Certification of Absolutely Entangled Sets in the Prepare-and-Measure Scenario

@misc{patra2026certification,
  title = {{Certification of Absolutely Entangled Sets in the Prepare-and-Measure Scenario}},
  author = {Ram Krishna Patra and Abdelmalek Taoutioui and Tamás Vértesi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13075},
  eprint = {2609.13075},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13075},
}

TY  - UNPB
TI  - Certification of Absolutely Entangled Sets in the Prepare-and-Measure Scenario
AU  - Ram Krishna Patra
AU  - Abdelmalek Taoutioui
AU  - Tamás Vértesi
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.13075
UR  - https://arxiv.org/abs/2609.13075
AB  - An absolutely entangled set (AES) is a collection of states for which at least one member remains entangled under any choice of global unitary transformation. We develop a semi-device-independent framework for certifying this property from dimensionally bounded prepare-and-measure correlations. A witness value above the maximum attainable with separable preparations of a given dimension rules out every non-AES realization. To upperbound this limit, we construct a semidefinite-programming (SDP) hierarchy tailored to separable preparations. For a two-qubit random-access-code witness, the SDP upper bound and the heuristic lower bound coincide to the reported precision, yielding a concrete AES certification. We also formulate a general construction of witnesses for extended preparation sets containing target pure-state AESs. Examples based on equiangular tight frames, a minimal AES, and mutually unbiased bases further illustrate the scope of the method. In summary, our results establish a systematic and experimentally feasible approach to the certification of AESs in semi-device-independent quantum information protocols.
ER  -