Postselected quantum systems and their time evolution in non-equilibrium thermo-field dynamics

A postselected quantum system is studied within the framework of non-equilibrium thermo-field dynamics, where an extended Hilbert space is used for describing a quantum system. A two-operator state defined on the extended Hilbert space is introduced to describe a property of a postselected quantum system. By imposing some conditions on the two-operator state, it reduces to the previously introduced quantities such as the two-vector state, the W-operator, the connection state and the 2-time quantum state. The correlation included in the two-operator state is clarified. Furthermore, time evolution of a postselected quantum system influenced by a Markovian environment is investigated. The linear response to an external field is also discussed. The results show the symmetric property of a postselected quantum system, even if time evolution is not unitary. © 2016, Chapman University.