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Journal of Optical Technology

Possibilities of using the concept of optical degrees of freedom to evaluate the informational properties of optical systems

Simon B. Gurevich, B. S. Gurevich

Published Feb 1, 2010• 1 citation
Publisher

Abstract

The concepts of optical degrees of freedom used in evaluating information properties are made more exact. It is pointed out that determining the number of degrees of freedom in optics has its own special features, and the amount of information, taking this number into consideration, can be estimated if the allowable influence of other light-based information channels is taken into account in the calculation.

DOI
10.1364/jot.77.000088

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The concepts of optical degrees of freedom used in evaluating information properties are made more exact. It is pointed out that determining the number of degrees of freedom in optics has its own special features, and the amount of information, taking this number into consideration, can be estimated if the allowable influence of other light-based information channels is taken into account in the calculation.
The Shannon number is shown to specify the number of degrees of freedom that can be resolved in a coherent object scrutinized by a distant optical instrument that extracts information about the object from the light passing through its aperture. The quantum-mechanical nature of the light is taken into account, and the problem of determining the object amplitude distribution is treated by means of quantum estimation theory, which defines a limitation on the accuracy of an estimate of the object distribution that cannot be surpassed by any means of processing the received light. Fundamentally, the limitation arises from the inability of more than a finite number of modes of excitation of the object to deposit a significant number of photons in the aperture.
We investigate how special relativity influences the transmission of classical information through quantum channels by evaluating the Holevo bound when the sender and the receiver are in (relativistic) relative motion. By using the spin degrees of freedom of spin-1/21/21/2 fermions to encode the classical information, we show that, for some configurations, the accessible information in the receiver can be increased when the spin detector moves fast enough. This is possible by allowing the momentum wave packet of one of the particles to be sufficiently wide while the momentum wave packets of other particles are kept relatively narrow. In this way, one can take advantage of the fact that boosts entangle the spin and momentum degrees of freedom of spin-1/21/21/2 fermions to increase the accessible information in the former. We close the paper with a discussion of how this relativistic quantum channel cannot in general be described by completely positive quantum maps.