A Quantum Theory with Non-Collapsing Measurements

Abstract

A collapse-free version of quantum theory is examined to systematically study the role of the projection postulate. This foil theory assumes "passive" measurements that do not update quantum states although measurement outcomes still occur probabilistically, and in accordance with Born's rule. The Hilbert space setting of quantum theory is retained. "Passive quantum theory" is shown to reproduce preparational uncertainty relations, the no-cloning theorem, and no-signalling, among other properties. Striking differences occur, however, if protocols involve post-measurement states. For example, a single system, rather than an ensemble, is sufficient to reconstruct the state of the system. The possibility to "observe" a state increases the computational power of some quantum algorithms. Passive quantum theory is not locally tomographic but capable of "simulating" quantum measurements modulo a finite delay. Outcome probabilities for composite systems may violate Bell inequalities, without however entailing an argument against local hidden variables.