Measuring unitary invariants with the quantum switch

TL;DR

This paper demonstrates how the quantum switch can be used to measure Bargmann invariants, which characterize unitary-invariant properties of quantum states, linking higher-order quantum processes with invariant-based quantum resource characterization.

Contribution

It introduces a method to measure Bargmann invariants using the quantum switch and simple Hadamard test circuits, connecting higher-order quantum maps with invariant-based quantum resource analysis.

Findings

Quantum switch can measure Bargmann invariants of any order.

Hadamard test circuits can simulate arbitrary unitary quantum switches.

Establishes a connection between higher-order maps and quantum resource invariants.

Abstract

Bargmann invariants, multivariate traces of states, completely characterize any unitary-invariant property of a set of states. Unitary invariants enable the description of quantum resources such as basis-independent coherence and imaginarity, nonstabilizerness, and contextuality. We show that the quantum switch, a higher-order process featuring indefinite causal order, can be used to measure Bargmann invariants of arbitrary order. We also show how simple Hadamard test circuits can deterministically simulate an arbitrary unitary quantum switch. Our results establish a solid bridge between the theory and applications of unitary invariants and higher-order maps in quantum mechanics.