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

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.

arXiv comment10 pages, 5 figures

References in corpus (54)

• Quantum entanglement
• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Quantum information with continuous variables
• Gaussian Quantum Information
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• Quantifying Entanglement
• Quantum key distribution using gaussian-modulated coherent states
• General Benchmarks for Quantum Repeaters
• Fundamental Limits of Repeaterless Quantum Communications
• The Role of Relative Entropy in Quantum Information Theory
• Advances in Quantum Teleportation
• Teleportation of Quantum States
• Advances in Photonic Quantum Sensing
• Continuous variable quantum information: Gaussian states and beyond
• Entanglement in continuous variable systems: Recent advances and current perspectives
• The characterization of Gaussian operations and Distillation of Gaussian States
• Quantum Cryptography without Switching
• High-rate quantum cryptography in untrusted networks
• Fundamental rate-loss tradeoff for optical quantum key distribution
• Hybrid quantum information processing
• Distributing Secret Keys with Quantum Continuous Variables: Principle, Security and Implementations
• Secure key from bound entanglement
• A No-Go Theorem for Gaussian Quantum Error Correction
• End-to-end capacities of a quantum communication network
• Symplectic invariants, entropic measures and correlations of Gaussian states
• Continuous Variable Quantum Cryptography using Two-Way Quantum Communication
• Teleportation as a Depolarizing Quantum Channel, Relative Entropy and Classical Capacity
• Quantum fidelity for arbitrary Gaussian states
• Direct and Reverse Secret-Key Capacities of a Quantum Channel
• Continuous variable quantum key distribution with two-mode squeezed states
• Characterization of Collective Gaussian Attacks and Security of Coherent-State Quantum Cryptography
• Second-order asymptotics for quantum hypothesis testing
• Universal teleportation with a twist
• Converse bounds for private communication over quantum channels
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Theory of channel simulation and bounds for private communication
• Trusted Noise in Continuous-Variable Quantum Key Distribution: a Threat and a Defense
• Unidimensional continuous-variable quantum key distribution
• Ultimate Precision of Adaptive Noise Estimation
• Feasibility of continuous-variable quantum key distribution with noisy coherent states
• Reverse Coherent Information
• Degradability of Bosonic Gaussian channels
• Gaussian hypothesis testing and quantum illumination
• General bounds for sender-receiver capacities in multipoint quantum communications
• Multiplicativity of completely bounded p-norms implies a new additivity result
• Information geometry of Gaussian channels
• Optimal continuous variable quantum teleportation with limited resources
• The entropy gain of infinite-dimensional quantum channels
• Upper bounds on secret key agreement over lossy thermal bosonic channels
• Simulation of Gaussian channels via teleportation and error correction of Gaussian states
• Characterizing teleportation in optics
• Finite-resource teleportation stretching for continuous-variable systems

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• Advances in Quantum Cryptography
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• Classical benchmarking for microwave quantum illumination
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• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier