Unsupervised state learning from pairs of states

Pranjal Agarwal, Nada Ali, Camilla Polvara, Martin Isbjörn Trappe, Berthold-Georg Englert, Mark Hillery
{"title":"Unsupervised state learning from pairs of states","authors":"Pranjal Agarwal, Nada Ali, Camilla Polvara, Martin Isbjörn Trappe, Berthold-Georg Englert, Mark Hillery","doi":"arxiv-2409.11120","DOIUrl":null,"url":null,"abstract":"Suppose you receive a sequence of qubits where each qubit is guaranteed to be\nin one of two pure states, but you do not know what those states are. Your task\nis to either determine the states or to construct a POVM (Positive Operator\nValued Measure) that will discriminate them. This can be viewed as a quantum\nanalog of unsupervised learning. A problem is that without more information,\nall that can be determined is the density matrix of the sequence, and, in\ngeneral, density matrices can be decomposed into pure states in many different\nways. To solve the problem additional information, either classical or quantum,\nis required. We show that if an additional copy of each qubit is supplied, that\nis, one receives pairs of qubits, both in the same state, rather than single\nqubits, the task can be accomplished. We then simulate numerically the\nmeasurement of a sequence of qubit pairs and show that the unknown states and\ntheir respective probabilities of occurrence can be found with high accuracy.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11120","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to either determine the states or to construct a POVM (Positive Operator Valued Measure) that will discriminate them. This can be viewed as a quantum analog of unsupervised learning. A problem is that without more information, all that can be determined is the density matrix of the sequence, and, in general, density matrices can be decomposed into pure states in many different ways. To solve the problem additional information, either classical or quantum, is required. We show that if an additional copy of each qubit is supplied, that is, one receives pairs of qubits, both in the same state, rather than single qubits, the task can be accomplished. We then simulate numerically the measurement of a sequence of qubit pairs and show that the unknown states and their respective probabilities of occurrence can be found with high accuracy.
从成对状态中进行无监督状态学习
假设你接收到一个量子比特序列,其中每个量子比特都保证处于两种纯粹状态之一,但你不知道这些状态是什么。你的任务要么是确定这些状态,要么是构建一个能够区分它们的 POVM(正向运算符值测量)。这可以看作是无监督学习的一个量表。问题在于,如果没有更多信息,所能确定的只是序列的密度矩阵,而一般来说,密度矩阵可以通过多种不同方式分解为纯状态。要解决这个问题,需要额外的信息,无论是经典信息还是量子信息。我们的研究表明,如果提供每个量子比特的额外拷贝,即接收成对处于相同状态的量子比特,而不是单个量子比特,就可以完成任务。然后,我们用数字模拟了一串量子比特对的测量主题,并证明可以高精度地找到未知状态及其各自的出现概率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信