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Physical Review A

Superposition of number eigenstates with thermal light

Apostol Vourdas

Published May 1, 1988• 20 citations
Publisher

Abstract

A density matrix that describes the superposition of number eigenstates with thermal light is presented, and its matrix elements are calculated. The maximum information that this beam can transmit is compared with the maximum information that can be transmitted (i) by coherent signals in thermal noise and (ii) by coherent signals with random phase, in thermal noise.

DOI
10.1103/physreva.37.3890

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Previous work of this contract on the waveshape aspects of light from a classical point of view led to an interest to investigate the quantum mechanical aspects of the waveshape of light. This work contains some results of this investigation. One of the results obtained is an upper bound on the channel capacity where the only noise in the channel is due to the zero point field. The P-representation of a general state in terms of the coherent states is utilized to obtain the probability densities of the in-phase component, quadrature component, envelope, and the number of photons of the field. This is done for thermal radiation and for radiation which is a mixture of thermal radiation and coherent radiation with the result that the thermal radiation behaves as pure Gaussian noise while the coherent radiation behaves as a classical signal. The quantum mechanical formalism is utilized to obtain the rules of superposition for a large class of fields. The results show that the signal part can be treated classically and the noise part is nearly the same as would be found from the classical superposition of noise.

•Sep 8, 1964•0 citations
A density matrix that describes the superposition of number eigenstates with thermal light is presented, and its matrix elements are calculated. The maximum information that this beam can transmit is compared with the maximum information that can be transmitted (i) by coherent signals in thermal noise and (ii) by coherent signals with random phase, in thermal noise.
When the phase of the transmittance between a unimodal transmitter and a unimodal receiver is uniformly distributed over(0,2\pi), the density operator of the received signal field commutes with the photon number operator, and the optimum detector of the signal counts photons. A simple formula is given for the probability generating function of the number of photons in terms of the quasi-probability distribution of the transmitted signal. It is used to determine the average error probability of an on-off binary communication system transmitting two-photon coherent-state signals, received in the presence of thermal noise.
The fluctuations in a thermal beam due to the superposition of two similar thermal beams are computed. The information loss due to superimposing a quasi-monochromatic thermal-noise beam on a similar signal beam is investigated for two types of noise beams, sample noise, and path noise. In the Wien and Rayleigh–Jeans limits, the information loss j23 per macrocell is found to depend only on the signal-to-noise ratio. The relative loss in maximum obtainable information, I3,max/I2,max, for given signal and noise beams is given as well as some numerical examples.
An analytical expression is given to the coherent information of the thermal radiation signal transmitted over the thermal radiation noise channel, one of the most essential quantum Gaussian channels. Focusing on the single normal mode of the thermal radiation signal and noise, we resolve the entangled state density operator, which characterizes quantum information transmission, into a direct product of two parts, with each part being a thermal radiation density operator. The calculation is aided by the technique known as ``integral within ordered product of operators".
Previous work of this contract on the waveshape aspects of light from a classical point of view led to an interest to investigate the quantum mechanical aspects of the waveshape of light. This work contains some results of this investigation. One of the results obtained is an upper bound on the channel capacity where the only noise in the channel is due to the zero point field. The P-representation of a general state in terms of the coherent states is utilized to obtain the probability densities of the in-phase component, quadrature component, envelope, and the number of photons of the field. This is done for thermal radiation and for radiation which is a mixture of thermal radiation and coherent radiation with the result that the thermal radiation behaves as pure Gaussian noise while the coherent radiation behaves as a classical signal. The quantum mechanical formalism is utilized to obtain the rules of superposition for a large class of fields. The results show that the signal part can be treated classically and the noise part is nearly the same as would be found from the classical superposition of noise.