Normal quantum channels and Markovian correlated two-qubit quantum errors

TL;DR

This paper introduces a framework for modeling correlated two-qubit quantum errors using normal quantum channels derived from diffusive random walks, which preserve Markovianity and differ from traditional error models like Pauli errors.

Contribution

It develops a novel approach to describe correlated quantum errors with normal quantum channels, extending the modeling capabilities for quantum error correction and communication.

Findings

Normal quantum channels can model correlated two-qubit errors.

These channels preserve Markovianity unlike some traditional models.

Different distributions can induce the same quantum channel in single qubits.

Abstract

We study general ``normally'' distributed random unitary transformations. These distributions can be defined in terms of a diffusive random walk in the respective group manifold, formally underpinned by the concept of infinite divisibility. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process, which can be generated by a Lindblad master equation. In the single qubit case, we show that it is possible to find different distributions which induce the same quantum channel. In the case of two qubits, the normal quantum channels, i.e. quantum channels induced by normal distributions in ${\rm SU}(2)\otimes{\rm SU}(2)$ provide an appropriate framework for modeling correlated quantum errors. In contrast to correlated Pauli errors, for instance, they conserve their Markovianity, and they lead to very different results in error correcting codes or entanglement distillation. We expect our work to find applications in the tomography and modeling of one- and two-qubit errors in current quantum computer platforms, but also in the distillation of Bell pairs across imperfect communication channels, where it is conceivable that subsequently transmitted qubits are subject to correlated errors.