Related papers: An Elementary Proof of a Classical Information-The…
Applying perturbation theory to the path-integral representation for the mutual information of the nonlinear communication channel described by the nonlinear Shr\"{o}dinger equation (NLSE) with the additive Gaussian noise we analyze the…
For a continuous-input-continuous-output arbitrarily distributed quantum channel carrying classical information, the channel capacity can be computed in terms of the distribution of the channel envelope, received signal strength over a…
The optimal rate at which information can be sent through a quantum channel when the transmitted signal must simultaneously carry some minimum amount of energy is characterized. To do so, we introduce the quantum-classical analogue of the…
Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\Psi({\bf r})$…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
The mutual information of a single-layer perceptron with $N$ Gaussian inputs and $P$ deterministic binary outputs is studied by numerical simulations. The relevant parameters of the problem are the ratio between the number of output and…
Many of the classical and recent relations between information and estimation in the presence of Gaussian noise can be viewed as identities between expectations of random quantities. These include the I-MMSE relationship of Guo et al.; the…
While Shannon's mutual information has widespread applications in many disciplines, for practical applications it is often difficult to calculate its value accurately for high-dimensional variables because of the curse of dimensionality.…
One of the key aspects of Shannon's theory is that it provides guidance for designing the most efficient systems, such as minimizing errors and clarifying the limits of coding. Such theories have made great developments in the 50 years…
In many complex systems, whether biological or artificial, the thermodynamic costs of communication among their components are large. These systems also tend to split information transmitted between any two components across multiple…
We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver's pre-shared ancilla. Instead of a pure state, we…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
It is shown on a simple classical model of a quantum particle at rest that information contained into the quantum state (quantum information) can be obtained by integrating the corresponding probability distribution on phase space, i.e. by…
The Quantum Reverse Shannon Theorem has been a milestone in quantum information theory. It states that asymptotically reliable simulation of a quantum channel, assisted by unlimited shared entanglement, requires a rate of classical…
This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…
Today, the vast majority of the world's digital information is represented using the fundamental assumption, introduced by Claude Shannon in 1948, that ``...the semantic aspects of communication are irrelevant to the engineering problem (of…
The information bottleneck problem (IB) of jointly stationary Gaussian sources is considered. A water-filling solution for the IB rate is given in terms of its SNR spectrum and whose rate is attained via frequency domain test-channel…
The information content of a source is defined in terms of the minimum number of bits needed to store the output of the source in a perfectly recoverable way. A similar definition can be given in the case of quantum sources, with qubits…
Existing information-theoretic frameworks based on maximum entropy network ensembles are not able to explain the emergence of heterogeneity in complex networks. Here, we fill this gap of knowledge by developing a classical framework for…
A probabilistic source is defined as the set of infinite words (over a given denumerable alphabet) endowed with a probability $\mu$. The paper deals with general binary sources where the distribution of any symbol (0 or 1) may depend on an…