In this work, 2099 experimental data of binary systems composed of CO₂ and ionic liquids are studied to predict solubility using a multilayer perceptron. The dataset includes 33 different types of ionic liquids over a wide range of temperatures, pressures, and solubilities. The main objective of this work is to propose a procedure for the prediction of CO₂ solubility in ionic liquids by establishing four stages to determine the model parameters: (1) selection of the learning algorithm, (2) optimization of the first hidden layer, (3) optimization of the second hidden layer, and (4) selection of the input combination. In this study, a bound is set on the number of model parameters: the number of model parameters must be less than the amount of predicted data. Eight different learning algorithms with (4,m,n,1)-type hidden two-layer architectures (m = 2, 4, …, 10 and n = 2, 3, …, 10) are studied, and the artificial neural network is trained with three input combinations with three combinations of thermodynamic variables such as temperature (T), pressure (P), critical temperature (Tc), critical pressure, the critical compressibility factor (Zc), and the acentric factor (ω). The results show that the 4-6-8-1 architecture with the input combination T-P-Tc-Pc and the Levenberg–Marquard learning algorithm is a very acceptable and simple model (95 parameters) with the best prediction and a maximum absolute deviation close to 10%.

Phase space methods, particularly Wigner functions, provide intuitive tools for representing and analyzing quantum states. We focus on systems with SU(2) dynamical symmetry, which naturally describes spin and a wide range of two-mode quantum models. We present a unified phase space framework tailored to these systems, highlighting its broad applicability in quantum optics, metrology, and information. After reviewing the core SU(2) phase-space formalism, we apply it to states designed for optimal quantum sensing, where their nonclassical features are clearly revealed in the Wigner representation. We then extend the approach to systems with an indefinite number of excitations, introducing a generalized framework that captures correlations across multiple SU(2)-invariant subspaces. These results offer practical tools for understanding both theoretical and experimental developments in quantum science.

In this paper we redesign the probabilistic teleportation scheme considered in Phys. Rev. A61, 034301 (2000) by Wan-Li Li et al., where the optimal state extraction protocol complements the basic teleportation process with a partially entangled pure state channel, in order to transfer the unknown state with fidelity 1. Unlike that scheme, where the information of the unknown state is lost if the state extraction fails, our proposal teleports exactly and optimally an unknown state, and allows to recover faithfully that state when the process has not succeeded. In order to study the resilience of the scheme, we apply it to the teleportation problem through a quantum channel in a mixed state with pure dephasing. We find that a successful process transfers an unfaithful state, namely, the outcome state acquires the decoherence of the channel, but the unknown state is recovered by the sender with fidelity 1 if the teleportation fails. In addition, in this case, the fidelity of the teleported state has quantum features only if the channel has an amount of entanglement different from zero.

In this work, four hundred and forty experimental solubility data points of 14 systems composed of methane and ionic liquids are considered to train a multilayer perceptron model. The main objective is to propose a simple procedure for the prediction of methane solubility in ionic liquids. Eight machine learning algorithms are tested to determine the appropriate model, and architectures composed of one input layer, two hidden layers, and one output layer are analyzed. The input variables of an artificial neural network are the experimental temperature (T) and pressure (P), the critical properties of temperature (Tc) and pressure (Pc), and the acentric (ω) and compressibility (Zc) factors. The findings show that a (4,4,4,1) architecture with the combination of T-P-Tc-Pc variables results in a simple 45-parameter model with an absolute prediction deviation of less than 12%.

The solubilities of 498 datasets of N₂O and ionic liquid systems were predicted using a multilayer perceptron. The data used to train the artificial neural network was subjected to the Gibbs–Duhem test to analyze their thermodynamic consistency. The Peng–Robinson cubic equation of state, combined with the Kwak–Mansoori mixing rule, was used as the thermodynamic model to implement the test. The analysis indicated that 71.9% of the data were declared thermodynamically inconsistent. The ability of artificial neural networks (ANNs) to predict the solubility of these systems using experimental datasets that do not satisfy the thermodynamic consistency criteria based on the Gibbs–Duhem equation was studied. The multilayer perceptron model achieved an average absolute deviation of 1.81% and a maximum individual deviation of 7.56%. These results highlight the potential of ANNs as robust predictive tools even when the available data do not fully satisfy thermodynamic consistency criteria.