Quantum mechanics of measurements distributed in time. II. Connections among formulations

Measurements distributed in time provide information about a system at more than one time; they cannot be described in terms of the conventional language of a system quantum state evolving in time. This paper, the second in a series, explores connections among various ways of formulating a quantum-mechanical description of time-distributed measurements. The natural formulation, involving a ‘‘sum over histories,’’ arises directly from Feynman’s rules for combining probability amplitudes. One equivalent formulation uses a standard measurement model, in which the system is coupled to a set of ‘‘measuring apparatuses.’’ A second equivalent formulation uses the language of ‘‘effects’’ and ‘‘operations.’’ Still a third formulation attempts to create a new language of multiple-time states and multiple-time eigenstates.