Petz-Renyi Relative Entropy of Quantum Guassian States

We study the Petz-Renyi α-relative entropy (PRRE) of quantum gaussian states with an emphasis to the infinite mode case and α>1. A formula to compute the PRRE of gaussian states both in the finite and infinite mode case is proved. Our approach provides a complete description of the PRRE of gaussian states which are tensor product of 1-mode states and determines the interval of α for which the entropy is finite. This is a joint work is George Androulakis.