arXiv subjects

H. Narnhofer

Publications and source records attributed to H. Narnhofer.

10 recordsLinked to original sources

arXiv2025

Cluster property and Bell's inequalities

Among the many loopholes that might be invoked to reconcile local realism with the experimental violations of Bell's inequalities, the space-dependence of the correlation functions appears particularly relevant for its connections with the so-called cluster property, one of the basic ingredient of axiomatic quantum field theory. The property states that the expectation values of products of observables supported within space-like separated space-time regions factorize. Actually, in some massive models the factorization is exponentially fast with respect to the distance between the systems possibly involved in actual experiments. It is then often argued that considering the space dependence of the quantities involved in the Bell's like inequalities would eventually not violate them and thus support the reproducibility of the quantum behaviour by a suitable local hidden variable model. In this note, we show when this is actually the case and how non-local effects can still be visible.

quant-ph↗

arXiv2023

A quantum fluctuation description of charge qubits

We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction. Starting from the microscopic description of the latter in terms of two tunneling BCS models in the strong-coupling quasi-spin formulation, we derive the Hamiltonian governing the quantum behavior of the circuit in the limit of a large number $N$ of quasi-spins. Our approach relies on the identification of suitable quantum fluctuations, i.e. of collective quasi-spin operators, which account for the presence of fluctuation operators in the superconducting phase that retain a quantum character in spite of the large-$N$ limit. We show indeed that these collective quantum fluctuations generate the Heisenberg algebra on the circle and that their dynamics reproduces the one of the quantized charge-qubit, without the need of a phenomenological ``third quantization'' of a semiclassically inspired model. As a byproduct of our derivation, we explicitly obtain the temperature dependence of the junction critical Josephson current in the strong coupling regime, a result which is not directly accessible using standard approximation techniques.

quant-ph↗

arXiv2017

Quantum Fluctuations in Mesoscopic Systems

Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations, that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in between the quantum microscopic scale and the classical macroscopic one. We hereby present the general theory of quantum fluctuations in mesoscopic systems and study their dynamics in a quantum open system setting, taking into account the unavoidable effects of dissipation and noise induced by the external environment. As in the case of microscopic systems, decoherence is not always the only dominating effect at the mesoscopic scale: certain type of environments can provide means for entangling collective fluctuations through a purely noisy mechanism.

quant-ph↗

arXiv2014

On reduction of the wave-packet, decoherence, irreversibility and the second law of thermodynamics

We prove a quantum version of the second law of thermodynamics: the (quantum) Boltzmann entropy increases if the initial (zero time) density matrix decoheres, a condition generally satisfied in Nature. It is illustrated by a model of wave-packet reduction, the Coleman-Hepp model, along the framework introduced by Sewell in his approach to the quantum measurement problem. Further models illustrate the monotonic-versus-non-monotonic behavior of the quantum Boltzmann entropy in time. As a last closely related topic, decoherence, which was shown by Narnhofer and Thirring to enforce macroscopic purity in the case of quantum K systems, is analysed within a different class of quantum chaotic systems, viz. the quantum Anosov models as defined by Emch, Narnhofer, Sewell and Thirring. A review of the concept of quantum Boltzmann entropy, as well as of some of the rigorous approaches to the quantum measurement problem within the framework of Schrödinger dynamics, is given, together with an overview of the C* algebra approach, which encompasses the relevant notions and definitions in a comprehensive way.

math-ph↗

arXiv2007

The geometry of bipartite qutrits including bound entanglement

We investigate the state space of bipartite qutrits. We construct an analog to the "magic" tetrahedron for bipartite qubits--a magic simplex W. It is formed by all convex combination of nine Bell states which are constructed using the Weyl operators. Due to the high symmetry it is enough to consider certain typical slices through W. Via optimal entanglement witnesses we find regions of bound entangled states inside W.

quant-ph↗

arXiv2005

Multi-distributed Entanglement in Finitely Correlated Chains

The entanglement-sharing properties of an infinite spin-chain are studied when the state of the chain is a pure, translation-invariant state with a matrix-product structure. We study the entanglement properties of such states by means of their finitely correlated structure. These states are recursively constructed by means of an auxiliary density matrix ρon a matrix algebra B and a completely positive map E: A \otimes B -> B, where A is the spin 2\times 2 matrix algebra. General structural results for the infinite chain are therefore obtained by explicit calculations in (finite) matrix algebras. In particular, we study not only the entanglement shared by nearest-neighbours, but also, differently from previous works, the entanglement shared between connected regions of the spin-chain. This range of possible applications is illustrated and the maximal concurrence C=1/\sqrt{2} for the entanglement of connected regions can actually be reached.

quant-ph↗

arXiv2004

Separability for lattice systems at high temperature

Equilibrium states of infinite extended lattice systems at high temperature are studied with respect to their entanglement. Two notions of separability are offered. They coincide for finite systems but differ for infinitely extended ones. It is shown that for lattice systems with localized interaction for high enough temperature there exists no local entanglement. Even more quasifree states at high temperature are also not distillably entangled for all local regions of arbitrary size. For continuous systems entanglement survives for all temperatures. In mean field theories it is possible, that local regions are not entangled but the entanglement is hidden in the fluctuation algebra.

quant-ph↗

arXiv2002

Broken Symmetries in the Entanglement of Formation

We compare some recent computations of the entanglement of formation in quantum information theory and of the entropy of a subalgebra in quantum ergodic theory. Both notions require optimization over decompositions of quantum states. We show that both functionals are strongly related for some highly symmetric density matrices. We discuss the presence of broken symmetries in relation with the structure of the optimal decompositions.

quant-ph↗

arXiv2002

A Geometric Picture of Entanglement and Bell Inequalities

We work in the real Hilbert space H_s of hermitian Hilbert-Schmid operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set S subset H_s of separable states. This violation equals the euclidean distance in H_s of the entangled state to S and thus entanglement, GBI and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.

quant-ph↗

arXiv2001

Thermal correlators of anyons in two dimensions

The anyon fields have trivial $α$-commutator for $α$ not integer. For integer $α$ the commutators become temperature-dependent operator valued distributions. The $n$-point functions do not factorize as for quasifree states.

math-ph↗