Can bound entanglement produce a device-independent secret key?
Let $\rho_{AB}$ be a finite-dimensional bipartite bound-entangled state: it is entangled, but its distillable entanglement under local operations and classical communication is zero. In a device-independent quantum key distribution protocol, Alice and Bob make local measurements on independent copies of $\rho_{AB}$ and communicate over a public classical channel; security requires that the final shared key be close to uniform and independent of the adversary for every quantum realization of the devices consistent with the observed input-output statistics. Peres conjectured that bound-entangled states cannot violate a Bell inequality; Vértesi and Brunner disproved this. Horodecki, Horodecki, Horodecki and Oppenheim showed that some bound-entangled states yield a secret key when the devices are trusted. Arnon-Friedman and Leditzky showed that the Vértesi–Brunner state, measured as in its Bell violation, yields no key in one-way device-independent protocols of a standard form.
Problem. Is it true that, for every such $\rho_{AB}$, independent copies of $\rho_{AB}$ cannot yield a positive asymptotic secret-key rate in any device-independent quantum key distribution protocol, including protocols with two-way public communication and tests other than a fixed Bell test?
Source: Arnon-Friedman and Leditzky (2021), Conjecture 11, the revised Peres conjecture, after Peres (1999).
Imported from github.com/MColbrook/AIM.
Classification
- Primary
- IT — Information Theory
- Secondary
- MP
- Keywords
- AIM Open Applied Problems, bound entanglement, quantum information, quantum key distribution
References
@article{arnonfriedman2021,
author = {Arnon-Friedman, Rotem and Leditzky, Felix},
title = {Upper bounds on device-independent quantum key distribution rates and a revised {P}eres conjecture},
journal = {IEEE Trans. Inform. Theory},
volume = {67},
number = {10},
year = {2021},
pages = {6606--6618},
doi = {10.1109/TIT.2021.3086505},
eprint = {2005.12325},
archivePrefix = {arXiv},
}
@article{peres1999,
author = {Peres, Asher},
title = {All the {B}ell inequalities},
journal = {Found. Phys.},
volume = {29},
number = {4},
year = {1999},
pages = {589--614},
doi = {10.1023/A:1018816310000},
eprint = {quant-ph/9807017},
archivePrefix = {arXiv},
}
@article{vertesi2014,
author = {V{\'e}rtesi, Tam{\'a}s and Brunner, Nicolas},
title = {Disproving the {P}eres conjecture by showing {B}ell nonlocality from bound entanglement},
journal = {Nat. Commun.},
volume = {5},
year = {2014},
pages = {5297},
doi = {10.1038/ncomms6297},
eprint = {1405.4502},
archivePrefix = {arXiv},
}
@article{horodecki2005,
author = {Horodecki, Karol and Horodecki, Micha{\l} and Horodecki, Pawe{\l} and Oppenheim, Jonathan},
title = {Secure key from bound entanglement},
journal = {Phys. Rev. Lett.},
volume = {94},
number = {16},
year = {2005},
pages = {160502},
doi = {10.1103/PhysRevLett.94.160502},
eprint = {quant-ph/0309110},
archivePrefix = {arXiv},
}
@misc{aim-revised-peres,
author = {Brunton, Steve and Colbrook, Matthew J. and de Hoop, Maarten V. and Stepaniants, George and Townsend, Alex and Ward, Rachel},
title = {{Can bound entanglement produce a device-independent secret key?}},
howpublished = {AIM --- Open Applied Problems, GitHub repository},
year = {2026},
url = {https://github.com/MColbrook/AIM/blob/a153f469ee0ea64e876b2ad97c79d252c19a3e22/problems/590-revised-peres.md},
note = {Entry 590 at commit a153f46, 2026-10-13},
}
Citing this problem
This identifier is permanent. It will not change if the problem is solved, reclassified or withdrawn.
OP-00378, "Can bound entanglement produce a device-independent secret key?", clopen.solutions.