Jae Sung Lee, Joonhyun Yeo
In this Comment, we show that the thermal Gibbs state given in terms of a time-independent system Hamiltonian is not a steady state solution of the quantum master equation introduced by Nathan and Rudner [Phys. Rev. B 102, 115109 (2020)], in contrast to their claim.
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In a recent comment, Lee and Yeo show that the Gibbs state is not generically an exact steady state of the Universal Lindblad Equation (ULE) that we developed in Phys. Rev. B 102, 115109 (2020). This non-controversial observation is precisely as expected for open quantum systems with finite system-bath coupling, where transition rates may be comparable to or larger than the level spacing of the system, and we made no claim to the contrary in our paper. The comment by Lee and Yeo hence highlights that the ULE captures contributions to the steady state due to finite system-bath coupling that are…
Quantifying the accuracy of steady states obtained from the Universal Lindblad Equation
该研究证明通用Lindblad方程（ULE）的稳态期望值精度与有效系统-浴耦合Γ线性相关，提出近恒等准局域记忆修饰逆变换解决了ULE在守恒量电流上的相对误差问题，实现弱耦合区电流高保真计算。
We develop a Markovian master equation in the Lindblad form that enables the efficient study of a wide range of open quantum many-body systems that would be inaccessible with existing methods. The validity of the master equation is based entirely on properties of the bath and the system-bath coupling, without any requirements on the level structure within the system itself. The master equation is derived using a Markov approximation that is distinct from that used in earlier approaches. We provide a rigorous bound for the error induced by this Markov approximation; the error is controlled by a…
It is by now well understood that quantum dissipative processes can be harnessed and turned into a resource for quantum-information processing tasks. In this paper we demonstrate yet another way in which this is true by providing a dissipation-assisted protocol for the simulation of general Markovian dynamics. More precisely, we show how a suitable coherent coupling of a quantum system to a set of Markovian dissipating qubits allows one to enact an effective Liouvillian generator of any Lindbladian form. This effective dynamical generator arises from high-order virtual-dissipative processes an…
To understand typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate Markovian completely positive evolution in the space of density matrices. Spectral properties of these operators, including the shape of the spectrum in the complex plane, are evaluated by using methods of free probabilities and explained with non-Hermitian random matrix models. We also demonstrate universality of the spectral features. The notion of ensemble of random generators of Markovian qauntum evolution constitutes a step towards categorizati…
Error bounds on the universal Lindblad equation in the thermodynamic limit
针对普适 Lindblad 方程在热力学极限下的近似误差问题，本文给出局域量时间演化的严格误差界，证明在体耗散加速条件下误差于弱耦合或奇异耦合极限中消失。
Universal Dilation of Linear Itô SDEs: Quantum Trajectories and Lindblad Simulation of Second Moments
本文提出了一种在量子计算机上模拟线性伊藤随机微分方程的通用框架，通过量子轨迹和李纳布兰特方程实现高效模拟。
From the universal Lindblad equation to Boltzmann equations: in-QGP quarkonium dynamics
该研究在NRQCD和pNRQCD框架下推导通用林德布拉德方程，首次从通用林德布拉德框架得到耦合单态-八态玻尔兹曼方程，还推导了单态玻尔兹曼方程的领头量子修正，为夸克偶素输运描述建立了更系统的理论基础。
The work reported in arXiv:1311.5619v1 proposes to produce continuous-variable cluster states through relativistic motion of cavities. This proposal does not produce the states claimed by the authors. The states actually produced are in general not known to be useful for measurement-based quantum computation.
An analisys is done about the paper "Impossibility of the existence of the universal density functional" of V.B. Bobrov and S.A. Trigger considering the constrained-search reformulation of DFT.
It is very common in the literature to write down a Markovian quantum master equation in Lindblad form to describe a system with multiple degrees of freedom and weakly connected to multiple thermal baths which can, in general, be at different temperatures and chemical potentials. However, the microscopically derived quantum master equation up to leading order in system-bath coupling is of the so-called Redfield form which is known to not preserve complete positivity in most cases. Additional approximations to the Redfield equation are required to obtain a Lindblad form. We lay down some fundam…
A Lie-Jordan Geometric Formulation of Lindblad Dynamics
基于先前工作的代数框架，为有限维开放量子动力学开发李 - 约旦几何表述。识别出通用三线性耗散映射，分离通用代数结构与模型相关物理信息，给出张量和仿射几何解释。
Unfolding system-environment correlation in open quantum systems: Revisiting master equations and the Born approximation
本文提出将开放量子系统的常见主方程重新表述为含系统-浴关联算符的通用形式，揭示了主方程中隐藏的系统-环境关联信息，并证明二阶通用类Lindblad方程能更准确地捕获关联。
Solving the Lindblad equation with methods from computational fluid dynamics
本文提出使用计算流体力学中的 Kurganov-Tadmor 中心有限体积格式在位置空间数值求解 Lindblad 方程，通过基准测试验证了其在初始条件、离散化和稳定性上的效率优势，并基于对流扩散方程的重新表述提供了新的定性见解。
For discrete-time systems, governed by Kraus maps, the work of D. Petz has characterized the set of universal contraction metrics. In the present paper, we use this characterization to derive a set of quadratic Lyapunov functions for continuous-time systems, governed by Lindblad differential equations, that have a steady-state with full rank. An extremity of this set is given by the Bures metric, for which the quadratic Lyapunov function is obtained by inverting a Sylvester equation. We illustrate the method by providing a strict Lyapunov function for a Lindblad equation designed to stabilize …
Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings signific…
A mathematical justification to apply the secular approximation to the Redfield equation
本文通过数学证明，展示了世俗近似在Redfield方程中的有效性，并通过数值比较证明其比通用Lindblad方程更准确。
We present a series of arguments against the results of the paper "Universal decoherence due to gravitational time dilation" by Pikovski et al. (arXiv:1311.1095).
We present a quantum-mechanical generalization of the work penalty equation (Eq. (6) in Phys. Rev. Lett., 127, 190602 (2021)) with an alternative derivation.
We address the three points raised by the authors of the above Comment.
Universal Predictors for Mixing Time more than Liouvillian Gap
本文研究了开放量子系统混合时间的决定因素，发现不仅由李普希兹间隙决定，还受每个衰减李普希兹本征模的迹范数影响。通过利用这些作为通用预测器，建立了快速和快速混合的一般条件。具体而言，推导了强弱耗散情况下快速混合的条件，以哈密顿量和本地李普希兹算符的稀疏性约束形式呈现。研究为计算混合时间提供了通用框架，并为设计耗散以实现所需混合速度提供了指导，对高效实验态制备有重要意义。
We introduce a universal scheme to divide the power output of a periodically driven quantum heat engine into a classical contribution and one stemming solely from quantum coherence. Specializing to Lindblad-dynamics and small driving amplitudes, we derive general upper bounds on both, the coherent and the total power. These constraints imply that, in the linear-response regime, coherence inevitably leads to power losses. To illustrate our general analysis, we explicitly work out the experimentally relevant example of a single-qubit engine.
Commentary on the decomposition of universal multiport interferometers: how it works in practice
本文评述通用多端口干涉仪的分解方法，提供自洽的数学细节和实用示例，用于确定门参数并应用相位修正，以实现目标结构。
In a recent preprint arXiv:2203.15521 G. X. Chan, P. Huang, and X. Wang claim that triple-quantum dot superexchange in a (1, 0, 1) charge configuration exhibits a change of sign (going from positive to negative) as a function of middle dot detuning. Furthermore, their claim is that charge sweet-spots exist for specific values of the inter-dot detuning. Their analysis is based on the Hubbard model and something to what they refer to as the full Configuration-Interaction method. All of this findings were already reported by M. J. Rančić and G. Burkard in Ref. Phys. Rev. B 96, 201304(R) (2017) ba…
Recently Dzhafarov and Kon published the paper advertising the possibility to use the coupling technique of classical probability theory to model incompatible observables in quantum physics and quantum-like models of psychology. Here I present comments on this paper by stressing advantages and disadvantages.
Universal Dynamical Scaling of Strong-to-Weak Spontaneous Symmetry Breaking in Open Quantum Systems
研究开放量子系统中强到弱自发对称破缺的出现，发现对称性决定动力学标度而非谱隙结构，揭示了不同对称性下相关长度的指数或幂律增长。
Speeding up Lindblad dynamics via time-rescaling engineering
通过时间重缩工程加速 Lindblad 动力学，提供精确的快速马尔可夫过程，适用于量子控制与计算。
We study the scaling behavior of the relaxation dynamics to thermal equilibrium when a quantum system is near the quantum critical point. In particular, we investigate systems whose relaxation dynamics is described by a Lindblad master equation. We find that the universal scaling behavior not only exhibits in the equilibrium stage at the long-time limit, but also manifests itself in the non-equilibrium relaxation process. While the critical behavior is dictated by the low-lying energy levels of the Hamiltonian, the dissipative part in the Lindblad equation also plays important roles in two asp…
In a recent letter [Phys. Rev. Lett. 91, 220801 (2003)], V. Mkrtchian and co-workers calculated the radiation pressure force on a moving body, assuming the electromagnetic field to be at temperature $T,$ and the velocity to be much smaller than $c.$ They considered both dielectrics and conductors, and related the effect to Casimir dissipative forces. Here we claim that their approach may only apply in the Rayleigh-Ganz scattering regime, which corresponds to very small particles and/or electromagnetically rarefied media. Moreover, we argue that their interpretation in terms of the Casimir effe…
Quantum dot-based high-fidelity universal quantum gates in noisy environment
本文针对噪声环境下的量子点自旋量子比特，利用Lindblad主方程对NOT门、Hadamard门和Toffoli门的自旋动力学与噪声过程进行建模，确定了外部磁场的工作范围以实现高保真度通用量子门操作，并提供了模拟更大规模量子处理器的通用框架。
Dissipative ground state preparation in ab initio electronic structure theory
本研究提出了一种基于利恩布兰德动力学的耗散方法，用于在量子计算机上高效准备从头电子结构问题的基态，通过两种通用类型的跳跃算符实现，且不依赖变分参数。
Even if Google AI's Sycamore processor is efficient for the particular task it has been designed for it fails to deliver universal computational capacity. Furthermore, even classical devices implementing transverse homoclinic orbits realize exponential speedups with respect to universal classical as well as quantum computations. Moreover, relative to the validity of quantum mechanics, there already exist quantum oracles which violate the Church-Turing thesis.
Dissipation can be used as a resource to control and simulate quantum systems. We discuss a modular model based on fast dissipation capable of performing universal quantum computation, and simulating arbitrary Lindbladian dynamics. The model consists of a network of elementary dissipation-generated modules and it is in principle scalable. In particular, we demonstrate the ability to dissipatively prepare all single qubit gates, and the CNOT gate; prerequisites for universal quantum computing. We also show a way to implement a type of quantum memory in a dissipative environment, whereby we can …
In a recent work [D. K. Burgarth et al., Nat. Commun. 5, 5173 (2014)] it was shown that a series of frequent measurements can project the dynamics of a quantum system onto a subspace in which the dynamics can be more complex. In this subspace even full controllability can be achieved, although the controllability over the system before the projection is very poor since the control Hamiltonians commute with each other. We can also think of the opposite: any Hamiltonians of a quantum system, which are in general noncommutative with each other, can be made commutative by embedding them in an exte…
On the linear friction many-body equation for dissipative spontaneous wavefunction collapse
本文构造了用二次量子化质量密度和流表示的普适耗散Lindblad主方程，在线性摩擦假设下给出严格约束，并推导分析了Diósi-Penrose和连续自发局域化模型的耗散扩展。
Operator-space fragmentation and integrability in Pauli-Lindblad models
本研究提出算符空间碎裂机制，通过挫折图和超算符代数分析Pauli-Lindblad模型，揭示碎片中自由费米子可积性与对称性增强混沌，并发现例外点相变，为开放系统量子纠错提供新原理。
Decoherence rate in random Lindblad dynamics
本文研究由随机 Lindblad 算符支配的开放混沌量子系统的退相干速率，发现其上限由 Hilbert 空间维度决定且与系综对称性无关，并揭示此类系统普遍表现出最快退相干。
Algebraic structures of the Lindblad equation
本文揭示有限维开放量子系统Lindblad方程背后的代数结构，通过引入Liouville超算符的算子表示，将动力学表述为与模型无关的Hermitian算子闭代数，并推导出递归关系以高效构造代数，从而降低计算成本。
Universal dissipators for driven open quantum systems and the correction to linear response
本文并行采用随机哈密顿量与时间无卷积投影算符框架，推导开放量子系统耗散子的通用项及源自三阶累积量的驱动相关修正，揭示记忆效应导致超越 Lindblad 形式的线性响应修正。
A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
本文提出虚时间利布兰达演化框架，用于研究开放系统中量子相变，揭示了稳态可观测量的非解析行为和临界现象。
When level repulsion fails: non-normality and chaos in open quantum systems
研究指出开放量子系统中Lindbladian谱的能级统计不能可靠诊断量子混沌，因Hamiltonian与Lindbladian谱行为不同，非正态性导致能级统计可任意调节而不影响动力学。
In [Phys. Rev. A 82, 042103 (2010)], the authors showed that "for a class of the non-Markovian master equations in time-local forms", the quantum Fisher information (QFI) flow can be decomposed into additive subflows corresponding to different dissipative channels. However, the paper does not specify the class of non-Markovian time-local master equations for which their analytic decomposition of the QFI flow is valid. Here we show that several suppositions have to be made in order to reach the central result of Ref. \cite{luwsun10}, which appears to be valid for a narrow class of density opera…
In 1976, Gorini, Kossakowski, Sudarshan and Lindblad independently discovered a general form of master equations for an open quantum Markovian dynamics. In honor of all the authors, the equation is nowadays called the GKLS master equation. In this paper, we show universal constraints on the relaxation times valid for any d-level GKLS master equations, which is a generalization of the well-known constraints for 2-level systems. Specifically, we show that any relaxation rate, the inverse-relaxation time, is not greater than half of the sum of all relaxation rates. Since the relaxation times are …
These lecture notes address an audience of physicists or mathematicians who have been exposed to a first course in quantum mechanics. We start with a brief discussion of the general "system-bath" paradigm of quantum dissipative systems, analyze in some detail the simplest example of "pure dephasing" of a two-level system, and review the basic concept of the density matrix. We then treat the general dissipative time-evolution, introducing completely positive maps, their relation to entanglement theory, and their Kraus decomposition. Restricting ourselves to Markovian evolution, we discuss the L…
We consider the problem of constructing a "universal set" of Markovian processes, such that any Markovian open quantum system, described by a one-parameter semigroup of quantum channels, can be simulated through sequential simulations of processes from the universal set. In particular, for quantum systems of dimension $d$, we explicitly construct a universal set of semigroup generators, parametrized by $d^2-3$ continuous parameters, and prove that a necessary and sufficient condition for the dynamical simulation of a $d$ dimensional Markovian quantum system is the ability to implement a) quant…
The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those properties are. Here, we address these issues by considering a different description of dissipative quantum systems, namely, the discrete-time Kraus map representation of completely positive quantum dynamics. Through random matrix theory (RMT) techniques and numerical exact diagonalization, we study random Kraus maps, allowing for a varying dissipation stren…
In this Comment we show that the temperature-dependent effective Hamiltonian derived by Reslen {\it et al} [Europhys. Lett., {\bf 69} (2005) 8] or that one by Liberti and Zaffino [arXiv:cond-mat/0503742] for the Dicke model cannot be correct for any temperature. They both violate a rigorous result. The former is correct only in the quantum (zero-temperature) limit while the last one only in the classical (infinite temperature) limit. The fact that the Dicke model belongs to the universality class of the infinitely coordinated transverse-field XY model is known for more then 30 years.
In a recent article, Chiang and Hsu [The Journal of Chemical Physics 153, 044103 (2020)] examine one and two site electronic junctions identically connected to finite reservoirs. For these two examples, they derive analytical solutions, as well as provide asymptotic analyses, for the steady-state current from the driven Liouville-von Neumann (DLvN) equation - an open system approach to transport in non-interacting systems where relaxation maintains a bias. The two site junction they examine has destructive interference, which they show leads to slow convergence of the DLvN to the Landauer limi…
Universal Bound for Entanglement Generation
本文利用Gorini-Kossakowski-Sudarshan-Lindblad描述，推导了白热噪声下一般双线性相互作用中纠缠生成的通用条件，并应用于引力诱导纠缠，表明引力相互作用必须主导热噪声才能产生纠缠，且该界限无法通过改变初始态或引入中介系统来放松。
Boltzmann to Lindblad: Classical and Quantum Approaches to Out-of-Equilibrium Statistical Mechanics
本文提出了一种将经典随机动力学扩展到量子领域的框架，通过分析谐振子动力学，确定了在哈密顿方程中包含摩擦和噪声的条件，以确保完全正性，并揭示了摩擦系数的普遍正性条件。
Weak-coupling limits of the quantum Langevin equation for an oscillator
本文研究谐振子量子朗之万方程在实施Born-Markov式近似后的弱耦合极限，并评述旋转波近似，揭示强耦合模型在弱耦合近似下的行为。
Comment on: "Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions"
本文评论了文献[1]中关于噪声下动力学量子相变的研究，指出其用纯态近似噪声平均混合态的方法在热力学极限下指数失效，并证明非零噪声下Loschmidt回声不可能为零，从而否定DQPTs存在。
Steady-state entanglement scaling in open quantum systems: A comparison between several master equations
本文比较非局域 Lindblad、Redfield 与 ULE 三种主方程，研究受驱耗散临界链稳态 FLN 的标度，发现弱耦合下均为对数增长，而 Redfield 与 ULE 在更强耦合时转为超对数标度。
Generalized Loschmidt echo and information scrambling in open systems
本文研究了开放系统中信息混饨的特性，推广了洛施密特回声和非时间序相关子的概念，并提出了测量OTOC的实验协议。
Decoherence from universal tomographic measurements
本文通过两种等效方法研究了从环境监控量子系统状态产生的退相干现象，展示了退相干如何使任意给定的 quasiprobability 分布显式正，从而在某种程度上建模经典性的出现。
Using relative entropy, we derive bounds on the time rate of change of geometric entanglement entropy for any relativistic quantum field theory in any dimension. The bounds apply to both mixed and pure states, and may be extended to curved space. We illustrate the bounds in a few examples and comment on potential applications and future extensions.
Universal Properties of the Spectral Form Factor in Open Quantum Systems
本文研究开放量子系统中谱形状因子的普适行为，发现其经历指数衰减、线性增长和饱和平台三个阶段，并推导了衰减指数与Lindblad算符、平台值与稳态数的普适关系，通过SYK模型、随机矩阵理论和Bose-Hubbard模型验证。
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