{"id":"2a31210d-dbbe-476b-950b-876e288a19eb","arxiv_id":"2507.19563","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A reply defending the counterfactual communication protocol by showing that Popescu's simplified scheme only communicates all-1s messages and is not equivalent to the original.","lead":"This paper replies to Popescu's critique of the authors' 2022 claim that counterfactual communication, sending a message without exchanging particles, is possible. It argues Popescu's simplified version is a different protocol that cannot send arbitrary messages, so the critique misses the original postselected setup.","discovery_kind":"incremental","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reply never derives the transfer of the toy protocol's no-particle conclusion to the multi-cycle protocol that actually transmits arbitrary messages.","rationale":"I read the reply as having two parts: (1) a logical refutation of Popescu's simplification, and (2) a defense of the postselected counterfactuality claim. Part (1) is sound: replacing the coin with a fixed block of pN live runs changes the statistics, and the reply correctly shows that under either natural reading of 'N runs', only all-ones messages survive in Popescu's simplified scheme. Part (2) is where the load-bearing gap sits. The authors themselves flag that their toy protocol can produce erroneous '0-bit' clicks while the multi-cycle protocol cannot; this means the toy and full protocol have different interference properties. The reply asserts applicability to the full protocol but provides no calculation of weak traces or consistent histories for the multi-cycle case, instead citing prior work. The self-flagged limitation that alternative path criteria would change the conclusion further weakens the unconditional reading of 'no particles are exchanged'. The cited experiment was performed on the single-cycle toy, not on the full protocol used for arbitrary messages. These considerations do not overturn the reply's valid point about Popescu's oversimplification, but they do prevent the reply from decisively resolving the controversy. The reader's CONDITIONAL verdict is therefore appropriate, and my concern identifies the same weakest assumption with a concrete way to settle it.","tokens_in":5181,"tokens_out":10250,"duration_ms":110531,"concrete_test":"Independently compute the weak-trace and consistent-histories assignment for the full two-outer-cycle Michelson-type protocol of Salih et al. (PRL 110, 170502), not the one-cycle toy, for both Bob settings (block and no-block) and for postselected D0/D1 outcomes. Write the explicit unitary for the two nested interferometers, including outer-cycle interference, and calculate the weak value of the projector onto Bob's channel as well as the consistent-history weights for paths that visit Bob. If either quantity is nonzero in the multi-cycle protocol, the toy is not representative and the reply's transfer claim fails; if both vanish, the concern is resolved. This check should be done directly, without relying on the authors' citation [11].","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reply's own text concedes that the toy protocol 'can give erroneous “0-bit” clicks, while in two-or-more outer-cycle versions of Salih et al's protocol, this is not the case'. That is a functional difference, not a cosmetic one: the multi-cycle protocol uses outer-interferometer interference precisely to suppress those erroneous clicks, while the toy omits that interference. The reply nevertheless asserts, without a derivation, that conclusions from the single-outer-cycle toy apply to any outer cycle of the full protocol. The only support offered is a parenthetical citation to [11] and the claim that in the relevant case no outer interference takes place, just as in the toy. But if that were literally true, the full protocol would not suppress the toy's erroneous '0-bit' clicks. Consequently, the central claim that postselected photons have never been to Bob—verified by weak trace and consistent histories—is established only for the toy, not for the protocol used to send arbitrary messages. The reply also concedes that 'one could quite easily come up with alternative definitions for particle presence, which would lead to different conclusions', so the no-particle conclusion is criterion-relative. Since Popescu's Comment challenges exactly this transfer, the reply leaves the decisive step unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript is a reply to Popescu's Comment on Salih et al. (2022), 'The laws of physics do not prohibit counterfactual communication'. The authors argue that Popescu's simplification is not equivalent to their protocol: with one run per bit, the simplified scheme can only communicate the all-1s message; with N runs per bit, it uses failed-run information that the original protocol discards. They further argue that, in the postselected case (detections at D0 or D1), their protocol lets Bob communicate an arbitrarily long binary message with arbitrarily high accuracy, and that by the weak trace and consistent histories criteria the postselected photons have never been to Bob. The reply relies on a single-outer-cycle toy protocol to establish the no-particle conclusion and asserts that this conclusion transfers to the full multi-cycle protocol that transmits arbitrary messages.","tokens_in":5386,"tokens_out":10736,"duration_ms":92542,"significance":"If the reply's central claims are correct, it would refute Popescu's Comment and defend the original paper's conclusion that the laws of physics do not prohibit counterfactual communication under the weak trace and consistent histories criteria. The reply usefully clarifies the distinction between the actual protocol and Popescu's simplification, and it correctly emphasizes that postselection is an essential part of the protocol. However, the significance is limited because the key no-particle conclusion is established only for a toy protocol, while the transfer to the full protocol is asserted without derivation. The paper also explicitly concedes that the conclusion is criterion-relative, which tempers the strength of the claim as stated in the abstract.","major_comments":[{"comment":"The reply's central claim—that postselected photons never visit Bob in the protocol that actually transmits arbitrary messages—depends on transferring the single-outer-cycle toy protocol's no-particle conclusion to the full multi-cycle protocol. This transfer is asserted, not derived. The reply concedes that the toy protocol 'can give erroneous “0-bit” clicks, while in two-or-more outer-cycle versions of Salih et al's protocol, this is not the case' and that the toy 'lacks features (e.g., interference between inner and outer path of outer interferometer) which Salih et al's 2013 protocol possesses.' It then asserts that this does not matter because 'when the inner interferometers are not blocked—i.e., bit “0”—no interference should take place in the outer interferometers, just as in the present single-outer-cycle protocol.' This is internally inconsistent: if no outer interference occurred in the relevant case, the multi-cycle protocol could not suppress the toy's erroneous clicks; if it does suppress them, the multi-cycle protocol has different interference properties in exactly the regime the no-particle conclusion must cover. The only support offered for the transfer is a citation to [11] without a specific result. The authors need to provide an explicit derivation or a precise theorem statement from [11], or limit the no-particle claim to the toy protocol.","section":"Toy protocol transfer (paragraphs 2–3)"},{"comment":"The bit labeling in the transfer argument is inconsistent with the protocol definition quoted earlier in the reply. The reply quotes from [2]: 'He blocks (does not block) his channel when X = 0 (X = 1).' But then it states: 'when the inner interferometers are not blocked—i.e., bit “0”—no interference should take place in the outer interferometers.' If bit '0' corresponds to blocking, then 'inner interferometers are not blocked' describes bit '1'. This inconsistency obscures which physical configuration is being analyzed. Since the rebuttal of Popescu's simplification depends on correctly identifying the 'counterfactual' bit configuration, the authors must correct this inconsistency and restate the argument coherently.","section":"Bit labeling in the transfer argument"},{"comment":"The reply both claims that the communication protocol is 'not a matter of interpretation' and concedes that 'one could quite easily come up with alternative definitions for particle presence, which would lead to different conclusions' and that a protocol being counterfactual 'by said criteria does not rule out there being indirect influences between Alice and Bob.' These statements are in tension: the abstract and conclusion assert that 'no particles are exchanged in the course of this communication' and 'the laws of physics do not prohibit counterfactual communication,' which read as unconditional claims. As written, the reply oscillates between a criterion-relative claim (about weak trace and consistent histories) and a stronger unconditional claim. The authors should either state the conclusion explicitly as conditional on these criteria throughout, or argue why these criteria are the correct ones for judging counterfactual communication.","section":"Criterion-relativity of the conclusion"}],"minor_comments":[{"comment":"The abstract contains a typo: 'creteria' and a double closing parenthesis 'path)).'","section":"Abstract"},{"comment":"The sentence 'one of the two aims of the protocol we construct in our paper construct one where' is ungrammatical and should be rewritten.","section":"Paragraph 1"},{"comment":"The phrase 'as does reference [11]' is vague; the authors should cite a specific section or theorem in [11] that establishes the transfer from the single-outer-cycle toy protocol to the full protocol.","section":"Paragraph 3"},{"comment":"The terms 'outer cycle' and 'inner interferometer' are used without definition; a brief definition or a pointer to the original paper would help readers who do not have [2] or [3] at hand.","section":"Paragraph 3"},{"comment":"The conclusion states that the reply has 'prove[n] experimentally using a setup consisting of a single outer cycle' the central claim, but the experimental setup is not described in this reply; citing [2] is acceptable, but the wording may overstate the directness of the evidence presented here.","section":"Conclusion"}],"recommendation":"major_revision","confidential_remarks":"This is a direct reply to a Comment, so the review should weigh the reply's scope. The most serious issue is the unproven transfer from the toy protocol to the full protocol, which the authors may be able to fix by providing a rigorous argument or a precise citation to [11]. The editor should check whether [11] indeed contains the claimed transfer result, since the reply cites it without specifics. The reply also relies heavily on the authors' own prior publications, which is expected in a reply but merits attention to ensure that citations are not being used in place of derivation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe reply makes one sharp point that survives contact with Popescu's Comment: his coin-free simplification is not their protocol. If you run the original protocol once per bit, the only N-bit message that can survive postselection is the all-ones string. Any other message fails, and you cannot fall back on the failed runs without using information Popescu said was unnecessary. That is a correct and pointed observation, and the authors are right to insist that the Comment's scheme has different statistics.\n\nThe paper is also honest about its own limits. They concede the toy protocol gives erroneous '0-bit' clicks that the multi-cycle version suppresses, and they admit that alternative definitions of particle presence would change the counterfactuality verdict. Those admissions are welcome.\n\nThe soft spot is the transfer step. The stress-test note is on target: the reply asserts, without deriving, that conclusions from the single-outer-cycle toy apply to every outer cycle of the 2013 protocol. The toy lacks outer-interferometer interference; the full protocol uses that interference precisely to fix the erroneous clicks. The authors try to have it both ways—saying no outer interference matters in the relevant case, while also relying on outer interference to make the full protocol work. If the toy really were representative, the full protocol would inherit its errors, and if the full protocol really suppresses them, the toy is not representative. The reply gives no calculation that bridges this, only a citation to [11].\n\nThe broader claim that postselected photons never visit Bob also remains criterion-relative. The reply's no-particle conclusion is established for the weak-trace and consistent-histories notions of path, and the authors themselves note that other criteria yield other answers. That is not a flaw in the reply's narrow logical point, but it does mean the reply does not decisively resolve the underlying controversy.\n\nWho should read this? Anyone tracking the counterfactual communication exchange. It is a competent reply, not a new result. The narrow point about the all-ones message is worth having on record. If this is submitted as a formal reply, it deserves peer review; a referee should focus on the toy-to-full-protocol transfer and ask for a derivation. I would not cite it in my own work, but I would bring it to the attention of people working on counterfactual protocols.\n\nRecommendation: send for peer review if the venue publishes replies. The logical rebuttal is sound, but the transfer step needs to be defended properly.","headline":"A competent reply that scores a real point about Popescu's simplification, but the toy-to-protocol transfer is asserted without derivation and the larger counterfactuality dispute remains open.","tokens_in":5905,"tokens_out":3017,"would_cite":false,"duration_ms":28833,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper argues that a critique of counterfactual communication replaces the postselected protocol with a different one, and that under the actual protocol any arbitrarily long binary message can be sent with arbitrarily high accuracy…","keywords":["counterfactual communication","postselection","weak trace","consistent histories","nested Mach-Zehnder interferometer","interaction-free measurement","quantum communication"],"falsifier":"A sensitive probe of whether the photon spends any time in Bob's arm, conditioned on Alice detecting the photon at D0 or D1 in the full multi-outer-cycle protocol, would settle the claim: any nonzero trace at Bob's location would show that a particle did visit him in an accepted run, contradicting the central counterfactuality claim.","tokens_in":4985,"feed_emoji":"⚛️","tokens_out":8921,"duration_ms":79114,"temperature":0.7,"pith_summary":"This is a reply to a Comment that claimed the 2022 counterfactual communication protocol does not work. The reply argues that the Comment misreads the claim: counterfactuality applies only to postselected runs, the ones in which Alice's photon triggers detector D0 or D1, and all other runs are discarded. It further argues that the Comment's simplified setup is a different protocol—one that can successfully transmit essentially only an all-ones message—whereas the original protocol lets Bob send any arbitrarily long binary string with arbitrarily high accuracy. If the reply is right, counterfactual communication remains compatible with the weak trace and consistent histories criteria for particle path, and the central 2022 conclusion stands.","feed_headline":"Postselected photons keep counterfactual communication alive","feed_subtitle":"For runs that succeed, any long binary message gets through with no photon visiting Bob under either path test.","key_machinery":"The load-bearing object is the postselected nested-interferometer protocol: a single-outer-cycle, Michelson-type layout in which Bob encodes a bit by blocking (0) or not blocking (1) the inner interferometer, and Alice keeps only outcomes D0 or D1. Postselection on those two detectors is what makes the counterfactuality claim well-defined: every discarded run is removed from the data, so the accepted message contains only rounds in which the photon demonstrably did not reach Bob, by the weak trace criterion and the consistent histories framework. The single-outer-cycle design is chosen so that those path analyses are tractable while still reproducing the no-interference-in-outer-arm behaviour relevant to bit 0 in the full multi-cycle protocol.","core_discovery":"The central claim is that the Comment attacks a protocol the authors did not present. In the protocol under discussion, Alice accepts a round only if her photon arrives at D0 (bit 0) or D1 (bit 1); any round ending at D3 or at Bob's blocker is thrown out along with the whole message it belongs to. Under that postselection, the reply states, any N-bit message chosen by Bob can be transmitted, with the accuracy made as high as desired by discarding more runs, and in every accepted run the photon has not been to Bob according to both the weak trace and consistent histories path criteria. The reply also defends the single-outer-cycle toy setup used in the 2022 paper as sufficient for testing exactly those path criteria, and notes that the Comment's coin-toss simplification changes the statistics rather than merely simplifying the optics.","pith_inferences":["Editorial inference: the reply effectively concedes that postselection does real work—Alice learns a message is invalid precisely because a photon went to Bob in other runs—so the result is best read as 'communication is possible using postselected counterfactual outcomes,' not as a claim that every emitted photon is counterfactual.","Editorial inference: the dispute is partly about which definition of a particle's path is authoritative; on a different path criterion, the same optics could receive a different counterfactuality verdict.","Editorial inference: a direct weak-trace calculation for the full multi-outer-cycle protocol, rather than the single-cycle analogue, would close the main gap the Comment identifies; the reply leaves that transfer asserted."],"forward_implications":["If the reply is correct, the Comment's simplification does not describe the same communication task: it can successfully transmit essentially only the all-ones message, while the postselected protocol transmits any N-bit string.","Any message that survives postselection is fully correlated with Bob's bits, so Alice never has to extract information from failed runs; discarding them does not weaken the communication claim.","The weak trace and consistent histories criteria, which motivated earlier objections, do not by themselves rule out counterfactual communication; the demonstration for one outer cycle is meant to transfer to each outer cycle of the full protocol.","Because the claimed result holds for postselected particles, it supports extending the same reasoning to counterfactual qubit transport, counterfactual ghost imaging, and exchange-free computation."],"supporting_citations":[{"why":"The Comment under reply; supplies the simplifications and objections that define the dispute.","marker":"[1]"},{"why":"The 2022 protocol being defended; establishes the postselected D0/D1 definition and the 16-bit example.","marker":"[2]"},{"why":"The original 2013 direct counterfactual communication protocol whose outer cycles the toy setup reproduces.","marker":"[3]"},{"why":"Supplies the weak trace criterion used to certify that the photon never visited Bob in accepted runs.","marker":"[4]"},{"why":"Supplies the consistent histories framework used as the second path criterion for counterfactuality.","marker":"[5]"},{"why":"Invoked to support transferring conclusions from the single-outer-cycle toy protocol to the full multi-cycle protocol and to broader counterfactual tasks.","marker":"[11]"},{"why":"Shows that removing the coin toss from the protocol was already known not to violate counterfactuality, rebutting one part of the Comment.","marker":"[16]"}],"fun_headline_variants":["Postselection keeps counterfactual comms alive","Reply: postselected photons refute the comment","Counterfactual comms survive via postselection","No photon at Bob: postselection saves the protocol","Postselect and communicate: counterfactual works"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The defense rests on the assumption that the simplified one-cycle version of the interferometer behaves like any single cycle of the full multi-cycle protocol; the Comment disputes this transfer, and the reply asserts it without presenting a new derivation.","fun_headline_variants_meta":{"raw":{"variants":["Postselection keeps counterfactual comms alive","Reply: postselected photons refute the comment","Counterfactual comms survive via postselection","No photon at Bob: postselection saves the protocol","Postselect and communicate: counterfactual works"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000348,"raw_usage":{"total_tokens":1895,"prompt_tokens":927,"completion_tokens":968,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":543,"completion_tokens_details":{"reasoning_tokens":896}},"tokens_in":543,"tokens_out":968,"duration_ms":8803,"temperature":1.0,"reasoning_tokens":896,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:53:26.796980+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A sensitive probe of whether the photon spends any time in Bob's arm, conditioned on Alice detecting the photon at D0 or D1 in the full multi-outer-cycle protocol, would settle the claim: any nonzero trace at Bob's location would show that a particle did visit him in an accepted run, contradicting the central counterfactuality claim.","supporting_citations":[{"cited_title":"Counterfactual communication not achieved yet – A Comment on Salih et al","cited_arxiv_id":null,"evidence_quote":"The Comment under reply; supplies the simplifications and objections that define the dispute."},{"cited_title":"The laws of physics do not prohibit counterfactual communication","cited_arxiv_id":null,"evidence_quote":"The 2022 protocol being defended; establishes the postselected D0/D1 definition and the 16-bit example."},{"cited_title":"Protocol for direct counterfactual quantum communication","cited_arxiv_id":null,"evidence_quote":"The original 2013 direct counterfactual communication protocol whose outer cycles the toy setup reproduces."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the weak trace criterion used to certify that the photon never visited Bob in accepted runs."},{"cited_title":"Consistent Quantum Theory","cited_arxiv_id":null,"evidence_quote":"Supplies the consistent histories framework used as the second path criterion for counterfactuality."},{"cited_title":"From counterportation to local wormholes","cited_arxiv_id":null,"evidence_quote":"Invoked to support transferring conclusions from the single-outer-cycle toy protocol to the full multi-cycle protocol and to broader counterfactual tasks."},{"cited_title":"After the paper: Traversable wormhole in the laboratory","cited_arxiv_id":null,"evidence_quote":"Shows that removing the coin toss from the protocol was already known not to violate counterfactuality, rebutting one part of the Comment."}],"review_version":2}