Limited Holism and Real-Vector-Space Quantum Theory

TL;DR

This paper explores theories more holistic than quantum mechanics, focusing on bilocal tomography, and demonstrates that real-vector-space quantum theory is bilocally but not locally tomographic, revealing new structural insights.

Contribution

It introduces and analyzes bilocal tomography, extending the understanding of holism in quantum-like theories and characterizing real-vector-space quantum theory within this framework.

Findings

Real-vector-space quantum theory is bilocally tomographic.

The number of state parameters can depend on the number of distinguishable states.

Theories more holistic than quantum theory can be constrained by bilocal tomography.

Abstract

Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by "bilocal tomography": the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space quantum theory, while not locally tomographic, is bilocally tomographic.