Efficient quantum communication under collective noise

TL;DR

This paper presents an efficient quantum communication protocol that uses decoherence-free subspaces to achieve optimal transmission rates under collective noise, with scalable encoding/decoding operations and minimal overhead.

Contribution

The authors develop a new quantum communication protocol leveraging decoherence-free subspaces that achieves optimal asymptotic rates with efficient, scalable encoding and decoding.

Findings

Achieves perfect transmission at rate m/(m+r) with minimal overhead.

Encoding and decoding require a linear number of elementary gates in the number of qudits.

Overhead scales at most as O(d^r), independent of the number of transmitted qudits.

Abstract

We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, m. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group G, i.e. with a discrete number, |G|, of possible noise operators, perfect transmission at a rate m/(m+r) is achieved with an overhead that scales at most as $\mathcal{O}(d^r)$ where the number of auxiliary qudits, r, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, m. For certain groups, e.g. cyclic groups, we find that the overhead scales only linearly with the number of group elements |G|.