PreprintarXiv licencearXiv
A Reduction Bound for Entanglement Detection by Positive Free Maps
Abstract
Collins, Hayden, and Nechita used free probability to construct families of k-positive but not (k+1)-positive maps and applied them to entanglement detection. We prove that positive free maps associated with compactly supported freely infinitely divisible distributions are no stronger than the reduction criterion in every ancillary dimension. In particular, these maps cannot detect positive partial transpose entanglement. The proof combines a joint Fock realization with an operator positivity certificate derived from free Lévy data.
Related
- No cardinality bound for squashed entanglement
- Simultaneous Reduction of Observables and Measured Qudits in Entanglement-Assisted Quantum Local Recovery
- Bound of automorphisms of fibred surfaces in positive characteristic
- An Upper Bound to the Undetected Error Exponent with Erasure Decoding at Positive Rates
- Entanglement breaking in self-referential quantum feedback: a record bound and an exactly solvable loop
BibTeX
@misc{lee2026reduction,
title = {{A Reduction Bound for Entanglement Detection by Positive Free Maps}},
author = {Chin-Yen Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34338},
eprint = {2610.34338},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34338},
}
RIS
TY - UNPB
TI - A Reduction Bound for Entanglement Detection by Positive Free Maps
AU - Chin-Yen Lee
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34338
UR - https://arxiv.org/abs/2610.34338
AB - Collins, Hayden, and Nechita used free probability to construct families of k-positive but not (k+1)-positive maps and applied them to entanglement detection. We prove that positive free maps associated with compactly supported freely infinitely divisible distributions are no stronger than the reduction criterion in every ancillary dimension. In particular, these maps cannot detect positive partial transpose entanglement. The proof combines a joint Fock realization with an operator positivity certificate derived from free Lévy data.
ER -