PIRSA:12060048

On the Preparation of States in Nonlinear Quantum Mechanics

Menicucci, N. (2012). On the Preparation of States in Nonlinear Quantum Mechanics. Perimeter Institute. https://pirsa.org/12060048

Menicucci, Nicolas. On the Preparation of States in Nonlinear Quantum Mechanics. Perimeter Institute, Jun. 28, 2012, https://pirsa.org/12060048 

          @misc{ pirsa_PIRSA:12060048,
            doi = {10.48660/12060048},
            url = {https://pirsa.org/12060048},
            author = {Menicucci, Nicolas},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {On the Preparation of States in Nonlinear Quantum Mechanics},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {jun},
            note = {PIRSA:12060048 see, \url{https://pirsa.org}}
          }

Nicolas Menicucci

DOI 10.48660/12060048
Collection
Talk Type Conference
Subject

Abstract

Recent analysis of closed timelike curves from an information-theoretic perspective has led to contradictory conclusions about their information-processing power. One thing is generally agreed upon, however, which is that if such curves exist, the quantum-like evolution they imply would be nonlinear, but the physical interpretation of such theories is still unclear. It is known that any operationally verifiable instance of a nonlinear, deterministic evolution on some set of pure states makes the density matrix inadequate for representing mixtures of those pure states. We re-cast the problem in the language of operational quantum mechanics, building on previous work to show that the no-signalling requirement leads to a splitting of the equivalence classes of preparation procedures. This leads to the conclusion that any non-linear theory satisfying certain minimal conditions must be regarded as inconsistent unless it contains distinct representations for the two different kinds of mixtures, and incomplete unless it contains a rule for determining the physical preparations associated with each type. We refer to this as the `preparation problem' for nonlinear theories.