Abstract
We propose a condition, called convex quasi-linearity, for deterministic nonlinear quantum evolutions. Evolutions satisfying this condition do not allow for arbitrary fast signaling, therefore, they cannot be ruled out by a standard argument. We also give an explicit example of a nonlinear qubit evolution satisfying quasi-linearity.
Highlights
For almost a century, quantum mechanics (QM), in a version based on the Hilbert space, was formulated as a linear theory preserving the superposition principle for pure states
Notice that there exist nonlinear stochastic evolution equations free of the problems with signaling [6]. Such models were proposed in various contexts, with one of the most important being collapse models. In this Rapid Communication we propose another condition for deterministic nonlinear quantum evolutions— quasilinearity [Eq (7)]
We have shown that time evolutions satisfying the quasilinearity property (12) are admissible in the convex set of density operators even if they are nonlinear
Summary
Quantum mechanics (QM), in a version based on the Hilbert space, was formulated as a linear theory preserving the superposition principle for pure states. Gisin’s arguments are based on the observation that deterministic nonlinear time evolution destroys the equivalence of quantum ensembles defining the same mixed state of the considered system. As a consequence, it creates the possibility of an instantaneous communication for spacelike separated observers with the help of systems of entangled particles. Notice that there exist nonlinear stochastic evolution equations free of the problems with signaling [6] Such models were proposed in various contexts, with one of the most important being collapse models The Gisin argument [7] does not work in this case
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