Dennis I. Martínez-Moreno

We quantify and optimize the predictability of local observables in bipartite quantum systems by employing the Bayes risk and the inference variance, two measures rooted in statistical learning theory. Specifically, we minimized these quantities when the prediction is improved by an additional quantum system, providing analytical expressions for arbitrary two-qubit states, and showcasing a connection with Einstein-Podolsky-Rosen steering criteria. Then, we embed our Bayes risk minimization into an entanglement-based quantum key distribution protocol, yielding asymptotically higher secure-key rates than standard BB84 under realistic noise. We applied these results to Bell states affected by local amplitude-damping noises, and spin correlation in top-antitop quark pairs from high-energy collisions.

Symmetries associated with the Hamiltonian describing bilayer graphene subjected to a constant magnetic field perpendicular to the plane of the bilayer are calculated using polar coordinates. These symmetries are then applied to explain some fundamental properties, such as the spectrum and the integer pseudo-spin character of the eigenfunctions. The probability and current densities of the bilayer Hamiltonian have also been calculated in polar coordinates and shown to be gauge invariant and scalar under generalized rotations. We also define appropriate coherent states of this system as eigenfunctions, with complex eigenvalues, of a suitable chose annihilation operator. In this framework, symmetries are also useful to show the meaning of the complex eigenvalue in terms of expected values. The local current density of these coherent states is shown to exhibit a kind of radial component interference effect, something that has gone unnoticed until now. Some of these results that have just been exposed are graphically illustrated throughout the manuscript.

The multiphoton coherent states, a generalization to coherent states, are derived for electrons in bilayer graphene placed in a constant homogeneous magnetic field which is orthogonal to the bilayer surface. For that purpose a generalized annihilation operator is constructed in order to determine the multiphoton coherent states as eigenstates of such operator with complex eigenvalue. In addition, some physical quantities are calculated for these states, as the Heisenberg uncertainty relation, the probability density and the mean energy value. Finally, in order to study the dynamics of the system the time evolution is explored and the time-correlation function is computed.

In this paper we consider the interaction of electrons in bilayer graphene with a constant homogeneous magnetic field which is orthogonal to the bilayer surface. Departing from the energy eigenstates of the effective Hamiltonian, the corresponding coherent states will be constructed. For doing this, first we will determine appropriate creation and annihilation operators in order to subsequently derive the coherent states as eigenstates of the annihilation operator with complex eigenvalue. Then, we will calculate some physical quantities, as the Heisenberg uncertainty relation, the probabilities and current density as well as the mean energy value. Finally, we will explore the time evolution for these states and we will compare it with the corresponding evolution for monolayer graphene coherent states.