How to say it in a way that Hasn't Yet Been said? Tong et al. [26] introduced a general theoretical framework to study geometric phases for nonunitary evolutions, based on quantum kinematics in interferometry. This approach catches another feature of nonunitary evolution, namely that the state of a quantum system in contact with an environment must be described by a density matrix, i.e., a statistical mixture of several wave functions. When these wave functions evolve, they acquire different geometric phases resulting in an overall geometric phase being a certain average over the statistical mixture. A key point of this approach is that it is kinematic, which means that it applies to any form of underlying dynamics. It has been used to demonstrate the existence of time [27] and temperature [28] scales on which the geometric phase is practically unaffected by decoherence and therefore useful for quantum computation.
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