Information geometric approach to the renormalisation group

We propose a general formulation of the renormalisation group as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally motivated information geometry, we induce the space of Hamiltonians with a corresponding metric geometry. The resulting structure allows one to quantify information loss along RG flows in terms of the distinguishability of thermal states. In particular, we introduce a family of functions, expressible in terms of two-point correlation functions, which are non increasing along the flow. Among those, we study the speed of the flow, and its generalization to infinite lattices.Comment: Accepted in Phys. Rev.

Area laws in quantum systems: mutual information and correlations

The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. This counterintuitive idea which has its roots in the nonextensive nature of black-hole entropy serves as a guiding principle in the search for the fundamental laws of Planck-scale physics. In this paper we show that a similar phenomenon emerges from the established laws of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of microscopic degrees of freedom, it may diverge as the inverse temperature in quantum systems. A rigorous relation between area laws and correlations is established and their explicit behavior is revealed for a large class of quantum many-body states beyond equilibrium systems.Comment: 5 pages, 2 figures, published version with appendi

Entanglement in squeezed two-level atom

In the previous paper, we adopted the method using quantum mutual entropy to measure the degree of entanglement in the time development of the Jaynes-Cummings model. In this paper, we formulate the entanglement in the time development of the Jaynes-Cummings model with squeezed states, and then show that the entanglement can be controlled by means of squeezing.Comment: 6 pages, 5 figures, to be published in J.Phys.

A generalized skew information and uncertainty relation

A generalized skew information is defined and a generalized uncertainty relation is established with the help of a trace inequality which was recently proven by J.I.Fujii. In addition, we prove the trace inequality conjectured by S.Luo and Z.Zhang. Finally we point out that Theorem 1 in {\it S.Luo and Q.Zhang, IEEE Trans.IT, Vol.50, pp.1778-1782 (2004)} is incorrect in general, by giving a simple counter-example.Comment: to appear in IEEE TI

Particle Propagation on a Circle with a Point Interaction

We study a particle propagation on a circle in the presence of a point interaction. We show that the one-particle Feynman kernel can be written into the sum of reflected and transmitted trajectories which are weighted by the elements of the n-th power of the scattering matrix evaluated on a line with a point interaction. As a by-product we find three-parameter family of trace formulae as a generalization of the Poisson summation formula.Comment: 21 pages, 12 figure

Correlation function and mutual information

Correlation function and mutual information are two powerful tools to characterize the correlations in a quantum state of a composite system, widely used in many-body physics and in quantum information science, respectively. We find that these two tools may give different conclusions about the order of the degrees of correlation in two specific two-qubit states. This result implies that the orderings of bipartite quantum states according to the degrees of correlation depend on which correlation measure we adopt.Comment: 4.2 pages, 4 figure

Extension of Information Geometry to Non-statistical Systems: Some Examples

Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a statistical manifold. An example of the former is the description of the Bose gas in the grand canonical ensemble. An example of the latter is the modeling of quantum systems with density matrices. Conditional expectations in the quantum context are reviewed. The border problem is discussed: through conditioning the model point shifts to the border of the differentiable manifold.Comment: 8 pages, to be published in the proceedings of GSI2015, Lecture Notes in Computer Science, Springe

Molecular epidemiology of infectious bursal disease virus in Zambia

Nucleotide sequences of the VP2 hypervariable region (VP2-HVR) of 10 infectious bursal disease viruses detected in indigenous and exotic chickens in Zambia from 2004 to 2005 were determined. Phylogenetic analysis showed that the viruses diverged into two genotypes and belonged to the African very virulent types (VV1 and VV2). In the phylogenetic tree, strains in one genotype clustered in a distinct group and were closely related to some strains isolated in western Africa (VV1), with nucleotide similarities of 95.7%– 96.5%. Strains in the other genotype were clustered within the eastern African VV type (VV2), with nucleotide similarities of 97.3%– 98.5%. Both genotypes were distributed in the southern parts of Zambia and had a unique conserved amino acid substitution at 300 (E→A) in addition to the putative virulence marker at positions 222(A), 242(I), 256(I), 294(I) and 299(S). These findings represent the first documentation of the existence of the African VV-IBDV variants in both indigenous and exotic chickens in Zambia

Complementarity and the algebraic structure of 4-level quantum systems

The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras. Complementary decompositions of a 4-level quantum system are described and a characterization of the Bell basis is obtained.Comment: 19 page