QUANTUM OPTIMALITY OF PHOTON COUNTING FOR TEMPERATURE MEASUREMENT OF THERMAL ASTRONOMICAL SOURCES

• Published in: The Astrophysical journal Vol. 808; no. 2; pp. 125 - 6
• Main Authors: Nair, Ranjith, Tsang, Mankei
• Format: Journal Article
• Language: English
• Published: United Kingdom The American Astronomical Society 01.08.2015
• Subjects: Approximation; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMIC RADIO SOURCES; Counting; Cramer-Rao bounds; instrumentation: detectors; methods: analytical; PHOTON COUNTING; Photons; radiation mechanisms: thermal; Radio astronomy; RADIOMETERS; SENSITIVITY; SIMULATION; SPECTRA; TEMPERATURE MEASUREMENT
• ISSN: 0004-637X; 1538-4357; 1538-4357
• DOI: 10.1088/0004-637X/808/2/125

ABSTRACT Using the quantum Cramér-Rao bound from quantum estimation theory, we derive a fundamental quantum limit on the sensitivity of a temperature measurement of a thermal astronomical source. This limit is expressed in terms of the source temperature Ts, input spectral bandwidth , and measurement duration T, subject to a long measurement time assumption . It is valid for any measurement procedure that yields an unbiased estimate of the source temperature. The limit agrees with the sensitivity of direct detection or photon counting, and also with that of the ideal radiometer in the regime for which the Rayleigh-Jeans approximation is valid, where is the center frequency at which the radiometer operates. While valid across the electromagnetic spectrum, the limit is especially relevant for radio astronomy in this regime, since it implies that no ingenious design or technological improvement can beat an ideal radiometer for temperature measurement. In this connection, our result refutes the recent claim of a radio astronomy technique with much-improved sensitivity over the radiometer.