On the structure of low-rank PPT entangled states violating Peres conjecture
Abstract
Bound-entangled states with positive partial transpose (PPT) can exhibit quantum steering and Bell nonlocality, disproving the long-standing Peres conjecture and its stronger steering counterpart. These counterexamples, obtained through explicit constructions or numerical searches, raise the question of whether they share a common structural origin. We address this question in the low-rank regime by asking whether known counterexamples can be obtained, up to invertible local filtering, from the complement of an unextendible product basis (UPB). We find that the answer depends crucially on the local dimension. In 3⊗3, the rank-four structure of PPT entangled states implies that both the steerable PPT state of Moroder \textit{et al.} and the Bell-nonlocal PPT state of Vértesi and Brunner can be obtained from UPB-complement states under invertible local filtering. For three qubits, in contrast, rank-four states that are PPT across every bipartition are separable across each cut. Moreover, comparison of the product-vector structure of the relevant kernels shows that the known three-qubit Bell-nonlocal PPT states cannot be obtained by invertible local filtering from the complement of any three-qubit UPB. Going beyond rank four, we further show that a known rank-eight three-qutrit state, supported on the complement of a UPB and PPT across every bipartition, is genuinely multipartite entangled. These results show that UPBs provide a unifying structural origin for important low-rank PPT entangled states in 3⊗3, but that nonlocal bound entanglement is not, in general, a UPB phenomenon.
Related
- The Fully Depolarizing Noise Conjecture for Entangled Physical States: A Twenty-Year Perspective
- Simulation of quantum entangled states by classical probabilistic models
- Associative Memory for Quantum Entangled States
- Searching for Lepton Flavor Violating decays of the Higgs Boson into μτ, eτ, and eμ final states at FCC-ee
- Corner entanglement scaling with projected entangled pair states
BibTeX
@misc{singh2026structure,
title = {{On the structure of low-rank PPT entangled states violating Peres conjecture}},
author = {Gurvir Singh and Manik Banik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19905},
eprint = {2610.19905},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19905},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the structure of low-rank PPT entangled states violating Peres conjecture
AU - Gurvir Singh
AU - Manik Banik
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19905
UR - https://arxiv.org/abs/2610.19905
AB - Bound-entangled states with positive partial transpose (PPT) can exhibit quantum steering and Bell nonlocality, disproving the long-standing Peres conjecture and its stronger steering counterpart. These counterexamples, obtained through explicit constructions or numerical searches, raise the question of whether they share a common structural origin. We address this question in the low-rank regime by asking whether known counterexamples can be obtained, up to invertible local filtering, from the complement of an unextendible product basis (UPB). We find that the answer depends crucially on the local dimension. In 3⊗3, the rank-four structure of PPT entangled states implies that both the steerable PPT state of Moroder \textit{et al.} and the Bell-nonlocal PPT state of Vértesi and Brunner can be obtained from UPB-complement states under invertible local filtering. For three qubits, in contrast, rank-four states that are PPT across every bipartition are separable across each cut. Moreover, comparison of the product-vector structure of the relevant kernels shows that the known three-qubit Bell-nonlocal PPT states cannot be obtained by invertible local filtering from the complement of any three-qubit UPB. Going beyond rank four, we further show that a known rank-eight three-qutrit state, supported on the complement of a UPB and PPT across every bipartition, is genuinely multipartite entangled. These results show that UPBs provide a unifying structural origin for important low-rank PPT entangled states in 3⊗3, but that nonlocal bound entanglement is not, in general, a UPB phenomenon.
ER -