Related papers: The Shannon-McMillan Theorem for Ergodic Quantum L…
We give an equivalent finitary reformulation of the classical Shannon-McMillan-Breiman theorem which has an immediate translation to the case of ergodic quantum lattice systems. This version of a quantum Breiman theorem can be derived from…
We define a large class of quantum sources and prove a quantum analog of the asymptotic equipartition property. Our proof relies on using local measurements on the quantum source to obtain an associated classical source. The classical…
We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs~\cite{Gacs} and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical…
We prove the ergodic version of the quantum Stein's lemma which was conjectured by Hiai and Petz. The result provides an operational and statistical interpretation of the quantum relative entropy as a statistical measure of…
We consider one-dimensional quantum spin chain, which is called XX model, XX0 model or isotropic XY model in a transverse magnetic field. We study the model on the infinite lattice at zero temperature. We are interested in the entropy of a…
For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…
We consider stationary ergodic processes indexed by $\mathbb Z$ or $\mathbb Z^n$ whose finite dimensional marginals have laws which are absolutely continuous with respect to Lebesgue measure. We define an entropy theory for these continuous…
The paper shows that, for large number of particles and for distinguishable and non-interacting identical particles, convergence to equiprobability of the $W$ microstates of the famous Boltzmann-Planck entropy formula $S=k \log(W)$ is…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
We address the task of compression of fermionic quantum information. Due to the parity superselection rule, differently from the case of encoding of quantum information in qubit states, part of the information carried by fermionic systems…
We consider some questions concerning the monotonicity properties of entropy and mean entropy of states on translationally invariant systems (classical lattice, quantum lattice and quantum continuous). By taking the property of strong…
Let \mu be a computable ergodic shift-invariant measure over the Cantor space. Providing a constructive proof of Shannon-McMillan-Breiman theorem, V'yugin proved that if a sequence x is Martin-L\"of random w.r.t. \mu then the strong…
For noncomposite systems in classical and quantum domains, we obtain new inequalities such as the subadditivity and strong subadditivity conditions for Shannon entropies and information determined by the probability distributions and for…
We prove Mermin-Wagner-type theorems for quantum lattice systems in the presence of multipole symmetries. These theorems show that the presence of higher-order symmetries protects against the breaking of lower-order ones. In particular, we…
Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…
We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating…
Quantum algorithms for classical physics problems expose new patterns of quantum information flow as compared to the many-body Schr\"{o}dinger equation. As a result, besides their potential practical applications, they also offer a valuable…
We review the postulates of quantum mechanics that are needed to discuss the von Neumann's entropy. We introduce it as a generalization of Shannon's entropy and propose a simple game that makes easier understanding its physical meaning.
We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy…