Certifying quantumness: benchmarks for the optimal processing of generalized coherent and squeezed states

Yang, Yuxiang; Chiribella, Giulio; Adesso, Gerardo

Abstract

Quantum technology promises revolutionary advantages in information processing and transmission compared to classical technology; however, determining which specific resources are needed to surpass the capabilities of classical machines often remains a nontrivial problem. To address such a problem, one first needs to establish the best classical solutions, which set benchmarks that must be beaten by any implementation claiming to harness quantum features for an enhanced performance. Here we introduce and develop a self-contained formalism to obtain the ultimate, generally probabilistic benchmarks for quantum information protocols including teleportation and approximate cloning, with arbitrary ensembles of input states generated by a group action, so-called Gilmore-Perelomov coherent states. This allows us to construct explicit fidelity thresholds for the transmission of multimode Gaussian and non-Gaussian states of continuous-variable systems, as well as qubit and qudit pure states drawn according to nonuniform distributions on the Bloch hypersphere, which accurately model the current laboratory facilities. The performance of deterministic classical procedures such as square-root measurement strategies is further compared with the optimal probabilistic benchmarks, and the state-of-the-art performance of experimental quantum implementations against our newly derived thresholds is discussed. This work provides a comprehensive collection of directly useful criteria for the reliable certification of quantum communication technologies.

Citation

Yang, Y., Chiribella, G., & Adesso, G. (2014). Certifying quantumness: benchmarks for the optimal processing of generalized coherent and squeezed states. Physical Review A, 90(4), https://doi.org/10.1103/PhysRevA.90.042319

• Journal Article Type: Article
• Acceptance Date: Aug 16, 2014
• Publication Date: Oct 16, 2014
• Deposit Date: Oct 11, 2017
• Publicly Available Date: Oct 11, 2017
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 90
• Issue: 4
• DOI: https://doi.org/10.1103/PhysRevA.90.042319
• Public URL: https://nottingham-repository.worktribe.com/output/738108
• Publisher URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.90.042319
• Additional Information: ©2014 American Physical Society