Conditional states and entropy in qudit-qubit systems

CANOSA, N.; BILKIS, M.; GIGENA, N.; ROSSIGNOLI, R.

Buenos Aires

Workshop; XXI Giambiagi Winter School; 2019

FCEyN UBA

We analyze, in correlated mixed states of qudit-qubit systems, the set of all conditional qubit states that can be reached after general remote local measurements at the qudit, based on rank one projectors. While for similar measurements at the qubit, the conditional post-measurement qudit states form the surface of an ellipsoid, for a measurement at the qudit the set of post-measurement qubit states can form more complex geometries. In particular, we show the emergence of sets which are the convex hull of solid ellipsoids and which may lead to cone and triangle-like shapes in limit cases. We also examine the associated measurement dependent conditional entropy, providing a full analytic determination of its minimum and the minimizing local measurement at the qudit for the states considered. Separable rank two mixtures are also discussed [1]. [1] M. Bilkis, N. Canosa, R. Rossignoli et al, Phys. Rev. A (2019, in press).