Robustly self-testing all maximally entangled states in every finite dimension
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908476667592704 |
|---|---|
| author | Meyer, Uta Isabella Šupić, Ivan Grosshans, Frédéric Markham, Damian |
| author_facet | Meyer, Uta Isabella Šupić, Ivan Grosshans, Frédéric Markham, Damian |
| contents | 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 $ε$-near-optimal strategy below that bound is, up to local isometries, within trace distance $δ= \mathcal{O}(\sqrtε)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robustly self-testing all maximally entangled states in every finite dimension Meyer, Uta Isabella Šupić, Ivan Grosshans, Frédéric Markham, Damian Quantum Physics 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 $ε$-near-optimal strategy below that bound is, up to local isometries, within trace distance $δ= \mathcal{O}(\sqrtε)$ 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. |
| title | Robustly self-testing all maximally entangled states in every finite dimension |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.01071 |