Geometric phase in open quantum system as a function of its history

A general expression for geometric phase in open quantum system is derived in the framework of a previously established operational approach. The system state gains geometric phase during propagation along a chain of Mach–Zehnder interferometers accompanied by acts of information exchange with the environment. Each act represents interaction with an environment element prepared in a standard state and subsequent measurement of its observable. The geometric phase appears to be a function of the system’s history, i.e. of a sequence of measurements outcomes. Numerical calculations of the geometric phase are made for a qubit-like quantum system and that of the environment and controlled phase shift as interaction.