将三量子位的GHZ SLOCC类在LU下划分为十族

IF 0.7 4区物理与天体物理 Q3 COMPUTER SCIENCE, THEORY & METHODS

Quantum Information & Computation Pub Date : 2023-04-01 DOI:10.26421/qic23.5-6-3

Dafa Li

{"title":"将三量子位的GHZ SLOCC类在LU下划分为十族","authors":"Dafa Li","doi":"10.26421/qic23.5-6-3","DOIUrl":null,"url":null,"abstract":"In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et al. obtained a finite yet systematic classification of multi-particle entanglement. It is well known that under SLOCC, pure states of three (four) qubits are partitioned into six (nine) families. Ac\\'{\\i}n et al. proposed the generalized Schmidt decomposition for three qubits and partitioned pure states of three qubits into five types. In this paper,we present a LU invariant and an entanglement measures for the GHZ SLOCC class of three qubits, and partition states of the GHZ SLOCC class of three qubits into ten families and each family into two subfamilies under LU. We give a necessary and sufficient condition for the uniqueness of the generalized Schmidt decomposition for the GHZ SLOCC class.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"40 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Partition GHZ SLOCC class of three qubits into ten families under LU\",\"authors\":\"Dafa Li\",\"doi\":\"10.26421/qic23.5-6-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et al. obtained a finite yet systematic classification of multi-particle entanglement. It is well known that under SLOCC, pure states of three (four) qubits are partitioned into six (nine) families. Ac\\\\'{\\\\i}n et al. proposed the generalized Schmidt decomposition for three qubits and partitioned pure states of three qubits into five types. In this paper,we present a LU invariant and an entanglement measures for the GHZ SLOCC class of three qubits, and partition states of the GHZ SLOCC class of three qubits into ten families and each family into two subfamilies under LU. We give a necessary and sufficient condition for the uniqueness of the generalized Schmidt decomposition for the GHZ SLOCC class.\",\"PeriodicalId\":54524,\"journal\":{\"name\":\"Quantum Information & Computation\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Information & Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26421/qic23.5-6-3\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information & Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26421/qic23.5-6-3","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

摘要

在[Science 340:1205，(2013)]中，Michael Walter等人通过纠缠多面体获得了多粒子纠缠的有限而系统的分类。众所周知，在SLOCC下，三(四个)量子比特的纯态被划分为六(九个)族。Ac\ {\i}n等人提出了三个量子比特的广义Schmidt分解，并将三个量子比特的纯态划分为五种类型。本文给出了三个量子比特的GHZ SLOCC类的LU不变量和纠缠度量，并在LU下将三个量子比特的GHZ SLOCC类的状态划分为十个族，每个族又划分为两个子族。给出了GHZ SLOCC类广义Schmidt分解唯一性的一个充分必要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Partition GHZ SLOCC class of three qubits into ten families under LU

In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et al. obtained a finite yet systematic classification of multi-particle entanglement. It is well known that under SLOCC, pure states of three (four) qubits are partitioned into six (nine) families. Ac\'{\i}n et al. proposed the generalized Schmidt decomposition for three qubits and partitioned pure states of three qubits into five types. In this paper,we present a LU invariant and an entanglement measures for the GHZ SLOCC class of three qubits, and partition states of the GHZ SLOCC class of three qubits into ten families and each family into two subfamilies under LU. We give a necessary and sufficient condition for the uniqueness of the generalized Schmidt decomposition for the GHZ SLOCC class.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Quantum Information & Computation 物理-计算机：理论方法

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

3.3 months

期刊介绍： Quantum Information & Computation provides a forum for distribution of information in all areas of quantum information processing. Original articles, survey articles, reviews, tutorials, perspectives, and correspondences are all welcome. Computer science, physics and mathematics are covered. Both theory and experiments are included. Illustrative subjects include quantum algorithms, quantum information theory, quantum complexity theory, quantum cryptology, quantum communication and measurements, proposals and experiments on the implementation of quantum computation, communications, and entanglement in all areas of science including ion traps, cavity QED, photons, nuclear magnetic resonance, and solid-state proposals.