https://doi.org/10.1140/epjd/e2006-00081-7
Retrodiction for coherent communication with homodyne or heterodyne detection
1
INFM-CNR and Dipartimento di Fisica e Matematica, Universita' dell'Insubria, Via Valleggio 11, 22100 Como, Italy
2
Department of Electronic Systems Engineering, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, UK
3
Department of Physics, University of Strathclyde, John Anderson Building, 107 Rottenrow, Glasgow, G4 0NG, UK
Corresponding author: a ottavia.jedrkiewicz@uninsubria.it
Received:
14
December
2005
Revised:
15
February
2006
Published online:
11
April
2006
Previous work on the retrodictive theory of direct
detection is extended to cover the homodyne detection of coherent optical
signal states 
and 
. The retrodictive input state probabilities are obtained by
the application of Bayes' theorem to the corresponding predictive
distributions, based on the probability operator measure (POM) elements for
the homodyne process. Results are derived for the retrodictive information
on the complex amplitude of the signal field obtainable from the difference
photocount statistics of both 4-port and 8-port balanced homodyne detection
schemes. The local oscillator is usually assumed much stronger than the
signal but the case of equal strengths in 4-port detection is also
considered. The calculated probability distributions and error rates are
illustrated numerically for values of signal and local oscillator strengths
that extend from the classical to the quantum regimes.
PACS: 42.50.-p – Quantum optics / 42.50.Dv – Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements / 03.67.Hk – Quantum communication
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006
