On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources-Reference-Cited by-同舟云学术

On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources

Published:2023-09-07 Issue: Volume:7 Page:1103
ISSN:2521-327X
Container-title:Quantum
language:en
Short-container-title:Quantum

Author:

Berta Mario¹²,Brandão Fernando G. S. L.³⁴,Gour Gilad⁵,Lami Ludovico⁶⁷⁸⁹,Plenio Martin B.⁶,Regula Bartosz¹⁰¹¹,Tomamichel Marco¹²¹³

Affiliation:

1. Institute for Quantum Information, RWTH Aachen University, Aachen, Germany

2. Department of Computing, Imperial College London, London, UK

3. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA

4. AWS Center for Quantum Computing, Pasadena, CA, USA

5. Department of Mathematics and Statistics, Institute for Quantum Science and Technology, University of Calgary, AB, Canada T2N 1N4

6. Institut für Theoretische Physik und IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany

7. QuSoft, Science Park 123, 1098 XG Amsterdam, The Netherlands

8. Korteweg–de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, The Netherlands

9. Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

10. Mathematical Quantum Information RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR) and RIKEN Center for Quantum Computing (RQC), Wako, Saitama 351-0198, Japan

11. Department of Physics, Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan

12. Center for Quantum Technologies, National University of Singapore, Singapore

13. Department of Electrical and Computer Engineering, College of Design and Engineering, National University of Singapore, Singapore

Abstract

We show that the proof of the generalised quantum Stein's lemma [Brandão & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brandão & Plenio is not known to hold. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement [Brandão & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brandão & Gour, Phys. Rev. Lett. 115, 070503 (2015)] under asymptotically resource non-generating operations. We discuss potential ways to recover variants of the newly unsettled results using other approaches.

Funder

ERC Grant Agreement

Japan Society for the Promotion of Science

NUS Startup Grant

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

Link

https://quantum-journal.org/papers/q-2023-09-07-1103/pdf/

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