Reconstructing quantum theory

TL;DR

This paper reconstructs quantum theory from a set of operational postulates, showing how these principles uniquely lead to quantum mechanics rather than classical probability theory.

Contribution

It identifies a minimal set of postulates that distinguish quantum theory from classical probability theory, providing a foundational reconstruction.

Findings

Postulates are consistent only with classical and quantum theories.

Additional requirement isolates quantum theory.

Reconstruction clarifies foundational principles of quantum mechanics.

Abstract

We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map between pure states and maximal effects such that we get unit probability. This maximal effect does not give probability equal to one for any other pure state. Information Locality: A maximal measurement is effected on a composite system if we perform maximal measurements on each of the components. Tomographic Locality: The state of a composite system can be determined from the statistics collected by making measurements on the components. Permutability: There exists a reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. Sturdiness: Filters are non-flattening. To single out quantum theory we need only add any requirement that is inconsistent with classical probability theory and consistent with quantum theory.