Three path interference using nuclear magnetic resonance: a test of the consistency of Born's rule

The Born rule is at the foundation of quantum mechanics and transforms our classical way of understanding probabilities by predicting that interference occurs between pairs of independent paths of a single object. One consequence of the Born rule is that three way (or three paths) quantum interference does not exist. In order to test the consistency of the Born rule, we examine detection probabilities in three path intereference using an ensemble of spin-1/2 quantum registers in liquid state nuclear magnetic resonance (LSNMR). As a measure of the consistency, we evaluate the ratio of three way interference to two way interference. Our experiment bounded the ratio to the order of $10^{-3} \pm 10^{-3}$, and hence it is consistent with Born's rule.Comment: 11 pages, 4 figures; Improved presentation of figures 1 and 4, changes made in section 2 to better describe the experiment, minor changes throughout, and added several reference

Information-Entropic Measure of Energy-Degenerate Kinks in Two-Field Models

We investigate the existence and properties of kink-like solitons in a class of models with two interacting scalar fields. In particular, we focus on models that display both double and single-kink solutions, treatable analytically using the Bogomol'nyi--Prasad--Sommerfield bound (BPS). Such models are of interest in applications that include Skyrmions and various superstring-motivated theories. Exploring a region of parameter space where the energy for very different spatially-bound configurations is degenerate, we show that a newly-proposed momentum-space entropic measure called Configurational Entropy (CE) can distinguish between such energy-degenerate spatial profiles. This information-theoretic measure of spatial complexity provides a complementary perspective to situations where strictly energy-based arguments are inconclusive

Thermal entanglement witness for materials with variable local spin lengths

We show that the thermal entanglement in a spin system using only magnetic susceptibility measurements is restricted to the insulator materials. We develop a generalization of the thermal entanglement witness that allows us to get information about the system entanglement with variable local spin lengths that can be used experimentally in conductor or insulator materials. As an application, we study thermal entanglement for the half-filled Hubbard model for linear, square and cubic clusters. We note that it is the itinerancy of electrons that favors the entanglement. Our results suggest a weak dependence between entanglement and external spin freedom degrees.Comment: 4 pages, 3 figure

Procedure to evaluate multivariate statistical process control using ARIMA-ARCH models

Technological development and production processes require statistical process control in the use of alternative techniques to evaluate a productive process. This paper proposes an alternative procedure for monitoring a multivariate productive process using residuals obtained from the principal component scores modeled by the general class of autoregressive integrated moving average (ARIMA) and the generalized autoregressive conditional heteroskedasticity (GARCH) processes. We seek to obtain and investigate non-correlated and independent residuals by means of X-bar and exponentially weighted moving average (EWMA) charts as a way to capture large and small variations in the productive process. The principal component analysis deals with the correlation among the variables and reduces the dimensions. The ARIMA-GARCH model estimates the mean and volatility of the principal components selected, providing independent residuals that are analyzed using control charts. Thus, a multivariate process can be assessed using univariate techniques, taking into account both the mean and the volatility behavior of the process. Therefore, we present an alternative procedure to evaluate a process with multivariate features to determine the level of volatility persistence in the productive process when an external action occurs