Quantum Discord, Geometric Discord, and Information Deficit in finite XY chains

N. CANOSA; L. CILIBERTI; R. ROSSIGNOLI

Paraty

Workshop; IV Quantum information school and workshop; 2013

The quantum correlations of spin pairs in the exact ground state of finite XY spin chains in a transverse field are examined, by evaluating the Quantum Discord, the Geometric Discord as well as the Information Deficit. We show that parity effects are of crucial importance for describing the behavior of these measures below the critical field, and imply full range in the immediate vicinity of the factorizing field, where they become independent of separation and coupling range. It is also shown that while these measures exhibit the same qualitative asymptotic behaviour for large separations or temperatures, at the same time important differences arise in the minimizing local measure that defines them. Whereas the Quantum Discord prefers a spin measurement perpendicular to the transverse field, the Geometric Discord and the Information Deficit exhibit a perpendicular to parallel transition as the field increases below the critical field, which subsists at all temperatures and for all separations. Illustrative numerical results of these measures in $XY$ as well as $XX$ spin chains are provided.