Tight bounds for private communication over bosonic Gaussian channels based on teleportation simulation with optimal finite resources

Year: 2019

Authors: Laurenza R., Tserkis S., Banchi L., Braunstein SL., Ralph TC., Pirandola S.

Autors Affiliation: Univ York, Dept Comp Sci, York YO10 5GH, N Yorkshire, England; INO CNR, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy; Univ Queensland, Sch Math & Phys, Ctr Quantum Computat & Commun Technol, St Lucia, Qld 4072, Australia; Univ Florence, Dept Phys & Astron, Via G Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; MIT, Res Lab Elect, 77 Massachusetts Ave, Cambridge, MA 02139 USA.

Abstract: Upper bounds for private communication over quantum channels can be derived by adopting channel simulation, protocol stretching, and relative entropy of entanglement. All these ingredients have led to single-letter upper bounds to the secret-key capacity which can be directly computed over suitable resource states. For bosonic Gaussian channels, the tightest upper bounds have been derived by employing teleportation simulation over asymptotic resource states, namely, the asymptotic Choi matrices of these channels. In this work, we adopt a different approach. We show that teleporting over an analytical class of finite-energy resource states allows us to closely approximate the ultimate bounds for increasing energy, so as to provide increasingly tight upper bounds to the secret-key capacity of one-mode phase-insensitive Gaussian channels. We then show that an optimization over the same class of resource states can be used to bound the maximum secret-key rates that are achievable in a finite number of channel uses.

Journal/Review: PHYSICAL REVIEW A

Volume: 100 (4)      Pages from: 042301-1  to: 042301-9

More Information: This research has been supported by the Australian Research Council (ARC) under the Centre of Excellence for Quantum Computation and Communication Technology (CE170100012), the EPSRC via the UK Quantum Communications Hub (EP/M013472/1), and the European Commission via ’Continuous Variable Quantum Communications’ (CiViQ, Project ID: 820466).
KeyWords: Quantum Information; Criterion; Entropy; Limits
DOI: 10.1103/PhysRevA.100.042301

Citations: 8
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