Robust genuine high-dimensional steering with many measurements

Abstract

Quantum systems of high dimensions are attracting a lot of attention because they feature interesting properties when it comes to observing entanglement or other forms of correlations. In particular, their improved resistance to noise is favourable for experiments in quantum communication or quantum cryptography. However, witnessing this high-dimensional nature remains challenging, especially when the assumptions on the parties involved are weak, typically when one of them is considered as a black box. In this context, the concept of genuine high-dimensional steering has been recently introduced and experimentally demonstrated [Phys. Rev. Lett. 126, 200404 (2021)]; it allows for a one-sided device-independent certification of the dimension of a bipartite shared state by only using two measurements. Here I overcome this limitation by developing, for more than two measurements, universal bounds on the incompatibility robustness, turned into meaningful dimension certificates. Interestingly, even though the resulting bounds are quite loose, they still often offer an increased resistance to noise and could then be advantageously employed in experiments.

9 pages, 3 figures, 3 tables

References in corpus (8)

• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Observation of one-way Einstein-Podolsky-Rosen steering
• Testing the Hilbert space dimension
• Joint measurability of generalized measurements implies classicality
• More efficient Bell inequalities for Werner states
• Deterministic distribution of multipartite entanglement and steering in a quantum network by separable states

Cited by in corpus (8)

• Noise-Robust and Loss-Tolerant Quantum Steering with Qudits
• Quantum steering with imprecise measurements
• Complete hierarchy for high-dimensional steering certification
• Unlimited One-Way Steering
• Semidefinite relaxations for high-dimensional entanglement in the steering scenario
• The Schmidt rank for the commuting operator framework
• Certifying high-dimensional quantum channels
• A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits