Experimental Test of the Principle of Tomographic Locality

TL;DR

This study experimentally tests the principle of tomographic locality in quantum systems using photonic polarization states, confirming its validity in standard quantum theory and detecting its failure in real-field quantum models.

Contribution

It provides the first direct experimental test of the principle of tomographic locality in quantum systems, validating it for complex quantum theory and illustrating its failure in real-field quantum models.

Findings

No violation of tomographic locality in standard quantum theory.

Detection of failure of tomographic locality in real-field quantum models.

Experimental validation of theoretical predictions about tomographic locality.

Abstract

The principle of tomographic locality states that the operational state of a multipartite system can be fully characterized by the statistics obtained from measurements that are local to the individual subsystems. This property holds in quantum theory and features prominently in axiomatic reconstructions of the theory, where it serves to rule out a wide class of alternatives. For instance, quantum theory with Hilbert spaces defined over the real field (rather than the complex field) is an example of a theory that is ruled out in this fashion. Given its foundational importance, it is worthwhile to subject this principle to a direct experimental test. Specifically, we consider an experiment on the polarization degrees of freedom of a pair of photonic modes in a prepare-and-measure scenario and analyze the resulting data within the framework of generalized probabilistic theories. The signature of a failure of tomographic locality is that there are pairs of states on the bipartite system that can only be distinguished by the statistics they yield for non-separable measurements. In the full quantum setting, we find no evidence of a violation of tomographic locality. As a test of our analysis method, we also verify that if we restrict attention to those states and measurements that lie within the fragment described by quantum theory over the real field, then a clear signature of the failure of tomographic locality is observed.