{
  "id": "oai:papers.qnfo.org:thermal-quantum-sensing-at-high-temperature-exact-fisher-information-bounds-univ",
  "slug": "thermal-quantum-sensing-at-high-temperature-exact-fisher-information-bounds-univ",
  "title": "Thermal Quantum Sensing at High Temperature: Exact Fisher‑Information Bounds, Universal Metrics, and the Work Cost of Quadratic Signals",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Thermal fluctuations are usually treated as a nuisance that degrades quantum‑enhanced sensing, yet for certain signal encodings heat can improve the metrological response of a probe. We study thermal quantum sensors governed by a Hamiltonian H and subjected to a unitary signal U(θ)=exp(-iθ G). Building on general results that relate monotone quantum Fisher‑information (QFI) metrics, their temperature dependence, and the work induced by a unitary signal, we derive closed‑form expressions for two exactly solvable models. For a single bosonic mode with a purely quadratic (squeezing‑type) generator of strength g, we obtain F_Q(β)=frac2g²(1+q)²1+q²,qquad q=e^-βω, which interpolates between F_Q(T=0)=2g² and F_Q(T → ∞)=4g², thereby achieving exactly twice the zero‑temperature QFI and the corresponding factor‑of‑two Cramér–Rao improvement, both derived here from first principles. At βω=0.1 the QFI already reaches 99.7491\\% of its infinite‑temperature value. For a qubit sensor we derive the exact SLD QFI F_K=tanh²(ℏω/2k_BT) and locate the crossover to the universal high‑temperature regime, which requires k_BTgtrsim2ℏω for few‑percent accuracy. The signal‑induced work is W(θ)=ωsinh²(gθ) coth left((βω)/(2)right) ≈ω g²θ² coth left((βω)/(2)right)quad(gθ≪1), which grows linearly with T at high temperature. All derivations are fully explicit and independently checkable.",
  "abstract_markdown": "Thermal fluctuations are usually treated as a nuisance that degrades quantum‑enhanced sensing, yet for certain signal encodings heat can improve the metrological response of a probe. We study thermal quantum sensors governed by a Hamiltonian $H$ and subjected to a unitary signal $U(\\theta)=\\exp(-i\\theta G)$. Building on general results that relate monotone quantum Fisher‑information (QFI) metrics, their temperature dependence, and the work induced by a unitary signal, we derive closed‑form expressions for two exactly solvable models. For a single bosonic mode with a purely quadratic (squeezing‑type) generator of strength $g$, we obtain  \n\\[\nF_Q(\\beta)=\\frac{2g^{2}(1+q)^{2}}{1+q^{2}},\\qquad q=e^{-\\beta\\omega},\n\\]  \nwhich interpolates between $F_Q(T=0)=2g^{2}$ and $F_Q(T\\!\\to\\!\\infty)=4g^{2}$, thereby achieving exactly twice the zero‑temperature QFI and the corresponding factor‑of‑two Cramér–Rao improvement, both derived here from first principles. At $\\beta\\omega=0.1$ the QFI already reaches $99.7491\\%$ of its infinite‑temperature value. For a qubit sensor we derive the exact SLD QFI $F_K=\\tanh^{2}(\\hbar\\omega/2k_{B}T)$ and locate the crossover to the universal high‑temperature regime, which requires $k_{B}T\\gtrsim2\\hbar\\omega$ for few‑percent accuracy. The signal‑induced work is  \n\\[\nW(\\theta)=\\omega\\sinh^{2}(g\\theta)\\,\\coth\\!\\left(\\frac{\\beta\\omega}{2}\\right)\n\\approx\\omega g^{2}\\theta^{2}\\,\\coth\\!\\left(\\frac{\\beta\\omega}{2}\\right)\\quad(g\\theta\\ll1),\n\\]  \nwhich grows linearly with $T$ at high temperature. All derivations are fully explicit and independently checkable.",
  "date": "2026-10-09",
  "first_published": "2026-10-09",
  "last_revised": "2026-10-19T21:11:08Z",
  "modified": "2026-10-19T21:11:08Z",
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  "language": "en",
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  "peer_review_status": "Not independently peer-reviewed",
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  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/thermal-quantum-sensing-at-high-temperature-exact-fisher-information-bounds-univ",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "708367240dddc20cdf3a42e56dddfa82e770c123ed712439ce007743af164789",
  "version_url": "https://papers.qnfo.org/papers/thermal-quantum-sensing-at-high-temperature-exact-fisher-information-bounds-univ/v/1.1.0",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Thermal Quantum Sensing at High Temperature: Exact Fisher‑Information Bounds, Universal Metrics, and the Work Cost of Quadratic Signals"
      }
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    "publicationYear": "2026",
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        "date": "2026-10-09",
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        "description": "Thermal fluctuations are usually treated as a nuisance that degrades quantum‑enhanced sensing, yet for certain signal encodings heat can improve the metrological response of a probe. We study thermal quantum sensors governed by a Hamiltonian H and subjected to a unitary signal U(θ)=exp(-iθ G). Building on general results that relate monotone quantum Fisher‑information (QFI) metrics, their temperature dependence, and the work induced by a unitary signal, we derive closed‑form expressions for two exactly solvable models. For a single bosonic mode with a purely quadratic (squeezing‑type) generator of strength g, we obtain F_Q(β)=frac2g²(1+q)²1+q²,qquad q=e^-βω, which interpolates between F_Q(T=0)=2g² and F_Q(T → ∞)=4g², thereby achieving exactly twice the zero‑temperature QFI and the corresponding factor‑of‑two Cramér–Rao improvement, both derived here from first principles. At βω=0.1 the QFI already reaches 99.7491\\% of its infinite‑temperature value. For a qubit sensor we derive the exact SLD QFI F_K=tanh²(ℏω/2k_BT) and locate the crossover to the universal high‑temperature regime, which requires k_BTgtrsim2ℏω for few‑percent accuracy. The signal‑induced work is W(θ)=ωsinh²(gθ) coth left((βω)/(2)right) ≈ω g²θ² coth left((βω)/(2)right)quad(gθ≪1), which grows linearly with T at high temperature. All derivations are fully explicit and independently checkable.",
        "descriptionType": "Abstract"
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