{"paper":{"title":"Covert Signaling for Communication and Sensing over the Bosonic Channels","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The optimal signal state for minimizing detectability in covert communication and sensing over lossy bosonic channels is a mixture of two consecutive photon-number states.","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Boulat A. Bash, Evan J.D. Anderson, Michael S. Bullock, Tianrui Tan","submitted_at":"2026-05-08T17:52:18Z","abstract_excerpt":"Preventing signal detection in communication and active sensing requires careful control of transmission power. In fact, the square-root laws (SRL) for covert classical and quantum communication and sensing prescribe that the average output energy per channel use scales as $1/\\sqrt{n}$ for $n$ channel uses. \\emph{Diffuse} and \\emph{sparse} signaling achieve this. The former transmits signals whose energy decays as $1/\\sqrt{n}$ over all $n$ channel uses, which is convenient for mathematical analysis. The latter transmits constant-energy signals only approximately $\\propto\\sqrt{n}$ times out of "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We characterize the input signal state that minimizes detectability. We find an unintuitive optimal quantum state structure: a mixture of just two consecutive photon-number states. In particular, in the low-brightness regime, the optimal signal state is a mixture of vacuum and a single photon.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis assumes the standard lossy thermal-noise bosonic channel model and that the eavesdropper's detection is governed by the square-root law framework without additional side information or non-standard noise statistics.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Sparse signaling over bosonic channels minimizes detectability with a two-consecutive-photon-number mixture (vacuum plus single photon at low brightness), revealing power thresholds that trade covertness against communication and sensing rates.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The optimal signal state for minimizing detectability in covert communication and sensing over lossy bosonic channels is a mixture of two consecutive photon-number states.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4599b9591e0b7ed9d4d52319804de160cdbce91f38c02a83ab5a46b5757178f2"},"source":{"id":"2605.08066","kind":"arxiv","version":2},"verdict":{"id":"4dc56212-b6cc-499c-86ce-808ea063e997","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-11T02:11:07.678836Z","strongest_claim":"We characterize the input signal state that minimizes detectability. We find an unintuitive optimal quantum state structure: a mixture of just two consecutive photon-number states. In particular, in the low-brightness regime, the optimal signal state is a mixture of vacuum and a single photon.","one_line_summary":"Sparse signaling over bosonic channels minimizes detectability with a two-consecutive-photon-number mixture (vacuum plus single photon at low brightness), revealing power thresholds that trade covertness against communication and sensing rates.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis assumes the standard lossy thermal-noise bosonic channel model and that the eavesdropper's detection is governed by the square-root law framework without additional side information or non-standard noise statistics.","pith_extraction_headline":"The optimal signal state for minimizing detectability in covert communication and sensing over lossy bosonic channels is a mixture of two consecutive photon-number states."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.08066/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T09:42:04.444927Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T04:39:49.897827Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T15:01:18.455696Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T11:15:14.019516Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"3a7b29888f10182d49d25de71dbe42071a4f457d0eef269dd0ce8cace44a8859"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}