A new device-independent dimension witness and its experimental implementation

Abstract

A dimension witness is a criterion that sets a lower bound on the dimension needed to reproduce the observed data. Three types of dimension witnesses can be found in the literature: device-dependent ones, in which the bound is obtained assuming some knowledge on the state and the measurements; device-independent prepare-and-measure ones, that can be applied to any system including classical ones; and device-independent Bell-based ones, that certify the minimal dimension of some entangled systems. Here we consider the Collins-Gisin-Linden-Massar-Popescu (CGLMP) Bell-type inequality for four outcomes. We show that a sufficiently high violation of this inequality witnesses $d\ge 4$ and present a proof-of-principle experimental observation of such a violation. This presents a first experimental violation of the third type of dimension witness beyond qutrits.

4 figures

References in corpus (11)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Secure device-independent quantum key distribution with causally independent measurement devices
• Testing the Hilbert space dimension
• Device-independent tests of classical and quantum dimensions
• A lower bound on the dimension of a quantum system given measured data
• Dimension witnesses and quantum state discrimination
• Robust and versatile black-box certification of quantum devices
• Quantum Random Access Codes using Single $d$-level Systems
• Secrecy extraction from no-signalling correlations
• Bounding the set of finite dimensional quantum correlations
• Device-independent certification of high-dimensional quantum systems

Cited by in corpus (19)

• High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments
• Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes
• Genuine high-dimensional quantum steering
• Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
• Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
• Witnessing irreducible dimension
• Concentration phenomena in the geometry of Bell correlations
• Quantum Correlations in the Minimal Scenario
• Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
• Device-independent certification of Hilbert space dimension using a family of Bell expressions
• Geometry of the quantum set on no-signaling faces
• Device-independent dimension tests in the prepare-and-measure scenario
• Robust certification of arbitrary outcome quantum measurements from temporal correlations
• Certifying dimension of quantum systems by sequential projective measurements
• Evidence-based certification of quantum dimensions
• Signaling between time steps does not allow for nonlocality beyond hidden nonlocality
• Orthogonal Projections on Hyperplanes Intertwined With Unitaries
• Quantum dimension test using the uncertainty principle
• Binarisation-loophole-free observation of high-dimensional quantum nonlocality