Accessible bounds for general quantum resources

Bromley, Thomas R.; Cianciaruso, Marco; Vourekas, Sofoklis; Regula, Bartosz; Adesso, Gerardo

Abstract

The recent development of general quantum resource theories has given a sound basis for the quantification of useful quantum effects. Nevertheless, the evaluation of a resource measure can be highly non-trivial, involving an optimisation that is often intractable analytically or intensive numerically. In this paper, we describe a general framework that provides quantitative lower bounds to any resource quantifier that satisfies the essential property of monotonicity under the corresponding set of free operations. Our framework relies on projecting all quantum states onto a restricted subset using a fixed resource non-increasing operation. The resources of the resultant family can then be evaluated using a simplified optimisation, with the result providing lower bounds on the resource contents of any state. This approach also reduces the experimental overhead, requiring only the relevant statistics of the restricted family of states. We illustrate the application of our framework by focusing on the resource of multiqubit entanglement and outline applications to other quantum resources.

Citation

Bromley, T. R., Cianciaruso, M., Vourekas, S., Regula, B., & Adesso, G. (2018). Accessible bounds for general quantum resources. Journal of Physics A: Mathematical and Theoretical, 51(32), https://doi.org/10.1088/1751-8121/aacb4a

• Journal Article Type: Article
• Acceptance Date: Jun 8, 2018
• Online Publication Date: Jun 8, 2018
• Publication Date: Jul 2, 2018
• Deposit Date: Jun 11, 2018
• Publicly Available Date: Jun 9, 2019
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 51
• Issue: 32
• DOI: https://doi.org/10.1088/1751-8121/aacb4a
• Keywords: quantum resource theories, entanglement, robustness
• Public URL: https://nottingham-repository.worktribe.com/output/944728
• Publisher URL: http://iopscience.iop.org/article/10.1088/1751-8121/aacb4a
• Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1751-8121/aacb4a.
• Contract Date: Jun 11, 2018