{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T11:25:48Z","timestamp":1773228348102,"version":"3.50.1"},"reference-count":40,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T00:00:00Z","timestamp":1773100800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation","award":["2315398"],"award-info":[{"award-number":["2315398"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"The heralded exact one-way distillable secret key is equal to the largest expected rate at which perfect secret key bits can be probabilistically distilled from a bipartite state by means of local operations and one-way classical communication. Here we define the set of super two-extendible states and prove that an arbitrary state in this set cannot be used for heralded exact one-way secret-key distillation. This broad class of states includes both erased states and all full-rank states. Comparing the heralded exact one-way distillable secret key with the more commonly studied approximate one-way distillable secret key, our results demonstrate an extreme gap between them for many states of interest, with the approximate one-way distillable secret key being much larger. Our findings naturally extend to heralded exact one-way entanglement distillation, with similar conclusions.<\/jats:p>","DOI":"10.22331\/q-2026-03-10-2020","type":"journal-article","created":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T14:24:24Z","timestamp":1773152664000},"page":"2020","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["No-go theorem for heralded exact one-way key distillation"],"prefix":"10.22331","volume":"10","author":[{"given":"Vishal","family":"Singh","sequence":"first","affiliation":[{"name":"School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14850, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark M.","family":"Wilde","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14850, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2026,3,10]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Feihu Xu, Xiongfeng Ma, Qiang Zhang, Hoi-Kwong Lo, and Jian-Wei Pan. ``Secure quantum key distribution with realistic devices''. Reviews of Modern Physics 92, 025002 (2020).","DOI":"10.1103\/RevModPhys.92.025002"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Christopher Portmann and Renato Renner. ``Security in quantum cryptography''. Reviews of Modern Physics 94, 025008 (2022).","DOI":"10.1103\/RevModPhys.94.025008"},{"key":"2","doi-asserted-by":"publisher","unstructured":"V\u00edctor Zapatero, Tim van Leent, Rotem Arnon-Friedman, Wen-Zhao Liu, Qiang Zhang, Harald Weinfurter, and Marcos Curty. ``Advances in device-independent quantum key distribution''. npj Quantum Information 9, 10 (2023).","DOI":"10.1038\/s41534-023-00684-x"},{"key":"3","unstructured":"Charles H. Bennett and Gilles Brassard. ``Quantum cryptography: Public key distribution and coin tossing''. In Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing. Page 175. India (1984)."},{"key":"4","doi-asserted-by":"publisher","unstructured":"Charles H. Bennett and Gilles Brassard. ``Quantum cryptography: Public key distribution and coin tossing''. Theoretical Computer Science 560, 7\u201311 (2014).","DOI":"10.1016\/j.tcs.2014.05.025"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Artur K. Ekert. ``Quantum cryptography based on Bell's theorem''. Physical Review Letters 67, 661\u2013663 (1991).","DOI":"10.1103\/PhysRevLett.67.661"},{"key":"6","doi-asserted-by":"publisher","unstructured":"Jonathan Katz and Yehuda Lindell. ``Introduction to modern cryptography: Principles and protocols''. Chapman and Hall\/CRC. (2007).","DOI":"10.1201\/9781420010756"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Marcos Curty, Maciej Lewenstein, and Norbert L\u00fctkenhaus. ``Entanglement as a precondition for secure quantum key distribution''. Physical Review Letters 92, 217903 (2004).","DOI":"10.1103\/PhysRevLett.92.217903"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Karol Horodecki, Micha\u0142 Horodecki, Pawe\u0142 Horodecki, and Jonathan Oppenheim. ``Secure key from bound entanglement''. Physical Review Letters 94, 160502 (2005). arXiv:quant-ph\/0309110.","DOI":"10.1103\/PhysRevLett.94.160502"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Karol Horodecki, Micha\u0142 Horodecki, Pawe\u0142 Horodecki, and Jonathan Oppenheim. ``General paradigm for distilling classical key from quantum states''. IEEE Transactions on Information Theory 55, 1898\u20131929 (2009). arXiv:quant-ph\/0506189.","DOI":"10.1109\/TIT.2008.2009798"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Micha\u0142 Horodecki, Pawe\u0142 Horodecki, and Ryszard Horodecki. ``Mixed-state entanglement and distillation: Is there a ``bound'' entanglement in nature?''. Physical Review Letters 80, 5239\u20135242 (1998). arXiv:quant-ph\/9801069.","DOI":"10.1103\/PhysRevLett.80.5239"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Igor Devetak and Andreas Winter. ``Distillation of secret key and entanglement from quantum states''. Proceedings of the Royal Society A 461, 207\u2013235 (2005). arXiv:quant-ph\/0306078.","DOI":"10.1098\/rspa.2004.1372"},{"key":"12","unstructured":"Matthias Christandl. ``The structure of bipartite quantum states\u2014insights from group theory and cryptography'' (2006). arXiv:quant-ph\/0604183."},{"key":"13","doi-asserted-by":"crossref","unstructured":"Matthias Christandl, Artur Ekert, Micha\u0142 Horodecki, Pawe\u0142 Horodecki, Jonathan Oppenheim, and Renato Renner. ``Unifying classical and quantum key distillation''. In Salil P. Vadhan, editor, Theory of Cryptography. Pages 456\u2013478. Berlin, Heidelberg (2007). Springer Berlin Heidelberg. arXiv:quant-ph\/0608199.","DOI":"10.1007\/978-3-540-70936-7_25"},{"key":"14","doi-asserted-by":"publisher","unstructured":"Karol Horodecki, Micha\u0142 Horodecki, Pawe\u0142 Horodecki, Debbie Leung, and Jonathan Oppenheim. ``Quantum key distribution based on private states: Unconditional security over untrusted channels with zero quantum capacity''. IEEE Transactions on Information Theory 54, 2604\u20132620 (2008). arXiv:quant-ph\/0608195.","DOI":"10.1109\/TIT.2008.921870"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Matthias Christandl, Norbert Schuch, and Andreas Winter. ``Entanglement of the antisymmetric state''. Communications in Mathematical Physics 311, 397\u2013422 (2012). arXiv:0910.4151.","DOI":"10.1007\/s00220-012-1446-7"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Mark M. Wilde, Marco Tomamichel, and Mario Berta. ``Converse bounds for private communication over quantum channels''. IEEE Transactions on Information Theory 63, 1792\u20131817 (2017). arXiv:1602.08898.","DOI":"10.1109\/TIT.2017.2648825"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Haoyu Qi, Kunal Sharma, and Mark M Wilde. ``Entanglement-assisted private communication over quantum broadcast channels''. Journal of Physics A: Mathematical and Theoretical 51, 374001 (2018). arXiv:1803.03976.","DOI":"10.1088\/1751-8121\/aad5f3"},{"key":"18","doi-asserted-by":"publisher","unstructured":"N. Cai, A. Winter, and R. W. Yeung. ``Quantum privacy and quantum wiretap channels''. Problems of Information Transmission 40, 318\u2013336 (2004).","DOI":"10.1007\/s11122-005-0002-x"},{"key":"19","doi-asserted-by":"publisher","unstructured":"I. Devetak. ``The private classical capacity and quantum capacity of a quantum channel''. IEEE Transactions on Information Theory 51, 44\u201355 (2005). arXiv:quant-ph\/0304127.","DOI":"10.1109\/TIT.2004.839515"},{"key":"20","doi-asserted-by":"publisher","unstructured":"Bartosz Regula. ``Probabilistic transformations of quantum resources''. Physical Review Letters 128, 110505 (2022). arXiv:2109.04481.","DOI":"10.1103\/PhysRevLett.128.110505"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Bartosz Regula. ``Tight constraints on probabilistic convertibility of quantum states''. Quantum 6, 817 (2022). arXiv:2112.11321.","DOI":"10.22331\/q-2022-09-22-817"},{"key":"22","doi-asserted-by":"publisher","unstructured":"Eneet Kaur, Siddhartha Das, Mark M. Wilde, and Andreas Winter. ``Extendibility limits the performance of quantum processors''. Physical Review Letters 123, 070502 (2019). arXiv:2108.03137.","DOI":"10.1103\/PhysRevLett.123.070502"},{"key":"23","doi-asserted-by":"publisher","unstructured":"Eneet Kaur, Siddhartha Das, Mark M. Wilde, and Andreas Winter. ``Resource theory of unextendibility and nonasymptotic quantum capacity''. Physical Review A 104, 022401 (2021). arXiv:1803.10710.","DOI":"10.1103\/PhysRevA.104.022401"},{"key":"24","doi-asserted-by":"publisher","unstructured":"Kun Wang, Xin Wang, and Mark M Wilde. ``Quantifying the unextendibility of entanglement''. New Journal of Physics 26, 033013 (2024). arXiv:1911.07433.","DOI":"10.1088\/1367-2630\/ad264e"},{"key":"25","doi-asserted-by":"publisher","unstructured":"Nilanjana Datta. ``Min- and max-relative entropies and a new entanglement monotone''. IEEE Transactions on Information Theory 55, 2816\u20132826 (2009). arXiv:0803.2770.","DOI":"10.1109\/TIT.2009.2018325"},{"key":"26","doi-asserted-by":"publisher","unstructured":"Reinhard F. Werner. ``An application of Bell's inequalities to a quantum state extension problem''. Letters in Mathematical Physics 17, 359\u2013363 (1989).","DOI":"10.1007\/BF00399761"},{"key":"27","doi-asserted-by":"publisher","unstructured":"A. C. Doherty, Pablo A. Parrilo, and Federico M. Spedalieri. ``Distinguishing separable and entangled states''. Physical Review Letters 88, 187904 (2002). arXiv:quant-ph\/0112007.","DOI":"10.1103\/PhysRevLett.88.187904"},{"key":"28","doi-asserted-by":"publisher","unstructured":"Andrew C. Doherty, Pablo A. Parrilo, and Federico M. Spedalieri. ``Complete family of separability criteria''. Physical Review A 69, 022308 (2004). arXiv:quant-ph\/0308032.","DOI":"10.1103\/PhysRevA.69.022308"},{"key":"29","doi-asserted-by":"publisher","unstructured":"Felix Leditzky, Nilanjana Datta, and Graeme Smith. ``Useful states and entanglement distillation''. IEEE Transactions on Information Theory 64, 4689\u20134708 (2018). arXiv:1701.03081.","DOI":"10.1109\/TIT.2017.2776907"},{"key":"30","unstructured":"Sumeet Khatri and Mark M. Wilde. ``Principles of quantum communication theory: A modern approach'' (2024). arXiv:2011.04672v2."},{"key":"31","doi-asserted-by":"publisher","unstructured":"Adrian Kent. ``Entangled mixed states and local purification''. Physical Review Letters 81, 2839\u20132841 (1998).","DOI":"10.1103\/PhysRevLett.81.2839"},{"key":"32","doi-asserted-by":"publisher","unstructured":"Kun Fang and Zi-Wen Liu. ``No-go theorems for quantum resource purification''. Physical Review Letters 125, 060405 (2020). arXiv:1909.02540.","DOI":"10.1103\/PhysRevLett.125.060405"},{"key":"33","doi-asserted-by":"publisher","unstructured":"Micha\u0142 Horodecki and Pawe\u0142 Horodecki. ``Reduction criterion of separability and limits for a class of distillation protocols''. Physical Review A 59, 4206\u20134216 (1999). arXiv:quant-ph\/9708015.","DOI":"10.1103\/PhysRevA.59.4206"},{"key":"34","doi-asserted-by":"publisher","unstructured":"Reinhard F. Werner. ``Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model''. Physical Review A 40, 4277\u20134281 (1989).","DOI":"10.1103\/PhysRevA.40.4277"},{"key":"35","doi-asserted-by":"publisher","unstructured":"Jens Eisert and Mark M. Wilde. ``A smallest computable entanglement monotone''. In 2022 IEEE International Symposium on Information Theory (ISIT). Pages 2439\u20132444. (2022). arXiv:2201.00835.","DOI":"10.1109\/ISIT50566.2022.9834375"},{"key":"36","doi-asserted-by":"publisher","unstructured":"Yury Polyanskiy and Sergio Verd\u00fa. ``Arimoto channel coding converse and R\u00e9nyi divergence''. In 2010 48th Annual Allerton Conference on Communication, Control, and Computing. Pages 1327\u20131333. IEEE (2010).","DOI":"10.1109\/ALLERTON.2010.5707067"},{"key":"37","doi-asserted-by":"publisher","unstructured":"T. Ogawa and H. Nagaoka. ``A new proof of the channel coding theorem via hypothesis testing in quantum information theory''. In Proceedings IEEE International Symposium on Information Theory. Page 73. (2002). arXiv:quant-ph\/0208139.","DOI":"10.1109\/ISIT.2002.1023345"},{"key":"38","doi-asserted-by":"publisher","unstructured":"Benjamin Schumacher and M. A. Nielsen. ``Quantum data processing and error correction''. Physical Review A 54, 2629\u20132635 (1996). arXiv:quant-ph\/9604022.","DOI":"10.1103\/PhysRevA.54.2629"},{"key":"39","unstructured":"Johann von Neumann. ``Thermodynamik quantenmechanischer gesamtheiten''. Nachrichten von der Gesellschaft der Wissenschaften zu G\u00f6ttingen, Mathematisch-Physikalische Klasse 1927, 273\u2013291 (1927). url: http:\/\/eudml.org\/doc\/59231."}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-03-10-2020\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T14:24:39Z","timestamp":1773152679000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-03-10-2020\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,10]]},"references-count":40,"URL":"https:\/\/doi.org\/10.22331\/q-2026-03-10-2020","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,10]]},"article-number":"2020"}}