Robust genuine high-dimensional steering with many measurements
arXiv:2110.14435 · doi:10.1103/PhysRevA.105.032430
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.
arXiv comment9 pages, 3 figures, 3 tables
References in corpus (31)
- Bell nonlocality
- Entanglement detection
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Multidimensional quantum entanglement with large-scale integrated optics
- On mutually unbiased bases
- Quantum Steering
- Optimal Cloning of Pure States
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Quantum steering: a review with focus on semidefinite programming
- Observation of one-way Einstein-Podolsky-Rosen steering
- Secure continuous variable quantum teleportation and Einstein-Podolsky-Rosen steering
- Testing the Hilbert space dimension
- Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
- An Invitation to Quantum Incompatibility
- Joint measurability of generalized measurements implies classicality
- Optimal Cloning of Pure States, Judging Single Clones
- One-to-one mapping between steering and joint measurability problems
- More efficient Bell inequalities for Werner states
- Quantifying quantum resources with conic programming
- Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
- Maximal randomness expansion from steering inequality violations using qudits
- Genuine high-dimensional quantum steering
- Quantifying measurement incompatibility of mutually unbiased bases
- Incompatibility robustness of quantum measurements: a unified framework
- Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits
- Deterministic distribution of multipartite entanglement and steering in a quantum network by separable states
- Witnessing irreducible dimension
- Most incompatible measurements for robust steering tests
- Adaptive strategy for joint measurements
- Experimental verification of multidimensional quantum steering
- Symmetries between measurements in quantum mechanics
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