Qudit Noisy Stabilizer Formalism

TL;DR

This paper introduces a formalism for efficiently modeling the evolution of noisy stabilizer states in qudit systems, enabling analysis of entanglement generation under noise in prime-power dimensions.

Contribution

The paper presents the qudit Noisy Stabilizer Formalism, extending stabilizer techniques to noisy qudit systems and demonstrating its efficiency for certain state evolutions.

Findings

Formalism applies to prime-power dimensions with generalized Pauli-diagonal noise.

Complexity scales linearly with initial qudits and exponentially with final qudits.

Efficiently describes entanglement generation from noisy states.

Abstract

We introduce the qudit Noisy Stabilizer Formalism, a framework for efficiently describing the evolution of stabilizer states in prime-power dimensions subject to generalized Pauli-diagonal noise under Clifford operations and generalized Pauli measurements. For arbitrary dimensions, the formalism remains applicable, though restricted to a subset of stabilizer states and operations. The computational complexity scales linearly with the number of qudits in the initial state and exponentially with the number of qudits in the final state. This ensures that when noisy qudit stabilizer states evolve via generalized Pauli measurements and Clifford operations to generate multipartite entangled states of a few qudits, their description remains efficient. We demonstrate this by analyzing the generation of a generalized Bell pair from a noisy linear cluster state subject to two distinct noise sources acting on each of the qudits.