Robustly self-testing all maximally entangled states in every finite dimension

• URL: http://arxiv.org/abs/2508.01071v1
• Date: Fri, 01 Aug 2025 21:02:07 GMT
• Title: Robustly self-testing all maximally entangled states in every finite dimension
• Authors: Uta Isabella Meyer, Ivan Šupić, Frédéric Grosshans, Damian Markham,
• Abstract summary: We prove a device-independent, noise-tolerant certification of maximally entangled states in every finite dimension $d$.<n>The protocol uses standard Heisenberg-Weyl operations and non-Clifford phase gates that are diagonal in the computational basis.
• Score: 1.2499537119440245
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish a device-independent, noise-tolerant certification of maximally entangled states in every finite dimension $d$. The core ingredient is a $d$-input, $d$-outcome Bell experiment that generalizes the Clauser-Horne-Shimony-Holt test from qubits to qudits, where each setting is a non-diagonal Heisenberg-Weyl observable. For every odd prime $d \geq 3$, the associated Bell operator has an exact sum-of-positive-operators decomposition, yielding the Cirelson bound in closed form, from which we reconstruct the Heisenberg-Weyl commutation relations on the support of the state. We then extend the Mayers-Yao local isometry from qubits to prime-dimensional systems and show that any $\epsilon$-near-optimal strategy below that bound is, up to local isometries, within trace distance $\delta = \mathcal{O}(\sqrt{\epsilon})$ of the ideal maximally entangled state; the implemented measurements are correspondingly close to the target observables. Via a tensor-factor argument, the prime-dimension result extends the self-testing protocol to every composite dimension $d$. The protocol uses standard Heisenberg-Weyl operations and non-Clifford phase gates that are diagonal in the computational basis, making it directly applicable to high-dimensional photonic and atomic platforms.

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