发布求助
文献互助 智能选刊 最新文献

Proceedings of the Steklov Institute of Mathematics最新文献

筛选
英文 中文
Generating Quantum Channels 生成量子通道
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010085
R. N. Gumerov, R. L. Khazhin
{"title":"Generating Quantum Channels","authors":"R. N. Gumerov, R. L. Khazhin","doi":"10.1134/s0081543824010085","DOIUrl":"https://doi.org/10.1134/s0081543824010085","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For composite quantum systems, we consider quantum channels that uniquely determine the channels of the subsystems. Such channels of composite systems are called generating channels. Examples of generating channels are given by tensor products of two quantum channels of subsystems and their convex combinations. The paper deals with the properties of generating channels. In particular, we show that these channels form a convex compact set in the norm topology. We prove a criterion for a quantum channel to be generating. For composite systems consisting of two qubits, we construct generating phase-damping channels. For subsystems, these channels generate both phase-damping channels and depolarizing channels. Examples of nongenerating phase-damping channels are also presented. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kinetic State and Emergence of Markovian Dynamics in Exactly Solvable Models of Open Quantum Systems 开放量子系统精确可解模型中的动力学状态和马尔可夫动力学的出现
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010188
A. S. Trushechkin
{"title":"Kinetic State and Emergence of Markovian Dynamics in Exactly Solvable Models of Open Quantum Systems","authors":"A. S. Trushechkin","doi":"10.1134/s0081543824010188","DOIUrl":"https://doi.org/10.1134/s0081543824010188","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Typically, the theory of open quantum systems studies the dynamics of the reduced state (density operator) of the system. However, in the early stages of evolution, it is impossible to separate the reservoir dynamics from the system dynamics. Among the consequences of this fact is the violation of the positivity of solutions of some quantum master equations for the reduced density operator. In this paper we study the joint dynamics of the system and reservoir at an early stage of evolution and the pre-relaxation of the joint state to a so-called kinetic state. A kinetic state of the system and reservoir is characterized by the fact that it is completely determined by the reduced density operator of the system alone. Only after the formation of a kinetic state, it becomes possible to describe the evolution of the reduced density operator of the system in terms of a semigroup. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Time-Dependent Projectors and a Generalization of the Thermodynamical Approach in the Theory of Open Quantum Systems 论开放量子系统理论中的时变投影器和热力学方法的一般化
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010140
Kh. Sh. Meretukov, A. E. Teretenkov
{"title":"On Time-Dependent Projectors and a Generalization of the Thermodynamical Approach in the Theory of Open Quantum Systems","authors":"Kh. Sh. Meretukov, A. E. Teretenkov","doi":"10.1134/s0081543824010140","DOIUrl":"https://doi.org/10.1134/s0081543824010140","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We develop a consistent perturbative technique for obtaining a time-local linear master equation based on projection methods in the case where the projection operator depends on time. Then we introduce a generalization of the Kawasaki–Gunton projection operator, which allows us to use this technique to derive, generally speaking, nonlinear master equations in the case of arbitrary ansatzes consistent with some set of observables. Most of the results obtained are of a very general nature, but when discussing them, we put emphasis on the application of these results to the theory of open quantum systems. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Structure of Postselective Transformations of Quantum States 论量子态后选择转变的结构
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010139
D. A. Kronberg
{"title":"On the Structure of Postselective Transformations of Quantum States","authors":"D. A. Kronberg","doi":"10.1134/s0081543824010139","DOIUrl":"https://doi.org/10.1134/s0081543824010139","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the properties of postselective transformations of quantum states, that is, transformations for which some classical results are declared “successful” while the rest are discarded. We demonstrate that for every postselective transformation there exists a distinguished orthonormal basis for which the transformation reduces to probabilistic blocking of the basis states followed by a deterministic transformation. We also describe a generalization of an arbitrary postselective transformation that corresponds to its partial version with a given success probability. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uncertainty Relations for Coherence Quantifiers of the Tsallis Type 查里斯类型相干量词的不确定性关系
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010176
A. E. Rastegin
{"title":"Uncertainty Relations for Coherence Quantifiers of the Tsallis Type","authors":"A. E. Rastegin","doi":"10.1134/s0081543824010176","DOIUrl":"https://doi.org/10.1134/s0081543824010176","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In quantum information theory, one needs to consider systems with incomplete information. To estimate a quantum system as an information resource, one uses various characteristics of non-classical correlations. Currently, much attention is paid to coherence quantifiers averaged over a set of specially selected states. In particular, mutually unbiased bases, symmetric informationally complete measurements, and some of their generalizations are of importance in this regard. The aim of the present study is to derive uncertainty relations for coherence quantifiers based on divergences of the Tsallis type. The obtained inequalities concern quantifiers averaged over a set of mutually unbiased bases and a set of states that form an equiangular tight frame. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Propagation of Branching Random Walk on Periodic Graphs 周期图上分支随机漫步的传播
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010073
E. Vl. Bulinskaya
{"title":"Propagation of Branching Random Walk on Periodic Graphs","authors":"E. Vl. Bulinskaya","doi":"10.1134/s0081543824010073","DOIUrl":"https://doi.org/10.1134/s0081543824010073","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A model of a branching random walk on <span>(mathbb Z^d)</span> with a periodic set of sources of reproduction and death of particles is studied. For this model, an asymptotic description of the propagation of the population of particles with time is obtained for the first time. The intensities of the sources may be different. The branching regime is assumed to be supercritical, and the tails of the jump distribution of the walk are assumed to be “light.” The main theorem establishes the Hausdorff-metric convergence of the properly normalized random cloud of particles that exist in the branching random walk at time <span>(t)</span> to the limit set, as <span>(t)</span> tends to infinity. This convergence takes place for almost all elementary outcomes of the event meaning nondegeneracy of the population of particles under study. The limit set in <span>(mathbb R^d)</span>, called the asymptotic shape of the population, is found in an explicit form. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Using and Optimizing Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System 使用并优化 Qutrit 系统随时间变化的退相干率和相干控制
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010152
Oleg V. Morzhin, Alexander N. Pechen
{"title":"Using and Optimizing Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System","authors":"Oleg V. Morzhin, Alexander N. Pechen","doi":"10.1134/s0081543824010152","DOIUrl":"https://doi.org/10.1134/s0081543824010152","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider an open qutrit system in which the evolution of the density matrix <span>(rho(t))</span> is governed by the Gorini–Kossakowski–Sudarshan–Lindblad master equation with simultaneous coherent (in the Hamiltonian) and incoherent (in the dissipation superoperator) controls. To control the qutrit, we propose to use not only coherent control but also generally time-dependent decoherence rates which are adjusted by the so-called incoherent control. In our approach, the incoherent control makes the decoherence rates time-dependent in a specific controlled manner and within a clear physical mechanism. We consider the problem of maximizing the Hilbert–Schmidt overlap between the final state <span>(rho(T))</span> of the system and a given target state <span>(rho_{text{target}})</span>, as well as the problem of minimizing the squared Hilbert–Schmidt distance between these states. For both problems, we perform their realifications, derive the corresponding Pontryagin functions, adjoint systems (with two variants of transversality conditions for the two terminal objectives), and gradients of the objectives, and adapt the one-, two-, and three-step gradient projection methods. For the problem of maximizing the overlap, we also adapt the regularized first-order Krotov method. In the numerical experiments, we analyze first the operation of the methods and second the obtained control processes, in respect of considering the environment as a resource via incoherent control. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Set of Basis Functions Generated by Pearson Type IV Distributions and Its Application to Problems of Statistical Data Analysis and Quantum Mechanics 皮尔逊 IV 型分布生成的基函数集及其在统计数据分析和量子力学问题中的应用
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010061
Yu. I. Bogdanov, N. A. Bogdanova, V. F. Lukichev
{"title":"The Set of Basis Functions Generated by Pearson Type IV Distributions and Its Application to Problems of Statistical Data Analysis and Quantum Mechanics","authors":"Yu. I. Bogdanov, N. A. Bogdanova, V. F. Lukichev","doi":"10.1134/s0081543824010061","DOIUrl":"https://doi.org/10.1134/s0081543824010061","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Using an example of Pearson type IV distributions, we propose a procedure of completing the classical probability distribution to a quantum state. We obtain a wave function corresponding to Pearson type IV distributions and construct the corresponding set of basis functions. Then we demonstrate how the developed method applies to problems of statistical data analysis and quantum mechanics, and show the efficiency of our approach for the problem of approximating statistical distributions with heavy tails. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Arveson’s Extension Theorem for Conditionally Unital Completely Positive Maps 有条件单元完全正映射的阿维森扩展定理
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010218
Vsevolod I. Yashin
{"title":"Arveson’s Extension Theorem for Conditionally Unital Completely Positive Maps","authors":"Vsevolod I. Yashin","doi":"10.1134/s0081543824010218","DOIUrl":"https://doi.org/10.1134/s0081543824010218","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Conditionally unital completely positive maps are used to characterize generators of unital completely positive semigroups on <span>(C^*)</span>-algebras. In this work, a generalization of this notion is proposed that includes maps between different operator systems. In terms of this generalization, conditionally unital completely positive maps are infinitesimal increments of unital completely positive maps. The basic properties of conditionally unital completely positive maps are studied, the Choi–Jamiołkowski duality is established, and an Arveson-type extension theorem for completely bounded conditionally unital completely positive maps is proved in the case of maps with values in finite-dimensional <span>(C^*)</span>-algebras. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Continuity of Operator Functions in the Topology of Local Convergence in Measure 测度局部收敛拓扑中算子函数的连续性
IF 0.5 4区 数学
Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s008154382401005x
A. M. Bikchentaev, O. E. Tikhonov
{"title":"Continuity of Operator Functions in the Topology of Local Convergence in Measure","authors":"A. M. Bikchentaev, O. E. Tikhonov","doi":"10.1134/s008154382401005x","DOIUrl":"https://doi.org/10.1134/s008154382401005x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Let a von Neumann algebra <span>(mathcal M)</span> of operators act on a Hilbert space <span>(mathcal{H})</span>, and let <span>(tau)</span> be a faithful normal semifinite trace on <span>(mathcal M)</span>. Let <span>(t_{tautext{l}})</span> be the topology of <span>(tau)</span>-local convergence in measure on the *-algebra <span>(S(mathcal M,tau))</span> of all <span>(tau)</span>-measurable operators. We prove the <span>(t_{tautext{l}})</span>-continuity of the involution on the set of all normal operators in <span>(S(mathcal M,tau))</span>, investigate the <span>(t_{tautext{l}})</span>-continuity of operator functions on <span>(S(mathcal M,tau))</span>, and show that the map <span>(Amapsto |A|)</span> is <span>(t_{tautext{l}})</span>-continuous on the set of all partial isometries in <span>(mathcal M)</span>. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
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
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
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