency tags from Bob’s mirrors, while Alice’s own mirror frequency is present. Thus, the weak value at Bob is zero for post-selected photons, experimentally demonstrating counterfactuality.
• Tunable fidelity: By adjusting HWP1 to reduce the photon’s chance of entering the inner chain, the fidelity of Alice’s bit inference can approach unity arbitrarily closely, though with reduced post-selection survival probability.
• Example performance: For an illustrative setting where the photon starts with probabilities 1/3 (arm A) and 2/3 (arm B) and many inner cycles, D1 clicks correspond perfectly to one bit value (100% accuracy), while D0 has 75% accuracy; roughly half the photons are lost on average in that setting.
• Analytical probabilities (infinite inner cycles): If Bob blocks: P(D0)=1−P, P(D1)=P, P(loss at D3)=0. If Bob does not block: P(D0)=1−P, P(D1)=0, P(loss at D3)=P.
• Comparative analysis: The Aharonov–Vaidman modification can satisfy the weak-trace criterion for both bits but fails the CH criterion due to non-orthogonal nonzero chain kets, so it cannot be deemed counterfactual under CH, unlike the present scheme.

The findings directly address the central question of whether true counterfactual communication—learning Bob’s bit without any of Alice’s informative photons entering Bob’s region—is possible. The authors’ protocol simultaneously satisfies two stringent criteria: (i) experimentally, the weak-trace condition shows no detectable influence from Bob’s mirrors in post-selected detections; (ii) conceptually, the Consistent Histories framework excludes any nonzero history where these post-selected photons reach Bob. This dual validation reduces loopholes present in earlier interpretations relying on a single criterion. The protocol moreover allows the fidelity of bit inference to be tuned arbitrarily close to unity via the initial polarization setting, though at the expense of decreased post-selection probability. The comparison with Aharonov–Vaidman highlights that merely null weak traces are insufficient; CH consistency is also required to claim counterfactuality. The results strengthen the case that the laws of physics do not forbid counterfactual communication and clarify the conditions under which such claims are valid.

The paper presents a protocol and experimental evidence demonstrating counterfactual communication that satisfies both weak-trace and Consistent Histories criteria: informative, post-selected photons detected by Alice were never at Bob. The scheme’s fidelity can be tuned arbitrarily close to unity, supported by both analytical probabilities and observed weak-measurement signatures. This advances foundational understanding of quantum information transfer without particle exchange and reconciles debates by fulfilling dual criteria. Future work could target improving efficiency (raising post-selection survival probability), mitigating losses and experimental imperfections, exploring security aspects, extending to multi-bit and higher-dimensional encodings, and integrating design features that preserve CH consistency while further suppressing inner-interferometer error pathways.

• Efficiency trade-off: Achieving near-unity fidelity requires tuning that lowers the post-selection survival probability, reducing throughput and increasing average photon loss.
• Not a security protocol: The authors do not claim security; potential side channels or exotic effects might leak information.
• Experimental imperfections: Residual leakage and imperfect interference can introduce small erroneous signals; some spurious peaks and harmonics are observed, though below noise at the relevant detector.
• Demonstrated for one outer cycle and idealized infinite inner-cycle analysis; practical multi-cycle implementations may face stability and alignment challenges.