Decoherence-Insensitive Quantum Communication by Optimal C^*-Encoding

TL;DR

This paper proposes a method for quantum communication that uses optimal C*-encoding to protect quantum information against decoherence, leveraging noiseless subspaces and geometric conditions for effective encoding.

Contribution

It introduces a novel C*-algebra based encoding scheme that optimally distributes quantum information across decoherence-free subspaces.

Findings

Derived geometric conditions for optimal encoding

Constructed explicit examples of encoding schemes

Showed robustness against phase damping noise

Abstract

The central issue in this article is to transmit a quantum state in such a way that after some decoherence occurs, most of the information can be restored by a suitable decoding operation. For this purpose, we incorporate redundancy by mapping a given initial quantum state to a messenger state on a larger-dimensional Hilbert space via a $C^*$-algebra embedding. Our noise model for the transmission is a phase damping channel which admits a noiseless or decoherence-free subspace or subsystem. More precisely, the transmission channel is obtained from convex combinations of a set of lowest rank yes/no measurements that leave a component of the messenger state unchanged. The objective of our encoding is to distribute quantum information optimally across the noise-susceptible component of the transmission when the noiseless component is not large enough to contain all the quantum information to be transmitted. We derive simple geometric conditions for optimal encoding and construct examples.