Least paradoxical states of the Schr\"{o}dinger cat

Abstract

Modeling the Schr\"{o}dinger cat by a two state system and assuming that the cat is coupled to the environment we look for the least paradoxical states of the Schr\"{o}dinger cat in the following way. We require the reduced density matrix of the cat for one of the two states in the superposition to be the same as the one for the total state while distinct from the reduced density matrix of the cat for the other state in the superposition. We then look for the reduced density matrices for which the cat is as alive as possible for the first state (and as dead as possible for the second state). The resulting states are those in which the probability for the cat to be alive (or dead) is $1/2+\sqrt 2/4\approx 0.854$