Abstract
The study of free-space quantum communications requires tools from quantum information theory, optics and turbulence theory. Here we combine these tools to bound the ultimate rates for key and entanglement distribution through a free-space link, where the propagation of quantum systems is generally affected by diffraction, atmospheric extinction, turbulence, pointing errors, and background noise. Besides establishing ultimate limits, we also show that the composable secret-key rate achievable by a suitable (pilot-guided and post-selected) coherent-state protocol is sufficiently close to these limits, therefore showing the suitability of free-space channels for high-rate quantum key distribution. Our work provides analytical tools for assessing the composable finite-size security of coherent-state protocols in general conditions, from the standard assumption of a stable communication channel (as is typical in fiber-based connections) to the more challenging scenario of a fading channel (as is typical in free-space links).
Highlights
In a future vision where quantum technologies are expected to be developed on a large scale, hybrid and flexible architectures represent a key strategy for their success [1]
We investigate the ultimate limits of free-space quantum communications, establishing upper and lower bounds on the maximum number of secret key bits that can be shared by two remote parties
IV, where we extend it to the case of CV-quantum key distribution (QKD) protocols over a fading channel as is the general case of free-space links affected by pointing errors and turbulence
Summary
In a future vision where quantum technologies are expected to be developed on a large scale, hybrid and flexible architectures represent a key strategy for their success [1]. Continuous-variable (CV) protocols of quantum key distribution (QKD) [12] To this aim, we develop a general theory for assessing the composable finite-size security of coherent-state protocols [13,14], starting from the standard assumption of a stable communication channel (e.g., as typical in fiber-based connections) to considering the more challenging scenario of a free-space fading channel, whose transmissivity rapidly fluctuates. We have designed a coherent-state protocol, aided by pilot pulses and a suitable postselection procedure, which is able to achieve high secret-key rates in conditions of weak turbulence, within one order of magnitude of the ultimate bounds In this way, we show that generally turbulent free-space channels are able to support high-rate QKD, with immediate consequences for wireless quantum communications.
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