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Conference on Lasers and Electro-Optics

Comparison of the capacities of communication channels with different statistics of information carriers

Mikhail A. Khodasevich, George V. Sinitsyn, Anatoly S. Yasukevich

Published Aug 29, 2005• 0 citations
Publisher

Abstract

Summary form only given. We investigate reliability of information transmission in the number-state model for fermionic (electronic) channel and consider a special case when the signal excites particles that are initially in the vicinity of fermi energy /sub F/ ("thermal" fermions) and a quantum of signal energy is much greater than kT/sub 0/, where k is Boltzman constant and to is the environment temperature.

DOI
10.1109/iqec.2000.908072

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Summary form only given. We investigate reliability of information transmission in the number-state model for fermionic (electronic) channel and consider a special case when the signal excites particles that are initially in the vicinity of fermi energy /sub F/ ("thermal" fermions) and a quantum of signal energy is much greater than kT/sub 0/, where k is Boltzman constant and to is the environment temperature.
On the base of entropy defect principle the models are considered of narrow-band quantum communication channels and compared with the classic description of information channels. The classic model is shown to be applicable in a wide range of channels' parameters. But in the case of fermionic channels it is necessary to take into account that values of signal power and channel capacity are limited. These maximum values can be approximated by the simple expressions. Bosonic channels are free of these limitations. The rough quantum model of narrow-band bosonic channels gives too high values of capacity at low communication rate as compared with accurate one.
We consider information transmission through a noiseless quantum channel, where the information is encoded into massive indistinguishable particles: bosons or fermions. We study the situation in which the particles are noninteracting. The encoding input states obey a set of physically motivated constraints on the mean values of the energy and particle number. In such a case, the determination of both classical and quantum capacity reduces to a constrained maximization of entropy. In the case of noninteracting bosons, signatures of Bose-Einstein condensation can be observed in the behavior of the capacity. A major motivation for these considerations is to compare the information-carrying capacities of channels that carry bosons with those that carry fermions. We show analytically that fermions generally provide higher channel capacity, i.e., they are better suited for transferring bits as well as qubits, in comparison to bosons. This holds for a large range of power-law potentials, and for moderate to high temperatures. Numerical simulations seem to indicate that the result holds for all temperatures. Also, we consider the low-temperature behavior for the three-dimensional box and harmonic trap, and again we show that the fermionic capacity is higher than the bosonic one for sufficiently low temperatures.
In the present paper we consider a simple model of stochastic systems, which include basic systems of quantum physics. In the framework of this model we demonstrate the Boltzman entropy, second law of thermodynamics and Gibbs theorem as classical achievements on one side, and several possible entropies of the Shannon theory, and their relations to the Boltzman entropy on the other side. We introduce an information transmission in the systems under consideration, define the Shannon information in a variable about the system state, and formulate the concept of information capacity of a system. We explicitly evaluate the capacity of a system governed by the Bose–Einstein law (a boson channel) and that governed by the Fermi–Dirac law (a fermion channel).
We are concerned with the detection of a set ofMmessages that are transmitted over a channel disturbed by chaotic thermal noise when quantum effects in the communication systems are taken into account. Our attention is restricted to the special case in which the density operators specifying the state of the received field are commutative. In particular, the performance of two special communication systems is evaluated. For a system in which orthogonal signals with known amplitudes and random phases are transmitted over an additive white Gaussian channel, the structure of an optimum receiver is found. Expressions for the system reliability function and channel capacity are derived. For a system in which orthogonal signals are transmitted over a Rayleigh fading channel, the optimum performance is obtained. The optimum degree of diversity for an equal-strength diversity system is found numerically as a function of the average thermal-noise energy and information rate.
We consider the capacity of classical information transfer for noiseless quantum channels carrying a finite average number of massive bosons and fermions. The maximum capacity is attained by transferring the Fock states generated from the grand-canonical ensemble. Interestingly, the channel capacity for a Bose gas indicates the onset of Bose-Einstein condensation, by changing its qualitative behavior at the criticality, while for a channel carrying weakly attractive fermions, it exhibits the signatures of Bardeen-Cooper-Schrieffer transition. We also show that, for noninteracting particles, fermions are better carriers of information than bosons.