Complete hierarchy for high-dimensional steering certification
- URL: http://arxiv.org/abs/2212.12544v1
- Date: Fri, 23 Dec 2022 19:00:01 GMT
- Title: Complete hierarchy for high-dimensional steering certification
- Authors: Carlos de Gois, Martin Pl\'avala, Ren\'e Schwonnek, Otfried G\"uhne
- Abstract summary: High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized.
We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
Related papers
- Certifying classes of $d$-outcome measurements with quantum steering [49.1574468325115]
We provide a construction of a family of steering inequalities tailored to large classes of $d$-outcomes projective measurements.
We prove that the maximal quantum violation of those inequalities can be used for certification of those measurements and the maximally entangled state of two qudits.
arXiv Detail & Related papers (2024-10-27T15:32:53Z) - Quantum steering with imprecise measurements [0.0]
We show that small measurement imprecision can have a large detrimental influence in terms of false positives for steering inequalities.
We then introduce a method for taking generic measurement imprecision into account in tests of bipartite steering inequalities.
arXiv Detail & Related papers (2023-08-29T14:52:40Z) - High-dimensional entanglement certification: bounding relative entropy
of entanglement in $2d+1$ experiment-friendly measurements [77.34726150561087]
Entanglement -- the coherent correlations between parties in a quantum system -- is well-understood and quantifiable.
Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging.
We present a novel certification method whose measurement requirements scale linearly with dimension subsystem.
arXiv Detail & Related papers (2022-10-19T16:52:21Z) - Regression of high dimensional angular momentum states of light [47.187609203210705]
We present an approach to reconstruct input OAM states from measurements of the spatial intensity distributions they produce.
We showcase our approach in a real photonic setup, generating up-to-four-dimensional OAM states through a quantum walk dynamics.
arXiv Detail & Related papers (2022-06-20T16:16:48Z) - Dynamical learning of a photonics quantum-state engineering process [48.7576911714538]
Experimentally engineering high-dimensional quantum states is a crucial task for several quantum information protocols.
We implement an automated adaptive optimization protocol to engineer photonic Orbital Angular Momentum (OAM) states.
This approach represents a powerful tool for automated optimizations of noisy experimental tasks for quantum information protocols and technologies.
arXiv Detail & Related papers (2022-01-14T19:24:31Z) - Robust genuine high-dimensional steering with many measurements [0.0]
Quantum systems of high dimensions feature interesting properties when it comes to observing entanglement or other forms of correlations.
Their improved resistance to noise is favourable for experiments in quantum communication or quantum cryptography.
The concept of genuine high-dimensional steering has been recently introduced and experimentally demonstrated.
arXiv Detail & Related papers (2021-10-27T13:47:43Z) - Observing a Topological Transition in Weak-Measurement-Induced Geometric
Phases [55.41644538483948]
Weak measurements in particular, through their back-action on the system, may enable various levels of coherent control.
We measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength.
Our results open new horizons for measurement-enabled quantum control of many-body topological states.
arXiv Detail & Related papers (2021-02-10T19:00:00Z) - Optimized detection of high-dimensional entanglement [1.6179087103822984]
Entanglement detection is one of the most conventional tasks in quantum information processing.
We introduce a highly flexible automated method to construct optimal tests for entanglement detection.
We experimentally certify 2- and 3-unfaithful entanglement in 4-dimensional photonic states.
arXiv Detail & Related papers (2020-11-04T10:38:45Z) - Genuine high-dimensional quantum steering [0.0]
We formalise and experimentally demonstrate a notion of genuine high-dimensional quantum steering.
We show that high-dimensional entanglement, as quantified by the Schmidt number, can lead to a stronger form of steering.
We report the experimental violation of these inequalities using macro-pixel photon-pair entanglement certifying genuine high-dimensional steering.
arXiv Detail & Related papers (2020-07-06T13:06:44Z) - Quantum probes for universal gravity corrections [62.997667081978825]
We review the concept of minimum length and show how it induces a perturbative term appearing in the Hamiltonian of any quantum system.
We evaluate the Quantum Fisher Information in order to find the ultimate bounds to the precision of any estimation procedure.
Our results show that quantum probes are convenient resources, providing potential enhancement in precision.
arXiv Detail & Related papers (2020-02-13T19:35:07Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.