Extensions of Born's rule to non-linear quantum mechanics, some of which do not imply superluminal communication

[摘要] Nonlinear modifications of quantum mechanics have a troubled history. They were initially studied for many promising reasons: resolving the measurement problem, formulating a theory of quantum mechanics and gravity, and understanding the limits of standard quantum mechanics. However, certain non-linear theories have been experimentally tested and failed. More significantly, it has been shown that, in general, deterministic non-linear theories can be used for superluminal communication. We highlight another serious issue: the distribution of measurement results predicted by non-linear quantum mechanics depends on the formulation of quantum mechanics. In other words, Born's rule cannot be uniquely extended to non-linear quantum mechanics. We present these generalizations of Born's rule, and then examine whether some exclude superluminal communication. We determine that a large class do not allow for superluminal communication, but many lack a consistent definition. Nonetheless, we find a single extension of Born's rule with a sound operational definition, and that does not exhibit superluminal communication. The non-linear time-evolution leading to a certain measurement event is driven by the state conditioned on measurements that lie within the past light cone of that event.

[发布机构] Institute of Quantum Information and Matter, Burke Institute of Theoretical Physics, M/C 350-17, California Institute of Technology, Pasadena; CA; 91125, United States^1

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Distribution of measurement results;Measurement problems;Non linear;Non-linear theory;Operational definition;Superluminal communication