Spectral Conditions on the State of a Composite Quantum System Implying its Separability

For any unitarily invariant convex function F on the states of a composite quantum system which isolates the trace there is a critical constant C such that F(w)<= C for a state w implies that w is not entangled; and for any possible D > C there are entangled states v with F(v)=D. Upper- and lower bounds on C are given. The critical values of some F's for qubit/qubit and qubit/qutrit bipartite systems are computed. Simple conditions on the spectrum of a state guaranteeing separability are obtained. It is shown that the thermal equilbrium states specified by any Hamiltonian of an arbitrary compositum are separable if the temperature is high enough.Comment: Corrects 1. of Lemma 2, and the (under)statement of Proposition 7 of the earlier version

Local Hidden Variable Theories for Quantum States

While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and non-locality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the problem of constructing local hidden variable theories for quantum states. The method is based on constructing a so-called symmetric quasi-extension of the quantum state that gives rise to a local hidden variable model with a certain number of settings for the observers Alice and Bob.Comment: 8 pages Revtex; v2 contains substantial changes, a strengthened main theorem and more reference

de Finetti reductions for correlations

When analysing quantum information processing protocols one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structure. de Finetti theorems provide such a structure for the case where certain symmetries hold. More precisely, they relate states that are invariant under permutations of subsystems to states in which the subsystems are independent of each other. This relation plays an important role in various areas, e.g., in quantum cryptography or state tomography, where permutation invariant systems are ubiquitous. The known de Finetti theorems usually refer to the internal quantum state of a system and depend on its dimension. Here we prove a different de Finetti theorem where systems are modelled in terms of their statistics under measurements. This is necessary for a large class of applications widely considered today, such as device independent protocols, where the underlying systems and the dimensions are unknown and the entire analysis is based on the observed correlations.Comment: 5+13 pages; second version closer to the published one; new titl

Quantum Statistical Mechanics of General Mean Field Systems

We consider mean field modules for n identical systems interacting with each other, and with another additional system. Each Hamiltonian H_n is taken to be symmetric with respect to permutations of the identical systems, and for large n and arbitrary k, (n+k)^(-1)H_(n+k) is approximately equal to n^(-1)H_n, taken as an operator of the larger system, and resymmetrised. The validity of the Gibbs Variational Principle is established; firstly, at the level of the states of the infinite system, then secondly at the level of the states of the single system. A generalized gap-equation is obtained at this second level. In some cases, the variational problem reduces further; this leads to a non-commutative version of the larger deviation results of Cramer-Varadhan for R^d-valued random variables

Free energy density for mean field perturbation of states of a one-dimensional spin chain

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).Comment: 29 pages, Section 5 added, to appear in Rev. Math. Phy

Validation of a small scale woody biomass downdraft gasification plant coupled with gas engine

In recent years, small scale cogeneration systems (< 500 kWe) distributed in different geographical locations using biomass has received special attention as economically competitive and environmentally friendly ways of producing energy. These systems can be integrated to industrial and agricultural activities where biomass residues are generated and can be converted into electricity and thermal energy by combustion or gasification. The legislations of many European countries such as Italy concerning renewable energy and energy efficiency along the taxation schemes have raised the incentives for small scale cogeneration plants. Consequently, there is a clear economic interest of the companies in this sector and there is also a scientific interest towards demonstration of their energetic efficiency, environmental performance and reliability. Among the suggested technologies for the biomass conversion into energy, downdraft gasification (using air as gasification agent), coupled with internal combustion engines, has the advantage of high electric efficiency (~ 25%) and low tar generation, making easier the gas cleaning process necessary for its use into engines. In the present work, the results of a measurement campaign performed on a commercial scale 350 kWth downdraft woodchips gasification plant, coupled with an SI internal combustion engine (ICE), are presented and discussed. The main goals of this first experimental campaign have been to verify the stability of gasifier and engine operation, operability of the plant and to determine its energy efficiency. The campaign verified a stable operation of the gasifier and the plant produced a syngas with a composition suitable for a gas engine. The energy balance resulted in a potential overall wood fuel to electricity efficiency of about 23 %

Crystal structure of samarium nickel tetraaluminide, SmNiAl4

Abstract Al4NiSm, orthorhombic, Cmcm (no. 63), a = 4.0948(6) Å, b = 15.582(3) Å, c = 6.610(1) Å, V = 421.8 Å3, Z = 4, Rgt(F) = 0.028, wRobs(F2) = 0.074, T = 293 K

One-and-a-half quantum de Finetti theorems

We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor product of U_mu and U_nu; let xi be the state obtained by tracing out U_nu. We show that xi is close to a convex combination of states Uv, where U is in U(d) and v is the highest weight vector in U_mu. When U_{mu+nu} is the symmetric representation, this yields the conventional quantum de Finetti theorem for symmetric states, and our method of proof gives near-optimal bounds for the approximation of xi by a convex combination of product states. For the class of symmetric Werner states, we give a second de Finetti-style theorem (our 'half' theorem); the de Finetti-approximation in this case takes a particularly simple form, involving only product states with a fixed spectrum. Our proof uses purely group theoretic methods, and makes a link with the shifted Schur functions. It also provides some useful examples, and gives some insight into the structure of the set of convex combinations of product states.Comment: 14 pages, 3 figures, v4: minor additions (including figures), published versio