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

• URL: http://arxiv.org/abs/2205.02813v4
• Date: Fri, 25 Aug 2023 11:04:32 GMT
• Title: On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
• Authors: Mario Berta, Fernando G. S. L. Brand\~ao, Gilad Gour, Ludovico Lami, Martin B. Plenio, Bartosz Regula, Marco Tomamichel
• Abstract summary: We show that the proof of the generalised quantum Stein's lemma is not correct due to a gap in the argument leading to Lemma III.9. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement.
• Score: 51.243733928201024
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that the proof of the generalised quantum Stein's lemma [Brand\~ao & 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\~ao & 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\~ao & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brand\~ao & 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.

Related papers

• Global Phase Helps in Quantum Search: Yet Another Look at the Welded Tree Problem [55.80819771134007]
  In this paper, we give a short proof of the optimal linear hitting time for a welded tree problem by a discrete-time quantum walk. The same technique can be applied to other 1-dimensional hierarchical graphs.
  arXiv  Detail & Related papers  (2024-04-30T11:45:49Z)
• Testing trajectory-based determinism via time probability distributions [44.99833362998488]
  Bohmian mechanics (BM) has inherited more predictive power than quantum mechanics (QM) We introduce a prescription for constructing a flight-time probability distribution within generic trajectory-equipped theories. We derive probability distributions that are unreachable by QM.
  arXiv  Detail & Related papers  (2024-04-15T11:36:38Z)
• On the optimal error exponents for classical and quantum antidistinguishability [3.481985817302898]
  Antidistinguishability has been used to investigate the reality of quantum states. We show that the optimal error exponent vanishes to zero for classical and quantum antidistinguishability. It remains an open problem to obtain an explicit expression for the optimal error exponent for quantum antidistinguishability.
  arXiv  Detail & Related papers  (2023-09-07T14:03:58Z)
• Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture [0.0]
  We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem. These problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We show that guidable local Hamiltonian problems for both classes of guiding states are $mathsfQCMA$-complete in the inverse-polynomial precision setting.
  arXiv  Detail & Related papers  (2023-02-22T19:00:00Z)
• Functional analytic insights into irreversibility of quantum resources [8.37609145576126]
  Quantum channels which preserve certain sets of states are contractive with respect to the base norms induced by those sets. We show that there exist qutrit magic states that cannot be reversibly interconverted under stabiliser protocols.
  arXiv  Detail & Related papers  (2022-11-28T19:00:00Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Events in quantum mechanics are maximally non-absolute [0.9176056742068814]
  We prove that quantum correlations can be maximally non-absolute according to both quantifiers. We show that chained Bell inequalities (and relaxations thereof) are also valid constraints for Wigner's experiment.
  arXiv  Detail & Related papers  (2021-12-19T21:15:16Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Quantum Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)
• Tightening the tripartite quantum memory assisted entropic uncertainty relation [0.0]
  In quantum information theory, Shannon entropy has been used as an appropriate measure to express the uncertainty relation. One can extend the bipartite quantum memory assisted entropic uncertainty relation to tripartite quantum memory assisted uncertainty relation.
  arXiv  Detail & Related papers  (2020-05-05T12:51:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.