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

Mario Berta; Fernando G.S.L. Brandão; Gilad Gour; Ludovico Lami; Martin B. Plenio; Bartosz Regula; Marco Tomamichel

doi:https://doi.org/10.22331/Q-2023-09-07-1103

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

Mario Berta, Fernando G.S.L. Brandão, Gilad Gour, Ludovico Lami, Martin B. Plenio, Bartosz Regula, Marco Tomamichel

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Quantum
Volume	7
DOIs	https://doi.org/10.22331/Q-2023-09-07-1103
State	Published - 2023
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

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https://doi.org/10.22331/Q-2023-09-07-1103

Cite this

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

abstract = "We show that the proof of the generalised quantum Stein's lemma [Brand{\~a}o & 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 Brand{\~a}o & 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 [Brand{\~a}o & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brand{\~a}o & 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.",

author = "Mario Berta and Brand{\~a}o, {Fernando G.S.L.} and Gilad Gour and Ludovico Lami and Plenio, {Martin B.} and Bartosz Regula and Marco Tomamichel",

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doi = "https://doi.org/10.22331/Q-2023-09-07-1103",

language = "الإنجليزيّة",

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T1 - On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources

AU - Berta, Mario

AU - Brandão, Fernando G.S.L.

AU - Gour, Gilad

AU - Lami, Ludovico

AU - Plenio, Martin B.

AU - Regula, Bartosz

AU - Tomamichel, Marco

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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VL - 7

JO - Quantum

JF - Quantum

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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