{"paper":{"title":"Quantum-Enhanced Single-Parameter Phase Estimation with Adaptive NOON States","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Optimizing eight circuit parameters via gradient descent on Fisher information raises NOON-state phase sensing from 36 percent to 58 percent of the Heisenberg limit at N=5 and multiplies useful events per pulse by up to 133 times.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Nandan S Bisht, Simanshu Kumar","submitted_at":"2026-04-14T05:55:58Z","abstract_excerpt":"Quantum metrology promises phase sensitivity surpassing the shot-noise limit by exploiting entanglement and photon-number correlations. NOON states-maximally path-entangled $N$-photon superpositions $(|N,0\\rangle + |0,N\\rangle)/\\sqrt{2}$ -achieve the Heisenberg limit $1/N$ for single-parameter estimation, as demonstrated experimentally by Afek et al. (2010) using hybrid coherent-plus-squeezed light up to $N=5$. We present an end-to-end differentiable quantum-optical framework-implemented in Strawberry Fields (Killoran et al., 2019) with a TensorFlow backend -that learns optimal circuit paramet"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The optimised probe reaches 82% of the Heisenberg limit at N=2 and improves from 36% to 58% at N=5, while useful measurement events per pulse improve by 8× to 133× across all N, making quantum-enhanced sensing at N≥3 experimentally practical.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the Strawberry Fields simulation with the chosen loss and noise model faithfully reproduces real experimental imperfections and that the Adam-optimized parameters found in simulation will translate directly to improved performance in a physical setup without additional unmodeled effects.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Optimizing eight circuit parameters via gradient descent on classical Fisher information yields up to 1598% CFI gains and 133x more useful events per pulse for N=5 NOON states, pushing performance closer to the Heisenberg limit than the Afek et al. 2010 setup.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Optimizing eight circuit parameters via gradient descent on Fisher information raises NOON-state phase sensing from 36 percent to 58 percent of the Heisenberg limit at N=5 and multiplies useful events per pulse by up to 133 times.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"256a713260fbb52bb9283b85cf3546dc5518a2042299a81bc8186ad6c6eb3d00"},"source":{"id":"2604.12323","kind":"arxiv","version":4},"verdict":{"id":"bd5b1c53-61eb-4303-9e36-4b3133eee041","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:07:48.094331Z","strongest_claim":"The optimised probe reaches 82% of the Heisenberg limit at N=2 and improves from 36% to 58% at N=5, while useful measurement events per pulse improve by 8× to 133× across all N, making quantum-enhanced sensing at N≥3 experimentally practical.","one_line_summary":"Optimizing eight circuit parameters via gradient descent on classical Fisher information yields up to 1598% CFI gains and 133x more useful events per pulse for N=5 NOON states, pushing performance closer to the Heisenberg limit than the Afek et al. 2010 setup.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the Strawberry Fields simulation with the chosen loss and noise model faithfully reproduces real experimental imperfections and that the Adam-optimized parameters found in simulation will translate directly to improved performance in a physical setup without additional unmodeled effects.","pith_extraction_headline":"Optimizing eight circuit parameters via gradient descent on Fisher information raises NOON-state phase sensing from 36 percent to 58 percent of the Heisenberg limit at N=5 and multiplies useful events per pulse by up to 133 times."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.12323/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}