Finite-resource teleportation stretching for continuous-variable systems

Abstract

We show how adaptive protocols of quantum and private communication through bosonic Gaussian channels can be simplified into much easier block versions that involve resource states with finite energy. This is achieved by combining the adaptive-to-block reduction technique devised earlier [S. Pirandola et al., Nat. Commun. 8, 15043 (2017)], based on teleportation stretching and relative entropy of entanglement, with an alternative simulation of Gaussian channels recently introduced by Liuzzo-Scorpo et al. [Phys. Rev. Lett. 119, 120503 (2017)]. In this way, we derive weak converse upper bounds for the secret-key capacity of phase-insensitive Gaussian channels, which approximate the optimal limit for infinite energy. Our results apply to both point-to-point and repeater-assisted private communications.

8 pages, 5 figures

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• Near-term quantum-repeater experiments with nitrogen-vacancy centers: Overcoming the limitations of direct transmission
• Fundamental limits to quantum channel discrimination
• Optimal continuous variable quantum teleportation with limited resources
• Simulation of Gaussian channels via teleportation and error correction of Gaussian states
• Finite-resource teleportation stretching for continuous-variable systems
• Teleportation simulation of bosonic Gaussian channels: Strong and uniform convergence
• Tight bounds for private communication over bosonic Gaussian channels based on teleportation simulation with optimal finite resources
• Adaptive estimation and discrimination of Holevo-Werner channels
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Discord, quantum knowledge and private communications
• Holographic Limitations and Corrections to Quantum Information Protocols