Quantum statistics in the minimal scenario

TL;DR

This paper provides a complete analytical characterization of quantum statistical distributions in minimal scenarios by identifying all self-testable states and measurements, offering new insights into quantum properties directly from observed data.

Contribution

It introduces an analytical description of the entire set of quantum statistics in minimal scenarios through extremal points, based on self-testing of states and measurements.

Findings

Complete set of quantum statistics described analytically

Identification of all self-testable bipartite states and measurements

Insights into quantum properties from measurement statistics

Abstract

In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing some of its core properties. So far, only partial descriptions have been known for this set, even in the simplest scenarios. Here, we obtain the analytical description of a complete set of quantum statistics in terms of extremal points. This is made possible by finding all bipartite quantum states and pairs of binary measurements which can be self-tested, i.e. identified from statistics only. Our description provides a direct insight into the properties and limitations of quantum theory. These are not expressed in terms of Hilbert spaces, but rather directly in terms of measurement observation statistics.