Related papers: The Shannon-McMillan Theorem for Ergodic Quantum L…
A brief review of a self-contained genuinely three-dimensional monodromy-matrix based non-perturbative covariant path-integral approach to {\it polynomial invariants} of knots and links in the framework of (topological) quantum Chern-Simons…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
We introduce a well-defined and unbiased measure of the strength of correlations in quantum many-particle systems which is based on the relative von Neumann entropy computed from the density operator of correlated and uncorrelated states.…
In this work we determine and discuss the entropic uncertainty measures of Shannon type for all the discrete stationary states of the multidimensional harmonic systems directly in terms of the states' hyperquantum numbers, the…
Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD(M) algebra, which essentially encodes how matter degrees of freedom are moved on a three-dimensional…
The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement present in its pure ground state. In this work, we establish scaling laws for this entanglement for critical quasi-free fermionic and…
We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and…
We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique…
We give a new proof of quantum Shannon-McMillan theorem, extending it to AF $C^*$-systems. Our proof is based on the variational principle, instead of the classical Shannon-McMillan theorem.
We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the…
General molecular dynamic approach, making possible direct calculation of eigen values and eigen functions for a quantum-mechanical system of an arbitrary symmetry is proposed. The method is based on analogy between discrete representation…
We present a general definition of quantum mutual entropy for infinitely extended quantum spin and fermion lattice systems. Using this, we establish a thermal area law in these infinitely extended quantum systems. The proof is based on the…
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual…
Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…
We investigate an asymptotically spatially flat Robertson-Walker spacetime from two different perspectives. First, using von Neumann entropy, we evaluate the entanglement generation due to the encoded information in spacetime. Then, we work…
A quantum mechanical theory is developed for the statistics of momentum transferred to the lattice by conduction electrons. Results for the electromechanical noise power in the semiclassical diffusive transport regime agree with a recent…
Bandlimited approaches to quantum field theory offer the tantalizing possibility of working with fields that are simultaneously both continuous and discrete via the Shannon Sampling Theorem from signal processing. Conflicting assumptions in…
Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…