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Information inequalities govern the ultimate limitations in information theory and as such play an pivotal role in characterizing what values the entropy of multipartite states can take. Proving an information inequality, however, quickly…
Quantum entropy inequalities are studied. Some quantum entropy inequalities are obtained by several methods. For entanglement breaking channel, we show that the entanglement-assisted classical capacity is upper bounded by $\log d$. A…
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…
We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications…
The information provided by a classical measurement is unambiguously determined by the mutual information between the output results and the measured quantity. However, quantum mechanically there are at least two notions of information…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel…
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.
There is a consensus in science that information theory and statistical physics have a close relationship but the literary proofs of the equivalence between most of the conceptions in the two disciplines are still missing. In this work,…
We consider a line with noise in the simplest case. Loss does not add noise. Amplification via phase insensitive amplifiers do add noise. A lower bound of this capacity is the quantum analog to the Shannon capacity of a linear channel with…
Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more…
Noisy quantum channels may be used in many information carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on…
The amount of information transmissible through a communications channel is determined by the noise characteristics of the channel and by the quantities of available transmission resources. In classical information theory, the amount of…
We consider Hamiltonian quantum systems with energy bandwidth \Delta E and show that each measurement that determines the time up to an error \Delta t generates at least the entropy (\hbar/(\Delta t \Delta E))^2/2. Our result describes…
A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the "classical capacity",…
The main topic of this thesis is the proof of two fundamental entropic inequalities for quantum Gaussian channels. Quantum Gaussian channels model the propagation of electromagnetic waves through optical fibers and free space in the quantum…
Recently, there have been considerable progresses on the bounds of various quantum channel capacities for bosonic Gaussian channels. Especially, several upper bounds for the classical capacity and the quantum capacity on the bosonic…
Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…
The paper establishes the equality condition in the I-MMSE proof of the entropy power inequality (EPI). This is done by establishing an exact expression for the deficit between the two sides of the EPI. Interestingly, a necessary condition…