Semidefinite relaxations for high-dimensional entanglement in the steering scenario
arXiv:2410.02554 · doi:10.1103/PhysRevLett.134.090802
Abstract
We introduce semidefinite programming hierarchies for benchmarking relevant entanglement properties in the high-dimensional steering scenario. Firstly, we provide a general method for detecting the entanglement dimensionality through certification of the Schmidt number. Its key feature is that the computational cost is independent of the Schmidt number under consideration. Secondly, we provide a method to estimate the fidelity of the source with any maximally entangled state. Using only basic computational means, we demonstrate the usefulness of these methods, which can be directly used to analyse experiments on high-dimensional systems.
References in corpus (36)
- Security of quantum key distribution using d-level systems
- Multidimensional quantum entanglement with large-scale integrated optics
- Quantum Steering
- Quantum steering: a review with focus on semidefinite programming
- Experimental EPR-Steering of Bell-local States
- A Schmidt number for density matrices
- Generation and Confirmation of a (100x100)-dimensional entangled Quantum System
- Closing the detection loophole in Bell experiments using qudits
- Measurements in two bases are sufficient for certifying high-dimensional entanglement
- Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole
- Simulating positive-operator-valued measures with projective measurements
- Experimental GHZ Entanglement beyond Qubits
- High-Dimensional Pixel Entanglement: Efficient Generation and Certification
- Genuine high-dimensional quantum steering
- Semidefinite Programming in Quantum Information Science
- Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
- Semidefinite programming relaxations for quantum correlations
- Inverse-design of high-dimensional quantum optical circuits in a complex medium
- Unbounded violation of quantum steering inequalities
- Entanglement Detection Beyond Measuring Fidelities
- Most incompatible measurements for robust steering tests
- Loss-tolerant EPR steering for arbitrary dimensional states: joint measurability and unbounded violations under losses
- Retrieving High-Dimensional Quantum Steering From a Noisy Environment with N Measurement Settings
- Noise-Robust and Loss-Tolerant Quantum Steering with Qudits
- Resource-efficient high-dimensional entanglement detection via symmetric projections
- Nonlocality, steering and quantum state tomography in a single experiment
- Exact Steering Bound for Two-Qubit Werner States
- Construction of efficient Schmidt number witnesses for high-dimensional quantum states
- Bounding entanglement dimensionality from the covariance matrix
- Quantum steering with positive operator valued measures
- Complete hierarchy for high-dimensional steering certification
- Optimized detection of high-dimensional entanglement
- Robust genuine high-dimensional steering with many measurements
- Compatibility of Generalized Noisy Qubit Measurements
- Experimental verification of multidimensional quantum steering
- Equivalence between simulability of high-dimensional measurements and high-dimensional steering
Cited by in corpus (6)
- Quantum stochastic communication via high-dimensional entanglement
- Bound entangled states are useful in prepare-and-measure scenarios
- Measurement-device-independent Schmidt number certification of all entangled states
- Detecting high-dimensional entanglement by randomized product projections
- Semi-device-independent certification of high-dimensional quantum channels
- Witness High-Dimensional Quantum Steering via Majorization Lattice