连续变量系统中总和不确定关系和量子纠缠的层析方法

Soumyabrata Paul, S. Lakshmibala, V. Balakrishnan, S. Ramanan
{"title":"连续变量系统中总和不确定关系和量子纠缠的层析方法","authors":"Soumyabrata Paul, S. Lakshmibala, V. Balakrishnan, S. Ramanan","doi":"10.3389/frqst.2023.1131798","DOIUrl":null,"url":null,"abstract":"Entropic uncertainty relations (EURs) have been examined in various contexts, primarily in qubit systems, including their links with entanglement, as they subsume the Heisenberg uncertainty principle. With their genesis in the Shannon entropy, EURs find applications in quantum information and quantum optics. EURs are state-dependent, and the state has to be reconstructed from tomograms (which are histograms readily available from experiments). This is a challenge when the Hilbert space is large, as in continuous variable (CV) systems and certain hybrid quantum (HQ) systems. A viable alternative approach therefore is to extract as much information as possible about the unknown quantum state directly from appropriate tomograms. Many variants of EURs can be extracted from tomograms, even for CV systems. In earlier work we have defined many tomographic entanglement indicators (TEIs) that can be readily calculated from tomograms without knowledge of the density matrix, and have reported on their efficacy as entanglement indicators in various contexts in both CV and HQ systems. The specific objectives of the present work are as follows: (i) To use the tomographic approach to investigate the links between EURs and TEIs in CV and HQ systems as they evolve in time. (ii) To identify the TEI that most closely tracks the temporal evolution of EURs. We consider two generic systems. The first is a multilevel atom modeled as a nonlinear oscillator interacting with a quantized radiation field. The second is the Λ-atom interacting with two radiation fields. The former model accomodates investigations on the role of the initial state of the field and the ratio of the strengths of interaction and nonlinearity in the connection between TEIs and EURs. The second model opens up the possibility of examining the connection between mixed state bipartite entanglement and EURs, when the number of atomic levels is finite. Since the tomogram respects the requirements of classical probability theory, this effort also sheds light on the extent to which TEIs reflect the temporal behaviour of those EURs which are rooted in the Shannon entropy.","PeriodicalId":108649,"journal":{"name":"Frontiers in Quantum Science and Technology","volume":"08 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A tomographic approach to the sum uncertainty relation and quantum entanglement in continuous variable systems\",\"authors\":\"Soumyabrata Paul, S. Lakshmibala, V. Balakrishnan, S. Ramanan\",\"doi\":\"10.3389/frqst.2023.1131798\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Entropic uncertainty relations (EURs) have been examined in various contexts, primarily in qubit systems, including their links with entanglement, as they subsume the Heisenberg uncertainty principle. With their genesis in the Shannon entropy, EURs find applications in quantum information and quantum optics. EURs are state-dependent, and the state has to be reconstructed from tomograms (which are histograms readily available from experiments). This is a challenge when the Hilbert space is large, as in continuous variable (CV) systems and certain hybrid quantum (HQ) systems. A viable alternative approach therefore is to extract as much information as possible about the unknown quantum state directly from appropriate tomograms. Many variants of EURs can be extracted from tomograms, even for CV systems. In earlier work we have defined many tomographic entanglement indicators (TEIs) that can be readily calculated from tomograms without knowledge of the density matrix, and have reported on their efficacy as entanglement indicators in various contexts in both CV and HQ systems. The specific objectives of the present work are as follows: (i) To use the tomographic approach to investigate the links between EURs and TEIs in CV and HQ systems as they evolve in time. (ii) To identify the TEI that most closely tracks the temporal evolution of EURs. We consider two generic systems. The first is a multilevel atom modeled as a nonlinear oscillator interacting with a quantized radiation field. The second is the Λ-atom interacting with two radiation fields. The former model accomodates investigations on the role of the initial state of the field and the ratio of the strengths of interaction and nonlinearity in the connection between TEIs and EURs. The second model opens up the possibility of examining the connection between mixed state bipartite entanglement and EURs, when the number of atomic levels is finite. Since the tomogram respects the requirements of classical probability theory, this effort also sheds light on the extent to which TEIs reflect the temporal behaviour of those EURs which are rooted in the Shannon entropy.\",\"PeriodicalId\":108649,\"journal\":{\"name\":\"Frontiers in Quantum Science and Technology\",\"volume\":\"08 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Frontiers in Quantum Science and Technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3389/frqst.2023.1131798\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Frontiers in Quantum Science and Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3389/frqst.2023.1131798","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

熵不确定性关系(EURs)已经在各种背景下进行了研究,主要是在量子位系统中,包括它们与纠缠的联系,因为它们包含了海森堡的不确定性原理。由于它们起源于香农熵,EURs在量子信息和量子光学中得到了应用。EURs是状态依赖的,并且状态必须从断层图(从实验中容易获得的直方图)中重建。当希尔伯特空间很大时,如在连续变量(CV)系统和某些混合量子(HQ)系统中,这是一个挑战。因此,一种可行的替代方法是直接从适当的层析图中提取尽可能多的关于未知量子态的信息。许多变体的EURs可以从层析图中提取,即使是CV系统。在早期的工作中,我们已经定义了许多层析缠结指标(TEIs),这些指标可以在不知道密度矩阵的情况下很容易地从层析图中计算出来,并报道了它们在CV和HQ系统的各种情况下作为缠结指标的功效。当前工作的具体目标如下:(i)使用层析成像方法调查CV和HQ系统中eur和tei之间的联系,因为它们随时间发展。(ii)找出最能密切追踪欧元时间演变的技术指标。我们考虑两个一般系统。第一种是将多能级原子建模为与量子化辐射场相互作用的非线性振荡器。第二个是Λ-atom与两个辐射场相互作用。前一种模型考虑了场初始状态的作用,以及tei和eur之间的相互作用强度和非线性的比值。当原子能级数量有限时,第二个模型开启了检验混合态二部纠缠和EURs之间联系的可能性。由于层析图尊重经典概率论的要求,这一努力也揭示了tei在多大程度上反映了那些植根于香农熵的EURs的时间行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A tomographic approach to the sum uncertainty relation and quantum entanglement in continuous variable systems
Entropic uncertainty relations (EURs) have been examined in various contexts, primarily in qubit systems, including their links with entanglement, as they subsume the Heisenberg uncertainty principle. With their genesis in the Shannon entropy, EURs find applications in quantum information and quantum optics. EURs are state-dependent, and the state has to be reconstructed from tomograms (which are histograms readily available from experiments). This is a challenge when the Hilbert space is large, as in continuous variable (CV) systems and certain hybrid quantum (HQ) systems. A viable alternative approach therefore is to extract as much information as possible about the unknown quantum state directly from appropriate tomograms. Many variants of EURs can be extracted from tomograms, even for CV systems. In earlier work we have defined many tomographic entanglement indicators (TEIs) that can be readily calculated from tomograms without knowledge of the density matrix, and have reported on their efficacy as entanglement indicators in various contexts in both CV and HQ systems. The specific objectives of the present work are as follows: (i) To use the tomographic approach to investigate the links between EURs and TEIs in CV and HQ systems as they evolve in time. (ii) To identify the TEI that most closely tracks the temporal evolution of EURs. We consider two generic systems. The first is a multilevel atom modeled as a nonlinear oscillator interacting with a quantized radiation field. The second is the Λ-atom interacting with two radiation fields. The former model accomodates investigations on the role of the initial state of the field and the ratio of the strengths of interaction and nonlinearity in the connection between TEIs and EURs. The second model opens up the possibility of examining the connection between mixed state bipartite entanglement and EURs, when the number of atomic levels is finite. Since the tomogram respects the requirements of classical probability theory, this effort also sheds light on the extent to which TEIs reflect the temporal behaviour of those EURs which are rooted in the Shannon entropy.
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
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