Complete hierarchy for high-dimensional steering certification
arXiv:2212.12544 · doi:10.1103/PhysRevLett.131.010201
Abstract
High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-dimensional steering is lacking a general certification procedure. We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario. These conditions are stated in terms of a hierarchy of semidefinite programs, which can also be used to quantify the phenomenon using the steering dimension robustness. To demonstrate the practical viability of our method, we characterize the dimensionality of entanglement in steering scenarios prepared with maximally entangled states measured in mutually unbiased bases. Our methods give significantly stronger bounds on the noise robustness necessary to experimentally certify high-dimensional entanglement.
arXiv comment5 + 2 pages, 3 figures, comments are welcome
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Cited by in corpus (12)
- Semidefinite programming relaxations for quantum correlations
- Quantum steering with imprecise measurements
- Unlimited One-Way Steering
- Semidefinite relaxations for high-dimensional entanglement in the steering scenario
- Quantum stochastic communication via high-dimensional entanglement
- Detecting quantum steering in networks
- Certifying high-dimensional quantum channels
- Steering nonlocality in high-speed telecommunication system without detection loophole
- Measurement-device-independent Schmidt number certification of all entangled states
- Certifying the dimensionality of any quantum channel with minimal assumptions
- Witness High-Dimensional Quantum Steering via Majorization Lattice
- Structure of quantum measurements implementable with one round of classical communication