IFLP   13074
INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
artículos
Título:
Generalized conditional entropy in bipartite quantum systems
Autor/es:
N. GIGENA; R. ROSSIGNOLI
Revista:
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Editorial:
IOP PUBLISHING LTD
Referencias:
Lugar: Londres; Año: 2013 p. 1530201 - 1530218
ISSN:
1751-8113
Resumen:
We analyze, for a general concave entropic form, the associated conditional entropy of a quantum system A+B, obtained as a result of a local measurement on one of the systems (B). This quantity is a measure of the average mixedness of A after such measurement, and its minimum over all local measurements is shown to be the associated entanglement of formation between A and a purifying third systemC. In the case of the vonNeumann entropy, thisminimum determines also the quantum discord. For classically correlated states and mixtures of a pure state with the maximally mixed state, we show that the minimizing measurement can be determined analytically and is universal, i.e., the same for all concave forms. While these properties no longer hold for general states, we also show that in the special case of the linear entropy, an explicit expression for the associated conditional entropy can be obtained, whose minimum among projective measurements in a general qudit?qubit state can be determined analytically, in terms of the largest eigenvalue of a simple 3×3 correlation matrix. Such minimum determines the maximum conditional purity of A, and the associated minimizing measurement is shown to be also universal in the vicinity of maximal mixedness. Results for X states, including typical reduced states of spin pairs in XY chains at weak and strong transverse fields, are also provided and indicate that the measurements minimizing the von Neumann and linear conditional entropies are typically coincident in these states, being determined essentially by the main correlation. They can differ, however, substantially from that minimizing the geometric discord.