Quantum theory is compatible with special relativity. In particular, though
measurements on entangled systems are correlated in a way that cannot be
reproduced by local hidden variables, they cannot be used for superluminal
signalling. As Czachor, Gisin and Polchinski pointed out, this is not true for
general nonlinear modifications of the Schroedinger equation. Excluding
superluminal signalling has thus been taken to rule out most nonlinear versions
of quantum theory. The no superluminal signalling constraint has also been used
for alternative derivations of the optimal fidelities attainable for imperfect
quantum cloning and other operations.
These results apply to theories satisfying the rule that their predictions
for widely separated and slowly moving entangled systems can be approximated by
non-relativistic equations of motion with respect to a preferred time
coordinate. This paper describes a natural way in which this rule might fail to
hold. In particular, it is shown that quantum readout devices which display the
values of localised pure states need not allow superluminal signalling,
provided that the devices display the values of the states of entangled
subsystems as defined in a non-standard, but natural, way. It follows that any
locally defined nonlinear evolution of pure states can be made consistent with
Minkowski causality.Comment: References update
