Structural precursor to the metal-insulator transition in V_2O_3

The temperature dependence of the local structure of V_2O_3 in the vicinity of the metal to insulator transition (MIT) has been investigated using hard X-ray absorption spectroscopy. It is shown that the vanadium pair distance along the hexagonal c-axis changes abruptly at the MIT as expected. However, a continuous increase of the tilt of these pairs sets in already at higher temperatures and reaches its maximum value at the onset of the electronic and magnetic transition. These findings confirm recent theoretical results which claim that electron-lattice coupling is important for the MIT in V_2O_3. Our results suggest that interactions in the basal plane play a decisive role for the MIT and orbital degrees of freedom drive the MIT via changes in hybridization.Comment: 6 pages, 5 figures, 2 table

Singular value decomposition and matrix reorderings in quantum information theory

We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyse the correspondence between quantum states and operations with the help of Jamiolkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.Comment: 11 pages, no figures, see http://zksi.iitis.pl/wiki/projects:mathematica-qi for related softwar

Electronic structure of nanoscale iron oxide particles measured by scanning tunneling and photoelectron spectroscopies

We have investigated the electronic structure of nano-sized iron oxide by scanning tunnelling microscopy (STM) and spectroscopy (STS) as well as by photoelectron spectroscopy. Nano particles were produced by thermal treatment of Ferritin molecules containing a self-assembled core of iron oxide. Depending on the thermal treatment we were able to prepare different phases of iron oxide nanoparticles resembling gamma-Fe2O3, alpha-Fe2O3, and a phase which apparently contains both gamma-Fe2O3 and alpha-Fe2O3. Changes to the electronic structure of these materials were studied under reducing conditions. We show that the surface band gap of the electronic excitation spectrum can differ from that of bulk material and is dominated by surface effects.Comment: REVTeX, 6 pages, 10 figures, submitted to PR

Generalized Induced Norms

Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the complex field C. An interesting problem in matrix theory is that "are there two norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for all A in M_n. We will investigate this problem and its various aspects and will discuss under which conditions ||.||_1=||.||_2.Comment: 8 page

Vacuum entanglement governs the bosonic character of magnons

It is well known that magnons, elementary excitations in a magnetic material, behave as bosons when their density is low. We study how the bosonic character of magnons is governed by the amount of a multipartite entanglement in the vacuum state on which magnons are excited. We show that if the multipartite entanglement is strong, magnons cease to be bosons. We also consider some examples, such as ground states of the Heisenberg ferromagnet and the transverse Ising model, the condensation of magnons, the one-way quantum computer, and Kitaev's toric code. Our result provides insights into the quantum statistics of elementary excitations in these models, and into the reason why a non-local transformation, such as the Jordan-Wigner transformation, is necessary for some many-body systems.Comment: 4 pages, no figur

Unitarity bounds and RG flows in time dependent quantum field theory

We generalize unitarity bounds on operator dimensions in conformal field theory to field theories with spacetime dependent couplings. Below the energy scale of spacetime variation of the couplings, their evolution can strongly affect the physics, effectively shifting the infrared operator scaling and unitarity bounds determined from correlation functions in the theory. We analyze this explicitly for large-$N$ double-trace flows, and connect these to UV complete field theories. One motivating class of examples comes from our previous work on FRW holography, where this effect explains the range of flavors allowed in the dual, time dependent, field theory.Comment: 38 page

Tight lower bound to the geometric measure of quantum discord

Dakic, Vedral and Brukner [Physical Review Letters \tf{105},190502 (2010)] gave a geometric measure of quantum discord in a bipartite quantum state as the distance of the state from the closest classical quantum (or zero discord) state and derived an explicit formula for a two qubit state. Further, S.Luo and S.Fu [Physical Review A \tf{82}, 034302 (2010)] obtained a generic form of this geometric measure for a general bipartite state and established a lower bound. In this brief report we obtain a rigorous lower bound to the geometric measure of quantum discord in a general bipartite state which dominates that obtained by S.Luo and S.Fu.Comment: 10 pages,2 figures. In the previous versions, a constraint was ignored while optimizing the second term in Eq.(5), in which case, only a lower bound on the geometric discord can be obtained. The title is also consequently changed. Accepted in Phys.Rev.

Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs

We prove multiplicativity of maximal output $p$ norm of classical noise channels and thermal noise channels of arbitrary modes for all $p>1$ under the assumption that the input signal states are Gaussian states. As a direct consequence, we also show the additivity of the minimal output entropy and that of the energy-constrained Holevo capacity for those Gaussian channels under Gaussian inputs. To the best of our knowledge, newly discovered majorization relation on symplectic eigenvalues, which is also of independent interest, plays a central role in the proof.Comment: 9 pages, no figures. Published Versio

Maximally entangled mixed states of two qubits

We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states. Three measures of entanglement are considered: entanglement of formation, negativity and relative entropy of entanglement. Surprisingly all states that maximize one measure also maximize the others. We will give a complete characterization of these generalized Bell states and prove that these states for fixed eigenvalues are all equivalent under local unitary transformations. We will furthermore characterize all nearly entangled states closest to the maximally mixed state and derive a new lower bound on the volume of separable mixed states

Bounds on Quantum Correlations in Bell Inequality Experiments

Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description. However, despite the importance of Bell inequalities, it is not known in general how to determine whether a given entangled state will violate a Bell inequality. This is because one can choose to make many different measurements on a quantum system to test any given Bell inequality and the optimization over measurements is a high-dimensional variational problem. In order to better understand this problem we present algorithms that provide, for a given quantum state, both a lower bound and an upper bound on the maximal expectation value of a Bell operator. Both bounds apply techniques from convex optimization and the methodology for creating upper bounds allows them to be systematically improved. In many cases these bounds determine measurements that would demonstrate violation of the Bell inequality or provide a bound that rules out the possibility of a violation. Examples are given to illustrate how these algorithms can be used to conclude definitively if some quantum states violate a given Bell inequality.Comment: 13 pages, 1 table, 2 figures. Updated version as published in PR