Assisted concentration of Gaussian resources

Lami, Ludovico; Takagi, Ryuji; Adesso, Gerardo

Abstract

In spite of their outstanding experimental relevance, Gaussian operations in continuous-variable quantum systems are subjected to fundamental limitations, as it is known that general resources cannot be distilled within the Gaussian paradigm. We show that these limitations can be overcome by considering a collaborative setting where one party distills resources with the aid of another party, whose operations are assumed to be Gaussian but are otherwise unrestricted; the two parties can only communicate classically. We show that in single-shot scenarios, unlike in the well-known case of entanglement theory, two-way classical communication does not lead to any improvement over one-way classical communication from the aiding party to the aided party. We then provide a concise general expression for the Gaussian resource of assistance, i.e., the distillable resource when the aiding party holds a purification of the aided party's state. To demonstrate the usefulness of this general expression, we apply it to two important kinds of resources, squeezing and entanglement, and find some simple analytic solutions. In the case of entanglement theory, we are able to find general upper bounds on the regularized Gaussian entanglement of assistance, and to establish additivity for tensor powers of thermal states. This allows us to draw a quantitative and enlightening comparison with the performance of assisted entanglement distillation in the non-Gaussian setting. On the technical side, we develop some variational expressions to handle functions of symplectic eigenvalues that may be of independent interest. Our results suggest further potential for Gaussian operations to play a major role in practical quantum information processing protocols.

Citation

Lami, L., Takagi, R., & Adesso, G. (2020). Assisted concentration of Gaussian resources. Physical Review A, 101(5), Article 052305

• Journal Article Type: Article
• Acceptance Date: Mar 20, 2020
• Online Publication Date: May 4, 2020
• Publication Date: May 4, 2020
• Deposit Date: May 7, 2020
• Publicly Available Date: May 7, 2020
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 101
• Issue: 5
• Article Number: 052305
• Keywords: Quantum Physics; Other Condensed Matter; Mathematical Physics
• Public URL: https://nottingham-repository.worktribe.com/output/2465562
• Publisher URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.052305
• Additional Information: Lami, Ludovico and Takagi, Ryuji and Adesso, Gerardo, Assisted concentration of Gaussian resources, Phys. Rev. A, 101, 5, 052305, 2020, American Physical Society, 10.1103/PhysRevA.101.052305,https://link.aps.org/doi/10.1103/PhysRevA.101.052305