Photon Detection as a Process of Information Gain

Making use of the equivalence between information and entropy, we have shown in a recent paper that particles moving with a kinetic energy ε carry potential information i p o t ( ε , T ) = 1 ln ( 2 ) ε k B   T relative to a heat reservoir of temperature T . In this paper we build on this result and consider in more detail the process of information gain in photon detection. Considering photons of energy E p h and a photo-ionization detector operated at a temperature T D , we evaluate the signal-to-noise ratio S N ( E p h , T D ) for different detector designs and detector operation conditions and show that the information gain realized upon detection, i r e a l ( E p h , T D ) , always remains smaller than the potential information i p o t ( E p h , T D ) carried with the photons themselves, i.e.,: i r e a l ( E p h , T D ) = 1 ln ( 2 ) ln ( S N ( E p h , T D ) ) ≤ i p o t ( E p h , T D ) = 1 ln ( 2 ) E p h k B T D   . This result is shown to be generally valid for all kinds of technical photon detectors, which shows that i p o t ( E p h , T D ) can indeed be regarded as an intrinsic information content that is carried with the photons themselves. Overall, our results suggest that photon detectors perform as thermodynamic engines that incompletely convert potential information into realized information with an efficiency that is limited by the second law of thermodynamics and the Landauer energy bounds on information gain and information erasure.