Certification of high-dimensional entanglement in continuous-variable systems
Abstract
The dimensionality of entanglement in high-dimensional quantum systems is quantified by the Schmidt number, whose large value signals potential advantages for quantum communication and quantum computation. A commonly used approach to practical Schmidt-number detection in finite-dimensional systems is based on the estimation of fidelities to pure states with large entanglement dimensionality or lower bounds to these fidelities. However, for mode-entangled continuous-variable systems, the corresponding measurements are typically difficult to realize. Here, we introduce and assess fidelity bounds for Schmidt-number detection based on practically more accessible measurements of the first and second statistical moments of arbitrary continuous-variable quantum states. We provide analytical formulas that allow evaluating these bounds and test them for families of Gaussian and non-Gaussian states, including two-mode squeezed thermal states and photon-added displaced two-mode squeezed vacuum states. We compare our bounds to other methods for the certification of high-dimensional entanglement based on the same measurements.
Related
- Direct Adaptive Certification of High-Dimensional Entanglement with Bell Tests
- Multiplexing of Continuous-Variable and Discrete-Variable Quantum Key Distribution Systems over Fibered and Free-Space Channels
- Reasoning about Continuous-Variable Quantum Systems
- Entanglement spectrum and magic in higher-dimensional free fermionic systems
- Symmetry-driven correlation patterns in one-dimensional periodic fermionic systems: closed-form expressions and exact selection rules for correlation functions, entanglement entropies and mutual information
BibTeX
@misc{mishra2026certification,
title = {{Certification of high-dimensional entanglement in continuous-variable systems}},
author = {Ida Mishra and Simon Morelli and Klára Baksová and Phila Rembold and Nicolai Friis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03113},
eprint = {2610.03113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03113},
}
RIS
TY - UNPB
TI - Certification of high-dimensional entanglement in continuous-variable systems
AU - Ida Mishra
AU - Simon Morelli
AU - Klára Baksová
AU - Phila Rembold
AU - Nicolai Friis
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03113
UR - https://arxiv.org/abs/2610.03113
AB - The dimensionality of entanglement in high-dimensional quantum systems is quantified by the Schmidt number, whose large value signals potential advantages for quantum communication and quantum computation. A commonly used approach to practical Schmidt-number detection in finite-dimensional systems is based on the estimation of fidelities to pure states with large entanglement dimensionality or lower bounds to these fidelities. However, for mode-entangled continuous-variable systems, the corresponding measurements are typically difficult to realize. Here, we introduce and assess fidelity bounds for Schmidt-number detection based on practically more accessible measurements of the first and second statistical moments of arbitrary continuous-variable quantum states. We provide analytical formulas that allow evaluating these bounds and test them for families of Gaussian and non-Gaussian states, including two-mode squeezed thermal states and photon-added displaced two-mode squeezed vacuum states. We compare our bounds to other methods for the certification of high-dimensional entanglement based on the same measurements.
ER -