Assessing the performance of quantum repeaters for all phase-insensitive Gaussian bosonic channels

TL;DR

This paper develops bounds on the performance of quantum repeaters for phase-insensitive Gaussian bosonic channels, providing benchmarks and capacity estimates crucial for advancing quantum communication technologies.

Contribution

It introduces a method to upper bound the squashed entanglement of these channels using sub-optimal squashing channels, improving capacity bounds and benchmarking quantum repeater performance.

Findings

Derived bounds for Gaussian bosonic channels with input photon number restrictions.

Established convexity of squashed entanglement across channels.

Calculated exact capacities for the erasure channel and bounds for others.

Abstract

One of the most sought-after goals in experimental quantum communication is the implementation of a quantum repeater. The performance of quantum repeaters can be assessed by comparing the attained rate with the quantum and private capacity of direct transmission, assisted by unlimited classical two-way communication. However, these quantities are hard to compute, motivating the search for upper bounds. Takeoka, Guha and Wilde found the squashed entanglement of a quantum channel to be an upper bound on both these capacities. In general it is still hard to find the exact value of the squashed entanglement of a quantum channel, but clever sub-optimal squashing channels allow one to upper bound this quantity, and thus also the corresponding capacities. Here, we exploit this idea to obtain bounds for any phase-insensitive Gaussian bosonic channel. This bound allows one to benchmark the implementation of quantum repeaters for a large class of channels used to model communication across fibers. In particular, our bound is applicable to the realistic scenario when there is a restriction on the mean photon number on the input. Furthermore, we show that the squashed entanglement of a channel is convex in the set of channels, and we use a connection between the squashed entanglement of a quantum channel and its entanglement assisted classical capacity. Building on this connection, we obtain the exact squashed entanglement and two-way assisted capacities of the $d$-dimensional erasure channel and bounds on the amplitude-damping channel and all qubit Pauli channels. In particular, our bound improves on the previous best known squashed entanglement upper bound of the depolarizing channel.