Information door · 9 min read · published
Annealing a Signal
Noise can be reduced by cooling a physical system, averaging observations, or slowly changing a computation. None of these procedures cleans a message without a model of what counts as signal.
Thesis
Signal recovery is not the removal of all variation. It is a controlled inference that uses physical constraints, redundancy, and a model of the source to distinguish relevant structure from noise while acknowledging uncertainty.
Noise is not the opposite of information
Supporting/contextual references: [anneal-shannon-1949] [anneal-wiener-1949]
[object Object]
[object Object]
Thermal noise has a temperature
Supporting/contextual references: [anneal-nyquist-1928] [anneal-shannon-1949]
[object Object]
[object Object]
Averaging buys confidence, not certainty
Supporting/contextual references: [anneal-kolmogorov-1933] [anneal-jaynes-2003]
[object Object]
[object Object]
Filters choose what to preserve
Supporting/contextual references: [anneal-wiener-1949] [anneal-shannon-1949]
[object Object]
[object Object]
[object Object]
Inference with a prior
Supporting/contextual references: [anneal-jaynes-2003] [anneal-kolmogorov-1933]
[object Object]
[object Object]
Quantum signals and measurement
Supporting/contextual references: [anneal-caves-2002] [anneal-giovannetti-2011]
[object Object]
[object Object]
Open research directions
Supporting/contextual references: [anneal-caves-2002] [anneal-giovannetti-2011] [anneal-jaynes-2003]
[object Object]
[object Object]
A cleaner account
Supporting/contextual references: [anneal-shannon-1949] [anneal-wiener-1949] [anneal-jaynes-2003]
[object Object]
[object Object]
The practical boundary
Supporting/contextual references: [anneal-shannon-1949] [anneal-wiener-1949] [anneal-jaynes-2003]
[object Object]
[object Object]
[object Object]
[object Object]
Sources & references
Supporting/contextual references, not claim-level proof.
- Harry Nyquist — Thermal Agitation of Electric Charge in ConductorsPhysical Review 32(1), 110–113, 1928.
- Claude E. Shannon — Communication in the Presence of NoiseProceedings of the IRE 37(1), 10–21, 1949.
- Norbert Wiener — Extrapolation, Interpolation, and Smoothing of Stationary Time SeriesMIT Press, 1949.
- Andrey N. Kolmogorov — Grundbegriffe der WahrscheinlichkeitsrechnungSpringer, 1933.
- Edwin T. Jaynes — Probability Theory: The Logic of ScienceCambridge University Press, 2003.
- C. M. Caves, C. A. Fuchs, and R. Schack — Unknown Quantum States: The Quantum de Finetti RepresentationJournal of Mathematical Physics 43(9), 4537–4559, 2002.
- V. Giovannetti, S. Lloyd, and L. Maccone — Advances in Quantum MetrologyNature Photonics 5, 222–229, 2011.