Environmental decoherence stabilizes quantum-dot cellular automata

Abstract

We consider the effects of interaction with the environment on decoherence in quantum-dot cellular automata (QCA). We model the environment as a Coulombically interacting random assembly of quantum double-dots. The time evolution of our model system + environment is unitary and maintains one coherent state. We explicitly calculate the reduced density operators for the system and for the environment from the full coherent state. From the reduced density matrix of the system, we calculate the coherence vector and the Von Neumann entropy. The entanglement of system and environmental degrees of freedom lead to decoherence, which drives the system into the Zurek pointer states. The quantum information lost by the system, quantified by the entropy, is present in the quantum mutual information between the system and the environment. We explore the competition between environmental decoherence and system dynamics. For even a modest environmental interaction, the pointer states are the QCA information-bearing degrees of freedom, so that environmental decoherence, while destructive of quantum information, tends to stabilize QCA bit information.