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arXiv · 2610.03113

Certification of high-dimensional entanglement in continuous-variable systems

Ida Mishra·Simon Morelli·Klára Baksová·Phila Rembold·Nicolai Friis
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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.

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Ida Mishra, Simon Morelli, Klára Baksová, Phila Rembold, Nicolai Friis. 2026-10-02. Certification of high-dimensional entanglement in continuous-variable systems. https://arxiv.org/abs/2610.03113

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