混合态量子异常与多部纠缠

IF 15.7 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Leonardo A. Lessa, Meng Cheng, Chong Wang
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More specifically, we consider lattice systems in d</a:mi></a:math> space dimensions with anomalous symmetry <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi>G</c:mi></c:math> where the anomaly is characterized by an invariant in the group cohomology <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:msup><e:mi>H</e:mi><e:mrow><e:mi>d</e:mi><e:mo>+</e:mo><e:mn>2</e:mn></e:mrow></e:msup><e:mo stretchy=\"false\">[</e:mo><e:mi>G</e:mi><e:mo>,</e:mo><e:mi>U</e:mi><e:mo stretchy=\"false\">(</e:mo><e:mn>1</e:mn><e:mo stretchy=\"false\">)</e:mo><e:mo stretchy=\"false\">]</e:mo></e:math>. 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Namely, such states are not symmetrically invertible and not gapped Markovian, generalizing familiar properties of anomalous pure states. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"209 1","pages":""},"PeriodicalIF":15.7000,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mixed-State Quantum Anomaly and Multipartite Entanglement\",\"authors\":\"Leonardo A. Lessa, Meng Cheng, Chong Wang\",\"doi\":\"10.1103/physrevx.15.011069\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. 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引用次数: 0

摘要

多体态的量子纠缠测量在表征物质的相位方面越来越有用。在这里,我们探索了混合态纠缠和t Hooft异常之间令人惊讶的联系。更具体地说,我们考虑d空间维度中具有异常对称G的晶格系统,其中异常以群上同调Hd+2中的不变量为特征[G,U(1)]。我们证明了在G下强对称的任何混合态ρ,即ρ∝ρ必然是(d+2)-不可分的,即不是Hilbert空间中d+2态张量积的混合。此外,这些态不能由任何(d+2)可分态利用有限深度局域量子通道制备,因此不可分性本质上是长程的。我们在d≤1条件下证明了这些结果,并在d>;1条件下给出了似是而非的论证。因此,异常-不可分性连接允许我们生成具有非平凡远程多部纠缠的混合状态的简单示例。特别地,在d=1中,我们发现了一个量子相的例子,在这个意义上,这个相位的状态不能通过有限深度的局部量子通道与任何纯态双向连接。我们还分析了一个混合异常,包括强对称性和弱对称性,包括受Lieb-Schultz-Mattis型异常约束的系统。我们发现,虽然强弱混合异常通常不约束量子纠缠,但它确实以非平凡的方式约束混合态的远程关联。也就是说,这样的状态不是对称可逆的,也不是间隙马尔可夫的,推广了反常纯态的熟悉性质。2025年由美国物理学会出版
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mixed-State Quantum Anomaly and Multipartite Entanglement
Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. Here, we explore a surprising connection between mixed-state entanglement and ’t Hooft anomaly. More specifically, we consider lattice systems in d space dimensions with anomalous symmetry G where the anomaly is characterized by an invariant in the group cohomology Hd+2[G,U(1)]. We show that any mixed state ρ that is strongly symmetric under G, in the sense that Gρρ is necessarily (d+2)-nonseparable, i.e., is not the mixture of tensor products of d+2 states in the Hilbert space. Furthermore, such states cannot be prepared from any (d+2)-separable states using finite-depth local quantum channels, so the nonseparability is long-ranged in nature. We provide proof of these results in d1 and plausibility arguments in d>1. The anomaly-nonseparability connection, thus, allows us to generate simple examples of mixed states with nontrivial long-ranged multipartite entanglement. In particular, in d=1 we find an example of quantum phase, in the sense that states in this phase cannot be two-way connected to any pure state through finite-depth local quantum channels. We also analyze a mixed anomaly involving both strong and weak symmetries, including systems constrained by the Lieb-Schultz-Mattis type of anomaly. We find that, while strong-weak mixed anomaly, in general, does not constrain quantum entanglement, it does constrain long-range correlations of mixed states in nontrivial ways. Namely, such states are not symmetrically invertible and not gapped Markovian, generalizing familiar properties of anomalous pure states. Published by the American Physical Society 2025
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来源期刊
Physical Review X
Physical Review X PHYSICS, MULTIDISCIPLINARY-
CiteScore
24.60
自引率
1.60%
发文量
197
审稿时长
3 months
期刊介绍: Physical Review X (PRX) stands as an exclusively online, fully open-access journal, emphasizing innovation, quality, and enduring impact in the scientific content it disseminates. Devoted to showcasing a curated selection of papers from pure, applied, and interdisciplinary physics, PRX aims to feature work with the potential to shape current and future research while leaving a lasting and profound impact in their respective fields. Encompassing the entire spectrum of physics subject areas, PRX places a special focus on groundbreaking interdisciplinary research with broad-reaching influence.
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