Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses

TL;DR

This paper introduces a new method based on quantum random access codes to certify the dimension and irreducibility of high-dimensional quantum states, demonstrated experimentally with a 1024-dimensional photonic state.

Contribution

It presents a novel class of dimension witnesses capable of certifying high-dimensional quantum states and their irreducibility, with experimental validation on a 1024-dimensional photonic system.

Findings

Successfully certified a 1024-dimensional photonic quantum state.

Demonstrated the ability to distinguish between decomposable and irreducible states.

Protocol applicable to high-dimensional quantum systems where tomography is infeasible.

Abstract

We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using non-coupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.