Abstract
Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification principle is violated, meaning that some mixed states are not the reduction of a pure state in a larger system. This allows us to derive the measurement postulates of quantum theory from the structure of pure states and reversible dynamics, and the requirement that the purification principle holds. The violation of the purification principle implies that there is some irreducible classicality in these theories, which appears like an important clue for the problem of deriving the Born rule within the many-worlds interpretation. We also prove that in all such modifications the task of state tomography with local measurements is impossible, and present a simple toy theory displaying all these exotic non-quantum phenomena. This toy model shows that, contrarily to previous claims, it is possible to modify the Born rule without violating the no-signalling principle. Finally, we argue that the quantum measurement postulates are the most non-classical amongst all alternatives.
Highlights
The postulates of quantum theory describe the evolution of physical systems by distinguishing between the cases where observation happens or not
Zurek begins by assuming the dynamical structure of quantum theory and the assumption that quantum theory is universal, which is to say that all the phenomena we observe can be explained in terms of quantum systems interacting
By assuming the dynamical structure of quantum theory and the assumption of universality Zurek shows that measurements are associated to orthonormal bases, and that outcome probabilities are given by the Born rule
Summary
The postulates of quantum theory describe the evolution of physical systems by distinguishing between the cases where observation happens or not. We prove that in each such alternative there are mixed states which are not the reduction of a pure state on a larger system This property singles out the (standard) quantum measurement postulates including the Born Rule. In our previous work [6] we constructed a complete classification of all alternative measurement postulates, by establishing a correspondence between these and certain representations of the unitary group. This classification did not involve the consistency constraints that arise from the compositional structure of the theory; which governs how systems combine to form multi-partite systems.
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