Evaluating Pauli errors on cluster states by weighted distances

Fuente: arXiv
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Main Authors: Shen, Choong Pak, Girolami, Davide
Format: Preprint
Published: 2023
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author Shen, Choong Pak
Girolami, Davide
author_facet Shen, Choong Pak
Girolami, Davide
contents We address the problem of evaluating the difference between quantum states before and after being affected by errors encoded in unitary transformations. Standard distance functions, e.g., the Bures length, are not fully adequate for such a task. Weighted distances are instead appropriate information measures to quantify distinguishability of multipartite states. Here, we employ the previously introduced weighted Bures length and the newly defined weighted Hilbert-Schmidt distance to quantify how much single-qubit Pauli errors alter cluster states. We find that different errors of the same dimension change cluster states in a different way, i.e., their detectability is in general different. Indeed, they transform an ideal cluster state into a state whose weighted distance from the input depends on the specific chosen Pauli rotation, as well as the position of the affected qubit in the graph related to the state. As these features are undetected by using standard distances, the study proves the usefulness of weighted distances to monitor key but elusive properties of many-body quantum systems.
format Preprint
id arxiv_https___arxiv_org_abs_2308_10810
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Evaluating Pauli errors on cluster states by weighted distances
Shen, Choong Pak
Girolami, Davide
Quantum Physics
Statistical Mechanics
Atomic Physics
We address the problem of evaluating the difference between quantum states before and after being affected by errors encoded in unitary transformations. Standard distance functions, e.g., the Bures length, are not fully adequate for such a task. Weighted distances are instead appropriate information measures to quantify distinguishability of multipartite states. Here, we employ the previously introduced weighted Bures length and the newly defined weighted Hilbert-Schmidt distance to quantify how much single-qubit Pauli errors alter cluster states. We find that different errors of the same dimension change cluster states in a different way, i.e., their detectability is in general different. Indeed, they transform an ideal cluster state into a state whose weighted distance from the input depends on the specific chosen Pauli rotation, as well as the position of the affected qubit in the graph related to the state. As these features are undetected by using standard distances, the study proves the usefulness of weighted distances to monitor key but elusive properties of many-body quantum systems.
title Evaluating Pauli errors on cluster states by weighted distances
topic Quantum Physics
Statistical Mechanics
Atomic Physics
url https://arxiv.org/abs/2308.10810