Abstract : Attempt is made to establish an upper bound on the information capacity of an electromagnetic wave propagation circuit between two apertures when quantum effects come into play. We first discuss the specifications of a signal, and find that we can associate approximately BT quantities with a signal of bandwidth B and duration T, and that the energy associated with these quantities must differ by at least one quantum of energy. We then consider radiative attenuation loss within the framework of quantum theory and find that the radiative attenuation introduces a random noise in the circuit which is analogous to partition tube noise. With the channel matrix determined, we discuss the problem of evaluating the channel capacity under average and peak power constraints. Due to mathematical difficulties we are only able to establish the channel capacity explicitly when the radiative losses become extreme. In this limiting case-as a byproduct-we also find that the best encoding procedure is a binary on-off system.
Abstract : Attempt is made to establish an upper bound on the information capacity of an electromagnetic wave propagation circuit between two apertures when quantum effects come into play. We first discuss the specifications of a signal, and find that we can associate approximately BT quantities with a signal of bandwidth B and duration T, and that the energy associated with these quantities must differ by at least one quantum of energy. We then consider radiative attenuation loss within the framework of quantum theory and find that the radiative attenuation introduces a random noise in the circuit which is analogous to partition tube noise. With the channel matrix determined, we discuss the problem of evaluating the channel capacity under average and peak power constraints. Due to mathematical difficulties we are only able to establish the channel capacity explicitly when the radiative losses become extreme. In this limiting case-as a byproduct-we also find that the best encoding procedure is a binary on-off system.
The process of attenuation of electromagnetic energy when transmitted over some communication channel is stochastic in nature. Hence one can expect that, since equivocation is imposed in the transmission, in addition to reduction of average signal power, there will be a consequent degradation in channel capacity. We have attempted to calculate the effect of this phenomenon on an otherwise noiseless photon channel and when the source itself is assumed to have no undesired fluctuations. In order to do so, we have employed a straightforward variational technique and introduced the partition function method of statistical mechanics to obtain an expression for channel capacity. Using approximate methods, we find that the maximum information transfer is achieved when the probability of receiving exactlykphotons goes down, asymptotically with largek, ase^{-ck}/ \sqrt{k}, wherecis a positive constant. For very large received average energyU(in photon number), the channel capacity behaves approximately asC = \frac{1}{2} \ln U, one-half the capacity of an ideal noiseless photon channel (given by Gordon's formula for the capacity of an electromagnetic wave). For very small received average energy, we find that the (optimum) received distribution is very nearly Bose-Einstein, and the channel capacity is not degraded below its ideal value. The results are applicable to an idealized laser oscillator and also to photoelectric detection. That is, both devices by themselves may be regarded as "channels" for which the input may be modulated as desired and the output is stochastically dependent on the input.
We consider a communication system consisting of an information source of electromagnetic radiation. It is assumed that the information source radiates an electromagnetic signal with an average power S, and the signal propagated through the electromagnetic channel is assumed to be perturbed by additive thermal noise at temperature T. For simplicity, we assume that the electromagnetic signal is one-dimensional (i.e., the photon fluctuation is restricted to only one polarized state), in which the propagation occurs in the same direction of the wave vectors. It is emphasized that the corresponding occupation number of the quantum levels can be fully described. Obviously, these occupation quantum levels correspond to the microsignal structure of the information source. It is therefore assumed that these occupation numbers can be uniquely determined for those representing an input signal ensemble. We further assume that an ideal receiver (an ideal photon counter) is used at the output end of the channel. That is, the receiver is able to detect the specified frequencies of the electromagnetic signal. It is also emphasized that in practice the interaction of the electromagnetic signal and the detector are strictly statistical, that is, a certain amount of information loss is expected at the output end of the receiver. The idealized model of the receiver we have proposed mainly simplifies the method by which the quantum effect on the communication channel can be easily calculated.
Thermal attenuator channels model the decoherence of quantum systems interacting with a thermal bath, e.g., a two-level system subject to thermal noise and an electromagnetic signal traveling through a fiber or in free-space. Hence determining the quantum capacity of these channels is an outstanding open problem for quantum computation and communication. Here we derive several upper bounds on the quantum capacity of qubit and bosonic thermal attenuators. We introduce an extended version of such channels which is degradable and hence has a single-letter quantum capacity, bounding that of the original thermal attenuators. Another bound for bosonic attenuators is given by the bottleneck inequality applied to a particular channel decomposition. With respect to previously known bounds we report better results in a broad range of attenuation and noise: we can now approximate the quantum capacity up to a negligible uncertainty for most practical applications, e.g., for low thermal noise.
Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are described here. Quantum channel capacity theory is reviewed for both steady state and burst communication. An analytic approximation is given for the maximum signal information possible with occupation number signal states as a function of mean signal energy. A theorem guaranteeing that these states are optimal for communication is proved. A heuristic "proof" of the linear bound on communication is given, followed by rigorous proofs for signals with specified mean energy, and for signals with given energy budget. And systems of many parallel quantum channels are shown to obey the linear bound for a natural channel architecture. The time-energy uncertainty principle is reformulated in information language by means of the linear bound. The quantum bound on information storage capacity of quantum mechanical and quantum field devices is reviewed. A simplified version of the analytic proof for the bound is given for the latter case. Solitons as information caches are discussed, as is information storage in one-dimensional systems. The influence of signal self-gravitation on communication is considered. Finally, it is shown that acceleration of a receiver acts to block information transfer.
Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are described here. Quantum channel capacity theory is reviewed for both steady state and burst communication. An analytic approximation is given for the maximum signal information possible with occupation number signal states as a function of mean signal energy. A theorem guaranteeing that these states are optimal for communication is proved. A heuristic "proof" of the linear bound on communication is given, followed by rigorous proofs for signals with specified mean energy, and for signals with given energy budget. And systems of many parallel quantum channels are shown to obey the linear bound for a natural channel architecture. The time-energy uncertainty principle is reformulated in information language by means of the linear bound. The quantum bound on information storage capacity of quantum mechanical and quantum field devices is reviewed. A simplified version of the analytic proof for the bound is given for the latter case. Solitons as information caches are discussed, as is information storage in one-dimensional systems. The influence of signal self-gravitation on communication is considered. Finally, it is shown that acceleration of a receiver acts to block information transfer.
I derive a universal upper bound on the capacity of any communication channel between two distant systems. The Holevo quantity, and hence the mutual information, is at most of order EΔt/ℏ, where E is the average energy of the signal, and Δt is the amount of time for which detectors operate. The bound does not depend on the size or mass of the emitting and receiving systems, nor on the nature of the signal. No restrictions on preparing and processing the signal are imposed. As an example, I consider the encoding of information in the transverse or angular position of a signal emitted and received by systems of arbitrarily large cross section. In the limit of a large message space, quantum effects become important even if individual signals are classical, and the bound is upheld.