Bipartite Bound Information Exists
Abstract
There exist bipartite quantum states that cost entanglement to create, yet from which no singlet can be distilled. This extreme irreversibility is known as bound entanglement. A quarter-century ago, Gisin and Wolf asked whether classical information theory admits the same phenomenon. Are there correlations, shared by two parties and an eavesdropper, that cost secret bits to create, yet from which none can be distilled? This question is part of a broader program exploring the relation between quantum and classical information theory. We answer it in the affirmative, providing a simple example, a distribution of two bits and a trit. Bound entanglement thus has a classical counterpart, bound information. An even more direct correspondence was originally conjectured, namely that measuring purifications of bound-entangled states yields distributions with bound information. The very states that motivated the conjecture, however, yield no bound information when measured in the standard basis, whereas suitable measurements of purifications of separable states do. The analogy between bound entanglement and bound information thus lies in the accounting of resources, not in a correspondence between individual quantum states and the classical probability distributions induced by measuring them.
Related
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BibTeX
@misc{pauwels2026bipartite,
title = {{Bipartite Bound Information Exists}},
author = {Jef Pauwels and Nicolas Gisin and Renato Renner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.25838},
eprint = {2607.25838},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25838},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bipartite Bound Information Exists
AU - Jef Pauwels
AU - Nicolas Gisin
AU - Renato Renner
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2607.25838
UR - https://arxiv.org/abs/2607.25838
AB - There exist bipartite quantum states that cost entanglement to create, yet from which no singlet can be distilled. This extreme irreversibility is known as bound entanglement. A quarter-century ago, Gisin and Wolf asked whether classical information theory admits the same phenomenon. Are there correlations, shared by two parties and an eavesdropper, that cost secret bits to create, yet from which none can be distilled? This question is part of a broader program exploring the relation between quantum and classical information theory. We answer it in the affirmative, providing a simple example, a distribution of two bits and a trit. Bound entanglement thus has a classical counterpart, bound information. An even more direct correspondence was originally conjectured, namely that measuring purifications of bound-entangled states yields distributions with bound information. The very states that motivated the conjecture, however, yield no bound information when measured in the standard basis, whereas suitable measurements of purifications of separable states do. The analogy between bound entanglement and bound information thus lies in the accounting of resources, not in a correspondence between individual quantum states and the classical probability distributions induced by measuring them.
ER -