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

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

Goodenough, K.D. (TU Delft QID/Wehner Group; TU Delft QuTech Advanced Research Centre)
Elkouss Coronas, D. (TU Delft QID/Wehner Group; TU Delft QuTech Advanced Research Centre)
Wehner, S.D.C. (TU Delft Quantum Information and Software; TU Delft QuTech Advanced Research Centre)

2016

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.

quantum information
quantum repeaters
quantum communication
secret key rate
quantum key distribution
squashed entanglement
private capacity

http://resolver.tudelft.nl/uuid:e54ec4fe-8536-4424-9f73-32a1e09e416c

https://doi.org/10.1088/1367-2630/18/6/063005

1367-2630

New Journal of Physics, 18, 1-21

Institutional Repository

journal article

© 2016 K.D. Goodenough, D. Elkouss Coronas, S.D.C. Wehner