Measurement-device-independent Schmidt number certification of all entangled states
arXiv:2502.13296 · doi:10.1103/nlz1-h6qr
Abstract
Bipartite quantum states with higher Schmidt numbers have been shown to outperform those with lower Schmidt numbers in various quantum information processing tasks, highlighting the operational advantage of entanglement dimensionality. Certifying the Schmidt number of such states is therefore crucial for efficient resource utilisation. Ideally, this certification should rely as little as possible on the certifying devices to ensure robustness against their potential imperfections. Fully device-independent certification via Bell-nonlocal games offers strong robustness but suffers from fundamental limitations: it cannot certify the Schmidt number of all entangled states. We demonstrate that this insufficiency of Bell-nonlocal games is not limited to entangled states that do not exhibit Bell-nonlocality. Specifically, we prove the existence of Bell-nonlocal states whose Schmidt number cannot be certified by any Bell-nonlocal game when the parties are restricted to local projective measurements. To overcome this, we develop a measurement-device-independent certification method based on semiquantum nonlocal games, which assume trusted preparation devices but treat measurement devices as black boxes. We prove that for any bipartite state with Schmidt number exceeding , there exists a semiquantum nonlocal game that can certify its Schmidt number. Finally, we provide an explicit construction of such a semiquantum nonlocal game based on an optimal Schmidt number witness operator.
21 pages, 3 figures; Close to published version
References in corpus (22)
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- High-dimensional quantum communication: benefits, progress, and future challenges
- Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States
- Fine-grained EPR-steering inequalities
- Local hidden--variable models for entangled quantum states
- Experimental device-independent verification of quantum steering
- Implementation of a Measurement-Device-Independent Entanglement Witness
- Bound entanglement provides convertibility of pure entangled states
- Discriminating multi-partite entangled states
- Characterizing entanglement dimensionality from randomized measurements
- On the relation between Bell inequalities and nonlocal games
- Symmetric extension in two-way quantum key distribution
- Complete hierarchy for high-dimensional steering certification
- Analyzing quantum entanglement with the Schmidt decomposition in operator space
- Enhanced Schmidt number criteria based on correlation trace norms
- Efficient measurement-device-independent detection of multipartite entanglement structure
- Bounding the amount of entanglement from witness operators
- On the Duality of Teleportation and Dense Coding
- High-dimensional entanglement witnessed by correlations in arbitrary bases
- Semidefinite relaxations for high-dimensional entanglement in the steering scenario
- Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps
- Experimental certification of high-dimensional entanglement with randomized measurements