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.

28 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 (9)

• Photonic quantum technologies
• Universal Quantum Computation with Continuous-Variable Cluster States
• A No-Go Theorem for Gaussian Quantum Error Correction
• Quantum Capacities of Bosonic Channels
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• The structure of degradable quantum channels
• Could Gaussian regenerative stations act as quantum repeaters?
• Upper bounds on the quantum capacity for general attenuator and amplifier
• Upper bounds on the private capacity for bosonic Gaussian channels

Cited by in corpus (11)

• Quantum capacity of bosonic dephasing channel
• Estimating Quantum and Private capacities of Gaussian channels via degradable extensions
• Restoring quantum communication efficiency over high loss optical fibres
• Magic Resource Can Enhance the Quantum Capacity of Channels
• Capacities of Gaussian Quantum Channels with Passive Environment Assistance
• Quantum Optical Communication in the presence of strong attenuation noise
• Passive environment-assisted quantum communication with GKP states
• Optimality Condition for the Petz Map
• Energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel
• Loss-robust crossband entanglement generation beyond the direct-transduction limit
• Classical capacity of quantum non-Gaussian attenuator and amplifier channels