Spacetime replication of continuous variable quantum information

TL;DR

This paper introduces continuous variable quantum error correction strategies for spacetime quantum information replication, enabling optical implementation and improving efficiency over qubit-based schemes.

Contribution

It presents a new class of homologically-constructed CV quantum error correcting codes and an optimized five-mode scheme for specific spacetime configurations.

Findings

CV schemes require half as many shares as qubit schemes

Detailed encoding and decoding procedures are provided

Recovery fidelity with finite squeezing is calculated

Abstract

The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically-constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics.