Bosonic quantum communication across arbitrarily high loss channels

Abstract

A general attenuator ${\Phi }_{\lambda ,\sigma }$ is a bosonic quantum channel that acts by combining the input with a fixed environment state $\sigma$ in a beam splitter of transmissivity $\lambda$. If $\sigma$ is a thermal state the resulting channel is a thermal attenuator, whose quantum capacity vanishes for $\lambda \le 1/2$. We study the quantum capacity of these objects for generic $\sigma$, proving a number of unexpected results. Most notably, we show that for any arbitrary value of $\lambda >0$ there exists a suitable single-mode state $\sigma (\lambda )$ such that the quantum capacity of ${\Phi }_{\lambda ,\sigma (\lambda )}$ is larger than a universal constant $c>0$. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity, provided that the environment state is appropriately controlled. We also find examples of states $\sigma$ such that the quantum capacity of ${\Phi }_{\lambda ,\sigma }$ is not monotonic in $\lambda$. These findings may have implications for the study of communication lines running across integrated optical circuits, of which general attenuators provide natural models.

arXiv comment28 pages, 4 figures; v2 is very close to the published version. In the SM we added Section I.D, on the comparison between quantum communication and non-locality distribution, and Section V, where we discuss a possible extension of our main result (Thm. 2)

References in corpus (49)

• Quantum entanglement
• Separability Criterion for Density Matrices
• Quantum information with continuous variables
• Gaussian Quantum Information
• Bell nonlocality
• Photonic quantum technologies
• Fundamental Limits of Repeaterless Quantum Communications
• General Benchmarks for Quantum Repeaters
• Universal Linear Optics
• Universal Quantum Computation with Continuous-Variable Cluster States
• The capacity of the noisy quantum channel
• On the impossibility of distilling Gaussian states with Gaussian operations
• The characterization of Gaussian operations and Distillation of Gaussian States
• Gaussian transformations and distillation of entangled Gaussian states
• Capacities of Quantum Erasure Channels
• Quantum channels and memory effects
• A No-Go Theorem for Gaussian Quantum Error Correction
• Extremality of Gaussian quantum states
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Continuity of quantum conditional information
• Quantum Capacities of Bosonic Channels
• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Asymptotic violation of Bell inequalities and distillability
• The structure of degradable quantum channels
• Gaussian quantum resource theories
• A solution of the Gaussian optimizer conjecture
• Limitations of quantum computing with Gaussian cluster states
• Operational resource theory of continuous-variable nonclassicality
• Narrow Bounds for the Quantum Capacity of Thermal Attenuators
• Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
• Energy-constrained private and quantum capacities of quantum channels
• Quantum trade-off coding for bosonic communication
• Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
• Optimal Gaussian Entanglement Swapping
• Could Gaussian regenerative stations act as quantum repeaters?
• Quantum Channel Capacities with Passive Environment Assistance
• The conditional entropy power inequality for Gaussian quantum states
• Gaussian States Minimize the Output Entropy of the One-Mode Quantum Attenuator
• The conditional Entropy Power Inequality for bosonic quantum systems
• Classical capacities of quantum channels with environment assistance
• Enhanced energy-constrained quantum communication over bosonic Gaussian channels
• Approximate reversal of quantum Gaussian dynamics
• All phase-space linear bosonic channels are approximately Gaussian dilatable
• Extendibility of bosonic Gaussian states
• Assisted concentration of Gaussian resources
• Upper bounds on the quantum capacity for general attenuator and amplifier
• Upper bounds on the private capacity for bosonic Gaussian channels

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