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.

arXiv:2610.03113 [quant-ph]

(or arXiv:2610.03113v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.03113 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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