Qubit representation of qudit states: correlations and state reconstruction

A method to establish a qubit decomposition of a general qudit state is presented. This new representation allows a geometrical depiction of any qudit state in the Bloch sphere. Additionally, we show that the nonnegativity conditions of the qudit state imply the existence of quantum correlations between the qubits which compose it. These correlations are used to define new inequalities which the density matrices components must satisfy. The importance of such inequalities in the reconstruction of a qudit state is addressed. As an example of the general procedure the qubit decomposition of a qutrit system is shown, which allows a classification of the qutrit states by fixing their invariants ${\rm Tr}(\hat{\rho}^2)$, ${\rm Tr}(\hat{\rho}^3)$.Comment: Accepted in Quantum Information Processing journa

Quantum ratchet with Lindblad rate equations

A quantum random walk model is established on a one-dimensional periodic lattice that fluctuates between two possible states. This model is defined by Lindblad rate equations that incorporate the transition rates between the two lattice states. Leveraging the system's symmetries, the particle velocity can be described using a finite set of equations, even though the state space is of infinite dimension. These equations yield an analytical expression for the velocity in the long-time limit, which is employed to analyze the characteristics of directed motion. Notably, the velocity can exhibit multiple inversions, and to achieve directed motion, distinct, nonzero transition rates between lattice states are required.Comment: 8 pages, 3 figure

Information theoretic analysis of Landau levels in monolayer phosphorene under magnetic and electric fields

This study has been partially financed by the Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía and European Regional Development Fund (ERDF), under projects with Ref. SOMM17/6105/UGR and FQM381, and by the spanish MICINN under project PGC2018-097831-B-I00. O. C. thanks support of the project DGAPA:IN101619.We analyze the structure of phosphorene Landau energy levels under electric and magnetic fields perpendicular to the material sheet. The electric field Δ provides a tunable band gap, and a topological phase transition occurs at a critical value Δc. Low energy Landau levels and edge states are analyzed with different information theoretic measures (like participation ratio, fidelity and entropy) and some order parameters, which turn out to be good markers of the topological phase transition.Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía and European Regional Development Fund (ERDF), under projects with Ref. SOMM17/6105/UGR and FQM381Spanish MICINN under project PGC2018-097831-B-I00Project DGAPA:IN10161

Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space

We propose a method to identify the order of a quantum phase transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the quantum cusp and four different paradigmatic boson models: Dicke, Lipkin-Meshkov-Glick, interacting boson model, and vibron model.We thank J. E. Garcia Ramos for useful discussion. Work in University of Huelva was funded trough MINECO Grants No. FIS2011-28738-C02-02 and No. FIS2014-53448-C2-2-P and by Spanish Consolider-Ingenio 2010 (Grant No. CPANCSD2007-00042). Work in University of Granada was supported by the Spanish Projects: MINECO Grant No. FIS2014-59386-P and Junta de Andalucia Projects No. P12.FQM.1861 and No. FQM-381