Quantum measurements performed with a single-electron transistor

Abstract

Low-capacitance Josephson junction systems as well as coupled quantum dots, in a parameter range where single charges can be controlled, provide physical realizations of quantum bits, discussed in connection with quantum computing. The necessary manipulation of the quantum states can be controlled by applied gate voltages. In addition, the state of the system has to be read out. Here we suggest to measure the quantum state by coupling a single-electron transistor to the $q$-bit. As long as no transport voltage is applied, the transistor influences the quantum dynamics of the $q$-bit only weakly. We have analyzed the time evolution of the density matrix of the transistor and $q$-bit when a voltage is turned on. For values of the capacitances and temperatures which can be realized by modern nanotechniques, the process constitutes a quantum measurement process.