Measurement in control and discrimination of entangled pairs under self-distortion

Quantum correlations and entanglement are fundamental resources for quantum information and quantum communication processes. Developments in these fields normally assume these resources stable and not susceptible of distortion. That is not always the case, Heisenberg interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e. g. for quantum computation or quantum cryptography). Experimental work shows how to produce entangled spin qubits in quantum dots and electron gases, so its identification and control are crucial for later applications. The presence of parasite magnetic fields modifies the expected properties and behavior for which the pair was intended. Quantum measurement and control help to discriminate the original state in order to correct it or, just to try of reconstruct it using some procedures which do not alter their quantum nature. Two different kinds of quantum entangled pairs driven by a Heisenberg Hamiltonian with an additional inhomogeneous magnetic field which becoming self-distorted, can be reconstructed without previous discrimination by adding an external magnetic field, with fidelity close to 1 (with respect to the original state, but without discrimination). After, each state can be more efficiently discriminated. The aim of this work is to show how combining both processes, first reconstruction without discrimination and after discrimination with adequate non-local measurements, it's possible a) improve the discrimination, and b) reprepare faithfully the original states. The complete process gives fidelities better than 0.9. In the meanwhile, some results about a class of equivalence for the required measurements were found. This property lets us select the adequate measurement in order to ease the repreparation after of discrimination, without loss of entanglement.Comment: 6 figure

Cotunneling theory of inelastic STM spin spectroscopy

We propose cotunneling as the microscopic mechanism that makes possible inelastic electron spectroscopy of magnetic atoms in surfaces for a wide range of systems, including single magnetic adatoms, molecules and molecular stacks. We describe electronic transport between the scanning tip and the conducting surface through the magnetic system (MS) with a generalized Anderson model, without making use of effective spin models. Transport and spin dynamics are described with an effective cotunneling Hamiltonian in which the correlations in the magnetic system are calculated exactly and the coupling to the electrodes is included up to second order in the tip-MS and MS-substrate. In the adequate limit our approach is equivalent to the phenomenological Kondo exchange model that successfully describe the experiments . We apply our method to study in detail inelastic transport in two systems, stacks of Cobalt Phthalocyanines and a single Mn atom on Cu$_2$N. Our method accounts both, for the large contribution of the inelastic spin exchange events to the conductance and the observed conductance asymmetry.Comment: 12 pages, 6 figure

Network-wide assessment of 4D trajectory adjustments using an agent-based model

This paper presents results from the SESAR ER3 Domino project. It focuses on an ECAC-wide assessment of two 4D-adjustment mechanisms, implemented separately and conjointly. These reflect flight behaviour en-route and at-gate, optimising given (cost) objective functions. New metrics designed to capture network effects are used to analyse the results of a microscopic, agent based model. The results show that some implementations of the mechanisms allow the protection of the network from ‘domino’ effects. Airlines focusing on costs may trigger additional side-effects on passengers, displaying, in some instances, clear trade-offs between passenger- and flight-centric metrics

Generating sequences and Poincar\'e series for a finite set of plane divisorial valuations

Let $V$ be a finite set of divisorial valuations centered at a 2-dimensional regular local ring $R$. In this paper we study its structure by means of the semigroup of values, $S_V$, and the multi-index graded algebra defined by $V$, \gr_V R. We prove that $S_V$ is finitely generated and we compute its minimal set of generators following the study of reduced curve singularities. Moreover, we prove a unique decomposition theorem for the elements of the semigroup. The comparison between valuations in $V$, the approximation of a reduced plane curve singularity $C$ by families of sets $V^{(k)}$ of divisorial valuations, and the relationship between the value semigroup of $C$ and the semigroups of the sets $V^{(k)}$, allow us to obtain the (finite) minimal generating sequences for $C$ as well as for $V$. We also analyze the structure of the homogeneous components of \gr_V R. The study of their dimensions allows us to relate the Poincar\'e series for $V$ and for a general curve $C$ of $V$. Since the last series coincides with the Alexander polynomial of the singularity, we can deduce a formula of A'Campo type for the Poincar\'e series of $V$. Moreover, the Poincar\'e series of $C$ could be seen as the limit of the series of $V^{(k)}$, $k\ge 0$

A minimal model for acoustic forces on Brownian particles

We present a generalization of the inertial coupling (IC) [Usabiaga et al. J. Comp. Phys. 2013] which permits the resolution of radiation forces on small particles with arbitrary acoustic contrast factor. The IC method is based on a Eulerian-Lagrangian approach: particles move in continuum space while the fluid equations are solved in a regular mesh (here we use the finite volume method). Thermal fluctuations in the fluid stress, important below the micron scale, are also taken into account following the Landau-Lifshitz fluid description. Each particle is described by a minimal cost resolution which consists on a single small kernel (bell-shaped function) concomitant to the particle. The main role of the particle kernel is to interpolate fluid properties and spread particle forces. Here, we extend the kernel functionality to allow for an arbitrary particle compressibility. The particle-fluid force is obtained from an imposed no-slip constraint which enforces similar particle and kernel fluid velocities. This coupling is instantaneous and permits to capture the fast, non-linear effects underlying the radiation forces on particles. Acoustic forces arise either because an excess in particle compressibility (monopolar term) or in mass (dipolar contribution) over the fluid values. Comparison with theoretical expressions show that the present generalization of the IC method correctly reproduces both contributions. Due to its low computational cost, the present method allows for simulations with many particles using a standard Graphical Processor Unit (GPU)