Generalized conditional entropy optimization for qudit-qubit states

• Autores: Gigena, Nicolás Alejandro; Rossignoli, Raúl Dante
• Año de publicación: 2014
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Física; Conditional entropy; Von neumann entropy; Physics; Statistical physics; Quantum discord; Conditional quantum entropy; Quantum relative entropy; Joint quantum entropy; Binary entropy function; Generalized relative entropy; Quantum mechanics
• Institución: Universidad Nacional de La Plata

We derive a general approximate solution to the problem of minimizing the conditional entropy of a qudit-qubit system resulting from a local measurement on the qubit, which is valid for general entropic forms and becomes exact in the limit of weak correlations. This entropy measures the average conditional mixedness of the postmeasurement state of the qudit, and its minimum among all local measurements represents a generalized entanglement of formation. In the case of the von Neumann entropy, it is directly related to the quantum discord. It is shown that at the lowest nontrivial order, the problem reduces to the minimization of a quadratic form determined by the correlation tensor of the system, the Bloch vector of the qubit and the local concavity of the entropy, requiring just the diagonalization of a 3×3 matrix. A simple geometrical picture in terms of an associated correlation ellipsoid is also derived, which illustrates the link between entropy optimization and correlation access and which is exact for a quadratic entropy. The approach enables a simple estimation of the quantum discord. Illustrative results for two-qubit states are discussed.
Instituto de Física La Plata