A large-N approximated field theory for multipartite entanglement

We study the characterization of multipartite entanglement for the random states of an $n$-qbit system. Unable to solve the problem exactly we generalize it, changing complex numbers into real vectors with $N_c$ components (the original problem is recovered for $N_c=2$). Studying the leading diagrams in the large-$N_c$ approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the large-$N_c$ limit.Comment: 12 pages, 15 figure

Polarized ensembles of random pure states

A new family of polarized ensembles of random pure states is presented. These ensembles are obtained by linear superposition of two random pure states with suitable distributions, and are quite manageable. We will use the obtained results for two purposes: on the one hand we will be able to derive an efficient strategy for sampling states from isopurity manifolds. On the other, we will characterize the deviation of a pure quantum state from separability under the influence of noise.Comment: 14 pages, 1 figur

Chiral charge dynamics in Abelian gauge theories at finite temperature

We study fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. We consider the presence of a chemical potential $\mu$ for the fermionic charge, and monitor its evolution with real-time classical lattice simulations. This method accounts for short-scale fluctuations not included in the usual effective magneto-hydrodynamics (MHD) treatment. We observe a self-similar decay of the chemical potential, accompanied by an inverse cascade process in the gauge field that leads to a production of long-range helical magnetic fields. We also study the chiral charge dynamics in the presence of an external magnetic field $B$, and extract its decay rate $\Gamma_5 \equiv -{d\log \mu\over dt}$. We provide in this way a new determination of the gauge coupling and magnetic field dependence of the chiral rate, which exhibits a best fit scaling as $\Gamma_5 \propto e^{11/2}B^2$. We confirm numerically the fluctuation-dissipation relation between $\Gamma_5$ and $\Gamma_{\rm diff}$, the Chern-Simons diffusion rate, which was obtained in a previous study. Remarkably, even though we are outside the MHD range of validity, the dynamics observed are in qualitative agreement with MHD predictions. The magnitude of the chiral/diffusion rate is however a factor $\sim 10$ times larger than expected in MHD, signaling that we are in reality exploring a different regime accounting for short scale fluctuations. This discrepancy calls for a revision of the implications of fermion number and chirality non-conservation in finite temperature Abelian gauge theories, though not definite conclusion can be made at this point until hard-thermal-loops (HTL) are included in the lattice simulations.Comment: 32 pages, 11 figures. V2: Improved introduction, added some discussions and references. Corrected typos. Corresponds to published versio

Local Hamiltonians for Maximally Multipartite Entangled States

We study the conditions for obtaining maximally multipartite entangled states (MMES) as non-degenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMES as eigenstates.Comment: 6 pages, 3 figures, published versio

A framework for trustworthiness assessment based on fidelity in cyber and physical domains

We introduce a method for the assessment of trust for n-open systems based on a measurement of fidelity and present a prototypical implementation of a complaint architecture. We construct a MAPE loop which monitors the compliance between corresponding figures of interest in cyber- and physical domains; derive measures of the system's trustworthiness; and use them to plan and execute actions aiming at guaranteeing system safety and resilience. We conclude with a view on our future work

A predictive model for the thermomechanical overstretching transition of double stranded DNA

By extending the classical Peyrard-Bishop model, we are able to obtain a fully analytical description for the mechanical resistance of DNA under stretching at variable values of temperature, number of base pairs and intrachains and interchains bonds stiffness. In order to compare elasticity and temperature effects, we first analyze the system in the zero temperature mechanical limit, important to describe several experimental effects including possible hysteresis. We then analyze temperature effects in the framework of equilibrium statistical mechanics. In particular, we obtain an analytical expression for the temperature dependent melting force and unzipping assigned displacement in the thermodynamical limit, also depending on the relative stability of intra vs inter molecular bonds. Such results coincide with the purely mechanical model in the limit of zero temperature and with the denaturation temperature that we obtain with the classical transfer integral method. Based on our analytical results, explicit analysis of the phase diagrams and cooperativity parameters are obtained, where also discreteness effect can be accounted for. The obtained results are successfully applied in reproducing the thermomechanical experimental melting of DNA and the response of DNA hairpins. Due to its generality, the proposed approach can be extended to other thermomechanically induced molecular melting phenomena