We discuss dephasing by the dissipative electromagnetic environment and by measurement in circuits consisting of small Josephson junctions. We present quantitative estimates and determine in which case the circuit might qualify as a quantum bit. Specifically, we analyze a three junction Cooper pair pump and discuss a measurement to determine the decoherence time ${\tau }_{\phi }.$

• Received 5 June 2001

DOI:https://doi.org/10.1103/PhysRevB.64.172509