Objective-collapse theory

An objective-collapse theory treats wave-function collapse as a physical process localized in spacetime, rather than only as an observer's update of information.

At a spacetime point $x$, the local quantum state is the reduced density operator obtained on spacelike hypersurfaces approaching the past light cone of $x$. It includes the effects of objective collapses in that past light cone and excludes spacelike-separated collapses.

A quantum state readout device at $x$ hypothetically outputs a classical description of the local quantum state under objective collapse without changing that state. Its output can respond to a remote collapse only after the collapse enters the past light cone of $x$, so the device preserves relativistic causality.

A proper mixed state represents classical uncertainty over states selected by an actual preparation or collapse. Once that selecting event lies in the readout point's past light cone, a quantum state readout device returns the selected component rather than merely the ensemble average.

An improper mixed state is the reduced density matrix of a subsystem entangled with unobserved degrees of freedom. A quantum state readout device returns that reduced state until a relevant collapse lies in its past light cone.