Bargmann Scenarios

TL;DR

This paper introduces Bargmann scenarios and polytopes to systematically characterize quantum coherence using Bargmann invariants, enhancing quantum resource certification.

Contribution

It develops a unified formalism for Bargmann invariants, connecting them to coherence detection and resource theories, with geometric and physical insights.

Findings

Bargmann polytopes bound invariant values for incoherent states.

The formalism links Bargmann invariants to existing coherence measures.

Illustrations demonstrate physical relevance and potential for device certification.

Abstract

Considerable effort has been devoted to developing techniques for witnessing and characterizing quantum resources that emerge from collective properties of a set of states. In this context, Bargmann invariants play a central role: they witness coherence and related resources, and underpin important applications. In this work, we introduce a unified formalism that fully characterizes and organizes the capability of Bargmann invariants to witness different manifestations of coherence in sets of states. It is formulated around the construction of Bargmann scenarios, which specify relevant tuples of Bargmann invariants, and Bargmann polytopes, which bound the values that said invariants can have when the states are incoherent. We study their basic geometry, connect them to existing formalisms, and illustrate their physical relevance. Our construction opens new opportunities for the certification of quantum devices and lays the path toward a full quantum resource theory based entirely on multivariate traces of states.