Tight Universal Bounds on Quantum Data Hiding with Multipartite Werner States
Abstract
Quantum data hiding concerns pairs of states which are highly distinguishable with global measurements, yet nearly indistinguishable when restricted to local operations and classical communication. More than two decades after Eggeling and Werner introduced a multipartite hiding scheme based on Werner states, the optimal dependence of its uniform security guarantee on the number of parties and local dimension remained unknown. We resolve this problem by showing that the distinguishing bias of any pair of n-qudit Werner states is O(n2/d) under measurements whose effects remain positive under partial transposition (PPT) across every bipartition. An explicit pair attains this scaling using only nonadaptive local measurements, establishing worst-case optimality and showing that the PPT relaxation preserves the optimal dependence on both the number of parties and the local dimension. At fixed security, this extends the certified hiding regime from n=O(d1/4) to n=O(√d). Beyond data hiding, the same bound implies that testing any nontrivial unitarily invariant property with adaptive single-copy measurements requires Ω(√d) copies, yielding separations for any property with dimension-independent sample complexity under collective measurements. Our proof reduces the distinguishing bias to trace norms of partially transposed operators and analyzes them using mixed Schur-Weyl duality, demonstrating the utility of representation theoretic methods developed for port-based teleportation to data hiding and quantum property testing.
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BibTeX
@misc{akresh2026tight,
title = {{Tight Universal Bounds on Quantum Data Hiding with Multipartite Werner States}},
author = {Oren Akresh and Jacob Beckey and Felix Leditzky},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40332},
eprint = {2609.40332},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40332},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tight Universal Bounds on Quantum Data Hiding with Multipartite Werner States
AU - Oren Akresh
AU - Jacob Beckey
AU - Felix Leditzky
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40332
UR - https://arxiv.org/abs/2609.40332
AB - Quantum data hiding concerns pairs of states which are highly distinguishable with global measurements, yet nearly indistinguishable when restricted to local operations and classical communication. More than two decades after Eggeling and Werner introduced a multipartite hiding scheme based on Werner states, the optimal dependence of its uniform security guarantee on the number of parties and local dimension remained unknown. We resolve this problem by showing that the distinguishing bias of any pair of n-qudit Werner states is O(n^2/d) under measurements whose effects remain positive under partial transposition (PPT) across every bipartition. An explicit pair attains this scaling using only nonadaptive local measurements, establishing worst-case optimality and showing that the PPT relaxation preserves the optimal dependence on both the number of parties and the local dimension. At fixed security, this extends the certified hiding regime from n=O(d^1/4) to n=O(√d). Beyond data hiding, the same bound implies that testing any nontrivial unitarily invariant property with adaptive single-copy measurements requires Ω(√d) copies, yielding separations for any property with dimension-independent sample complexity under collective measurements. Our proof reduces the distinguishing bias to trace norms of partially transposed operators and analyzes them using mixed Schur-Weyl duality, demonstrating the utility of representation theoretic methods developed for port-based teleportation to data hiding and quantum property testing.
ER -