A three state invariant

TL;DR

This paper establishes exact constraints on fidelities among triples of probability measures and quantum states, introduces a quantum invariant called phase, and demonstrates the unique reconstructibility of pure quantum state sequences from fidelities and phases.

Contribution

It provides the first precise constraints on fidelities for triples of states and introduces a novel quantum invariant called phase for state reconstruction.

Findings

Fidelities among triples of states are constrained by exact conditions.

Impossible to distinguish quantum from classical models using fidelities alone.

Pure quantum state sequences are uniquely reconstructible from fidelities and phases.

Abstract

For triples of probability measures, pure quantum states and mixed quantum states we obtain the exact constraints on the fidelities of pairs in the sequence. We show that it is impossible to decide between a quantum model, either pure or mixed, and a classical model on the basis of the fidelities alone. Next, we introduce a quantum three state invariant called phase and show that any sequence of pure quantum states is uniquely reconstructible given the fidelities and phases.