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Physical Review A 2023年第4期108卷 042620-042620页

作者： Sohail Arun K. Pati Vijeth Aradhya Indranil Chakrabarty Subhasree Patro Quantum Information and Computation Group Harish-Chandra Research Institute A CI of Homi Bhabha National Institute Chhatnag Road Jhunsi Prayagraj 211019 India Centre for Quantum Science and Technology International Institute of Information Technology Hyderabad Gachibowli Hyderabad-500032 Telangana India Center for Security Theory and Algorithmic Research International Institute of Information Technology Hyderabad Gachibowli Hyderabad-500032 Telangana India Department of Computer Science National University of Singapore 117417 Singapore Computer science and physics department Utrecht University 3584 CS Utrecht The Netherlands Algorithms and complexity group QuSoft Centrum Wiskunde and Informatica 1098XG Amsterdam The Netherlands

We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a smaller number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a nonmaximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's laboratory in terms of the composition of the completely positive maps corresponding to the shared resource state and a joint positive operator-valued measure (POVM) performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is perfectly possible with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with Werner states and show that even when Werner states become separable, the amount of teleported coherence is nonzero, implying the possibility of teleportation of coherence without entanglement.

关键词： Quantum coherence & coherence measures Quantum communication Quantum correlations in quantum information Quantum information theory Quantum protocols

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Input-to-state stabilization for a 2 × 2 hyperbolic system cascaded with an ODE

Input-to-state stabilization for a 2 × 2 hyperbolic system ...

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Youth Academic Annual Conference of Chinese Association of Automation (YAC)

作者： Han-Wen Zhang Jun-Min Wang Jing Wang School of Automation and Software Engineering Shanxi University Taiyuan Shanxi China School of Mathematics and Statistics & Key Laboratory of Mathematical Theory and Computation in Information Security Beijing Institute of Technology Beijing China Delft Institute of Applied Mathematics Delft University of Technology Mekelweg 4 Delft Netherlands

ISBN: (纸本)9781665465373

The paper deals with the input-to-state stabilization for the 2×2 system of first-order hyperbolic equations, which convect in opposite directions cascaded with an unstable ODE equation. First, an inverse backstepping transformation is introduced to obtain a target system. Then, by active disturbance rejection control (ADRC) method, the disturbance is estimated via a disturbance estimator with time-varying gain. When the unmatched disturbances are absent, the disturbance estimator is exponentially convergent to the matched disturbance. Furthermore, in order to reject the matched disturbance and obtain the input-to-state stability of the system, the controller is proposed by using the disturbance estimator. Finally, numerical simulations are presented to validate theoretical results.

关键词： Robust control Backstepping Automation Numerical simulation Control systems Mathematical models Stability analysis

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Impossibility of cloning of quantum coherence

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Physical Review A 2021年第2期103卷 022422-022422页

作者： Dhrumil Patel Subhasree Patro Chiranjeevi Vanarasa Indranil Chakrabarty Arun Kumar Pati Department of Computer Science and Engineering Louisiana State University Baton Rouge 70803 LA United States QuSoft CWI Amsterdam and University of Amsterdam Amsterdam 1098 XG Netherlands Center for Security Theory and Algorithmic Research International Institute of Information Technology-Hyderabad Gachibowli Telangana 500032 India Center for Security Theory and Algorithmic Research International Institute of Information Technology-Hyderabad Gachibowli Telangana 500032 India Quantum Information and Computation Group Harish-Chandra Research Institute HBNI Allahabad 211019 India

It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no cloning of quantum coherence. Here, in this article, we show that it is impossible to clone the coherence of an arbitrary quantum state. In particular, with an ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which coherence cloning will be possible for a given choice of machine. Furthermore, we find the maximum range of states whose coherence can be cloned perfectly. The impossibility proof also holds when we do not include machine states. Lastly, we generalize the impossibility of cloning of coherence in terms of dimension of the quantum state and coherence measure taken into consideration.

关键词： Quantum coherence & coherence measures Quantum information processing

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Observer Design for a Reaction-Diffusion Equation with Delayed Boundary Measurement

Observer Design for a Reaction-Diffusion Equation with Delay...

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International Conference on Control and Robots (ICCR)

作者： Jing Zhang Wen Kang School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing China Shunde Innovation School University of Science and Technology Beijing Foshan China MIIT Key Laboratory of Mathematical Theory and Computation in Information Security School of Mathematics and Statistics Beijing Institute of Technology Beijing China

This paper addresses the problem of observer design for a reaction-diffusion equation with delayed boundary measurement. The predictor method is employed for the delay compensation. The reaction coefficient of the plant is considered, which may lead to the instability. To obtain the stability result, the backstepping transformation is introduced to determine the observer gains. Linear matrix inequalities (LMIs) conditions are derived to guarantee the exponential stability of the error system. The numerical simulation is provided to validate the proposed results.

关键词： Backstepping Observers Numerical simulation Mathematical models Stability analysis Delays Linear matrix inequalities

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Graded dimensions and monomial bases for the cyclotomic quiver hecke superalgebras

arXiv

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arXiv 2021年

作者： Hu, Jun Shi, Lei MIIT Key Laboratory of Mathematical Theory and Computation in Information Security Beijing Institute of Technology Beijing102488 China School of Mathematical and Statistics Beijing Institute of Technology Beijing100081 China

MSC Codes 20C08In this paper we derive a closed formula for the (Z × Z2)-graded dimension of the cyclotomic quiver Hecke superalgebra RΛ(β) associated to an arbitrary Cartan superdatum (A, P, Π, Π∨), polynomials (Qi,j(x1, x2))i,j∈I, β ∈ Q+n and Λ ∈ P +. As applications, we obtain a necessary and sufficient condition for which e(ν) 6= 0 in RΛ(β). We construct an explicit monomial basis for the bi-weight space e(νe)RΛ(β)e(νe), where νe is a certain specific ntuple defined in (1.4). In particular, this gives rise to a monomial basis for the cyclotomic odd nilHecke algebra. Finally, we consider the case when β = α1 +α2 +· · ·+αn with α1, · · ·, αn distinct. We construct an explicit monomial basis of RΛ(β) and show that it is indecomposable in this case. Copyright © 2021, The Authors. All rights reserved.

关键词： Algebra

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Teleportation of quantum coherence

arXiv

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arXiv 2023年

作者： Sohail Pati, Arun K. Aradhya, Vijeth Chakrabarty, Indranil Patro, Subhasree Quantum Information and Computation Group Harish-Chandra Research Institute A CI of Homi Bhabha National Institute Chhatnag Road Jhunsi Prayagraj211019 India Centre for Quantum Science and Technology International Institute of Information Technology-Hyderabad Gachibowli Hyderabad India Center for Security Theory and Algorithmic Research International Institute of Information Technology-Hyderabad Gachibowli Hyderabad India Department of Computer Science National University of Singapore 117417 Singapore Utrecht University Utrecht3584 CS Netherlands QuSoft Centrum Wiskunde & Informatica Amsterdam1098 XG Netherlands

We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a lesser number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a non-maximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob’s lab in terms of the composition of the completely positive maps corresponding to the shared resource state and joint POVM performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is possible perfectly with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with the Werner states and show that even when the Werner states become separable, the amount of teleported coherence is non-zero, implying the possibility of teleportation of coherence without entanglement. Copyright © 2023, The Authors. All rights reserved.

关键词： Qubits

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Optimization Models and Interpretations for Three Types of Adversarial Perturbations against Support Vector Machines

arXiv

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arXiv 2022年

作者： Su, Wen Li, Qingna Cui, Chunfeng School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Key Laboratory of Mathematical Theory and Computation in Information Security Beijing Institute of Technology Beijing100081 China The Ministry of Education School of Mathematical Sciences Beihang University 100191 China

Adversarial perturbations have drawn great attentions in various deep neural networks. Most of them are computed by iterations and cannot be interpreted very well. In contrast, little attentions are paid to basic machine learning models such as support vector machines. In this paper, we investigate the optimization models and the interpretations for three types of adversarial perturbations against support vector machines, including sample-adversarial perturbations (sAP), class-universal adversarial perturbations (cuAP) as well as universal adversarial perturbations (uAP). For linear binary/multi classification support vector machines (SVMs), we derive the explicit solutions for sAP, cuAP and uAP (binary case), and approximate solution for uAP of multi-classification. We also obtain the upper bound of fooling rate for uAP. Such results not only increase the interpretability of the three adversarial perturbations, but also provide great convenience in computation since iterative process can be avoided. Numerical results show that our method is fast and effective in calculating three types of adversarial perturbations. Copyright © 2022, The Authors. All rights reserved.

关键词： Support vector machines

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ON THE DECAY PROPERTY OF THE CUBIC FOURTH-ORDER SCHRÖDINGER EQUATION

arXiv

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arXiv 2022年

作者： Yu, Xueying Yue, Haitian Zhao, Zehua Department of Mathematics University of Washington C138 Padelford Hall Box 354350 SeattleWA98195 United States Institute of Mathematical Sciences ShanghaiTech University Pudong Shanghai China Department of Mathematics and Statistics Beijing Institute of Technology MIIT Key Laboratory of Mathematical Theory and Computation in Information Security Beijing China

In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on d (5 ≤ d ≤ 8) enjoys the same (pointwise) decay property as its linear solution does. This result is proved via a bootstrap argument based on the corresponding global result Pausader [24]. This result can be extended to more general dispersive equations (including some more 4NLS models) with scattering asymptotics. Copyright © 2022, The Authors. All rights reserved.

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Corrigendum to “Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras” [J. Pure Appl. Algebra 227(4) (2023) 107281]

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Journal of Pure and Applied Algebra 2025年第6期229卷

作者： Zhekun He Jun Hu Huang Lin School of Mathematics and Statistics Beijing Institute of Technology Beijing 100081 PR China MIIT Key Laboratory of Mathematical Theory and Computation in Information Security School of Mathematics and Statistics Beijing Institute of Technology Beijing 100081 PR China

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ON DECAYING PROPERTIES OF NONLINEAR SCHRÖDINGER EQUATIONS

arXiv

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arXiv 2022年

作者： Fan, Chenjie Staffilani, Gigliola Zhao, Zehua Academy of Mathematics and Systems Science Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences Beijing China Department of Mathematics Massachusetts Institute of Technology CambridgeMA02139 United States Department of Mathematics and Statistics Beijing Institute of Technology Beijing China MIIT Key Laboratory of Mathematical Theory and Computation in Information Security Beijing China

In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schrödinger equation with various initial data, deterministic and random. We show that nonlinear solutions enjoy the same decay rate as the linear ones. The regularity assumption on the initial data is much lower than in previous results (see [20] and the references therein) and moreover we quantify the decay, which is another novelty of this work. Furthermore, we show that the (physical) randomization of the initial data can be used to replace the L1-data assumption (see [23] for the necessity of the L1-data assumption). At last, we note that this method can be also applied to derive decay estimates for other nonlinear dispersive equations. Copyright © 2022, The Authors. All rights reserved.

关键词： Nonlinear equations

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