Long-distance quantum communication over noisy networks without long-time quantum memory

TL;DR

This paper demonstrates that long-distance entanglement can be achieved over noisy 2D networks without long-term quantum memory by using syndrome measurements and a novel encoding scheme based on topological quantum memory.

Contribution

It introduces a new encoding and decoding scheme for noisy 2D networks that enables long-distance entanglement without requiring long-time quantum memory, leveraging topological quantum codes.

Findings

Long-distance entanglement is possible in noisy 2D networks.

A simple syndrome-based encoding scheme is proposed for 3D networks.

Fidelity bounds are analytically derived for the encoding and decoding process.

Abstract

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension $D$ and transmission of quantum information in a $D+1$-dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.