{
  "id": "oai:papers.qnfo.org:distinguishability-induced-degradation-of-monolithic-quantum-error-correction-a-",
  "slug": "distinguishability-induced-degradation-of-monolithic-quantum-error-correction-a-",
  "title": "Distinguishability-Induced Degradation of Monolithic Quantum Error Correction: A Reconciled Analytic Study of Syndrome-Checking Constraints",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Quantum error-correcting codes rely on the assumption that the environment cannot distinguish which error occurred on which codeword. Residual Zeeman, Stark, and anharmonic shifts in physical platforms break this assumption by imprinting error-dependent photon frequencies on the environment, converting an otherwise correctable noise process into one with inflated effective Kraus rank. We construct a minimal analytic model of this mechanism: a single logical error whose two environment branches carry Gaussian photon wavepackets separated in frequency by Δω. We derive the recovered fidelity F = (1)/(2)(1+Res) for an equal-superposition input, where s is the environment-state overlap, and prove the bound F ≥ 1 - D/2 in terms of the distinguishability D = 1-|s|² = 1-e^-(Δωσ)² for wavepacket duration σ. We then derive an operational syndrome-checking constraint T_check ≤ √ln(1/(1-D_max))/Δω and evaluate it numerically: for a $1$ MHz frequency separation and a tolerable distinguishability of 10^-2, the checking interval must not exceed 1.60× 10^-8 s ($16.0$ ns). [...]",
  "abstract_markdown": "Quantum error-correcting codes rely on the assumption that the environment cannot distinguish which error occurred on which codeword. Residual Zeeman, Stark, and anharmonic shifts in physical platforms break this assumption by imprinting error-dependent photon frequencies on the environment, converting an otherwise correctable noise process into one with inflated effective Kraus rank. We construct a minimal analytic model of this mechanism: a single logical error whose two environment branches carry Gaussian photon wavepackets separated in frequency by $\\Delta\\omega$. We derive the recovered fidelity $F = \\frac{1}{2}(1+\\operatorname{Re}s)$ for an equal-superposition input, where $s$ is the environment-state overlap, and prove the bound $F \\ge 1 - D/2$ in terms of the distinguishability $D = 1-|s|^2 = 1-e^{-(\\Delta\\omega\\sigma)^2}$ for wavepacket duration $\\sigma$. We then derive an operational syndrome-checking constraint $T_{\\mathrm{check}} \\le \\sqrt{\\ln(1/(1-D_{\\max}))}/\\Delta\\omega$ and evaluate it numerically: for a $1$ MHz frequency separation and a tolerable distinguishability of $10^{-2}$, the checking interval must not exceed $1.60\\times 10^{-8}$ s ($16.0$ ns). [...]",
  "date": "2026-10-09",
  "first_published": "2026-10-09",
  "last_revised": "2026-10-09T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/distinguishability-induced-degradation-of-monolithic-quantum-error-correction-a-",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Distinguishability-Induced Degradation of Monolithic Quantum Error Correction: A Reconciled Analytic Study of Syndrome-Checking Constraints"
      }
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    "publicationYear": "2026",
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        "description": "Quantum error-correcting codes rely on the assumption that the environment cannot distinguish which error occurred on which codeword. Residual Zeeman, Stark, and anharmonic shifts in physical platforms break this assumption by imprinting error-dependent photon frequencies on the environment, converting an otherwise correctable noise process into one with inflated effective Kraus rank. We construct a minimal analytic model of this mechanism: a single logical error whose two environment branches carry Gaussian photon wavepackets separated in frequency by Δω. We derive the recovered fidelity F = (1)/(2)(1+Res) for an equal-superposition input, where s is the environment-state overlap, and prove the bound F ≥ 1 - D/2 in terms of the distinguishability D = 1-|s|² = 1-e^-(Δωσ)² for wavepacket duration σ. We then derive an operational syndrome-checking constraint T_check ≤ √ln(1/(1-D_max))/Δω and evaluate it numerically: for a $1$ MHz frequency separation and a tolerable distinguishability of 10^-2, the checking interval must not exceed 1.60× 10^-8 s ($16.0$ ns). [...]",
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