Decoherence is the process by which a quantum superposition state decays into a classical, statistical mixture of states, resulting from entangling interactions between the system and its environment. One aspect of this transition from the quantum to the classical is the emergence of a joint probability distribution over random variables whose expectation values are taken in the corresponding quantum state. Suppes and Zanotti (1981) have derived a necessary and sufficient condition for the existence of a joint probability distribution for three random variables. Using a master equation approach, we study the time evolution of a GHZ state and examine its decay into a classical state under the influence of decoherence. To do so, a new group theoretical superoperator method is developed, which can be applied to a large class of problems in quantum optics and quantum information theory. We show that a joint probability distribution emerges after about 20% of the half time of the system and discuss the implications of this result. The talk is based on joint work with Patrick Suppes (Stanford).
Université de Tilburg