Time-invariant negativity and persistent bound entanglement in a cyclic two-qutrit family
Abstract
We study the entanglement dynamics of two qutrits under collective dephasing for a family of states obtained by mixing a maximally entangled state that lives in the decoherence-free subspace with three nonstationary two-term states sharing a common amplitude ratio r. We obtain exact PPT and separability regions along the whole trajectory, a specialization of known results on cyclic sign invariant states, and we supply explicit certificates: a finite product decomposition, three fixed positive-map witnesses, and a closed realignment formula that detects every PPT-entangled state, so that no state is left undecided. The negativity is computed in closed form. It shows that the entanglement is time-invariant, positive and constant from the initial time although the state changes, exactly when the weight of the maximally entangled state exceeds the threshold Ur=r/(1+r+r2). To our knowledge, this is the first demonstration of time-invariant entanglement for qutrit--qutrit systems under collective dephasing. For smaller weights the entanglement decays and vanishes at a finite time: the state either becomes separable (entanglement sudden death) or, for r≠1 in an intermediate range, loses distillability suddenly and remains bound entangled at all later times. Every state with negative partial transpose is one-copy distillable by a fixed local projection. The same trajectories arise from the global dephasing map and from a correlated local random-unitary semigroup, although the two channels differ on product inputs. Exact rational benchmarks and embeddings of the Horodecki and Ha--Kye--Park families are provided.
Related
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- Sparse anisotropic positive maps for qutrit entanglement: exact indecomposability and PPT geometry
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- Exact Temporal Criticalities of Entanglement and Negativity in Gaussian and Non-Gaussian Dissipative Kitaev Chains
BibTeX
@misc{zhang2026timeinvariant,
title = {{Time-invariant negativity and persistent bound entanglement in a cyclic two-qutrit family}},
author = {Wenlin Zhang and Mazhar Ali and Haobo Ma},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04568},
eprint = {2611.04568},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04568},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Time-invariant negativity and persistent bound entanglement in a cyclic two-qutrit family
AU - Wenlin Zhang
AU - Mazhar Ali
AU - Haobo Ma
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04568
UR - https://arxiv.org/abs/2611.04568
AB - We study the entanglement dynamics of two qutrits under collective dephasing for a family of states obtained by mixing a maximally entangled state that lives in the decoherence-free subspace with three nonstationary two-term states sharing a common amplitude ratio r. We obtain exact PPT and separability regions along the whole trajectory, a specialization of known results on cyclic sign invariant states, and we supply explicit certificates: a finite product decomposition, three fixed positive-map witnesses, and a closed realignment formula that detects every PPT-entangled state, so that no state is left undecided. The negativity is computed in closed form. It shows that the entanglement is time-invariant, positive and constant from the initial time although the state changes, exactly when the weight of the maximally entangled state exceeds the threshold U_r=r/(1+r+r^2). To our knowledge, this is the first demonstration of time-invariant entanglement for qutrit--qutrit systems under collective dephasing. For smaller weights the entanglement decays and vanishes at a finite time: the state either becomes separable (entanglement sudden death) or, for r≠1 in an intermediate range, loses distillability suddenly and remains bound entangled at all later times. Every state with negative partial transpose is one-copy distillable by a fixed local projection. The same trajectories arise from the global dephasing map and from a correlated local random-unitary semigroup, although the two channels differ on product inputs. Exact rational benchmarks and embeddings of the Horodecki and Ha--Kye--Park families are provided.
ER -