B. A. Nikolov
It is shown on a simple classical model of a quantum particle at rest that information contained into the quantum state (quantum information) can be obtained by integrating the corresponding probability distribution on phase space, i.e. by reduction of the information contained into the classical state.
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Classical optimisation of reduced density matrix estimations with classical shadows using N-representability conditions under shot noise considerations
本文通过改进经典阴影层析成像的估计器并重新表述优化约束，在相同测量射击预算下提升了N-可表示性条件强制执行性能，并量化了潜在节省。
Classicality of the Bogoliubov transformations and the dynamical Casimir effect through the reduced state of the field
本研究基于场的约化态形式体系推导Bogoliubov变换的半经典条件，并将其应用于运动介质中的动力学卡西米尔效应，分析该效应的经典与量子特性。
The notion of classicality of quantum evolution of light is an object of both conceptual and practical importance. The main goal of this work is to derive the exact conditions for the classicality of quantum Gaussian evolution, i.e. the evolution of Gaussian states of light and their convex combinations, a model which is of great significance in quantum optics and information. Several examples, ranging from Gaussian thermal operations to entanglement-maximizing dissipative engineering, are discussed. Our results are obtained using the recently introduced mesoscopic theory of the reduced state …
We introduce QRDM-NEVPT2: a hybrid quantum-classical implementation of strongly-contracted N-electron Valence State $2^{nd}$-order Perturbation Theory (SC-NEVPT2), in which the Complete Active Space Configuration Interaction (CASCI) step, capturing static correlation effects, is replaced by a simulation performed on a quantum computer. Subsequently, n-particle Reduced Density Matrices (n-RDMs) measured on a quantum device are used directly in a classical SC-NEVPT2 calculation, which recovers remaining dynamic electron correlation effects approximately. We also discuss the use of the cumulant e…
Learning quantum disentanglement scheduling from reduced states via modular hybrid policies
本文研究了在部分观测下通过多量子比特解缠调度进行量子控制的问题，提出了一种模块化混合量子-经典策略框架，通过预处理、参数化量子电路和后处理实现高效解缠调度，发现预处理是性能主导因素，量子模块提供条件紧凑表示，且增加电路宽度比深度更有效。
Consider a bipartite quantum system with at least one of its two components being itself a composite system. By tracing over part of one (or both) of these two subsystems it is possible to obtain a reduced (separable) state that exhibits quantum correlations even if the original state of the full system is endowed only with classical correlations. This effect, first pointed out by Li and Luo in (2008), is of considerable interest because there is a growing body of evidence suggesting that quantum correlations in non-entangled, mixed states may constitute a useful resource to implement non triv…
Emergence of the Partial Trace from Classical Probability Theory
本文基于经典概率理论，通过要求Born规则与概率质量函数的边缘化一致，推导出量子力学中部分追踪操作的起源，揭示其作为概率结构自然结果的本质。
Efficient Estimation of Reduced QAOA Expressibility on Acyclic Graphs
本文针对树结构上的对称约化QAOA，提出一种多项式时间经典算法，可高效估计约化DLA，实现表达能力诊断与可控子系统证明，为变分量子算法的量子动力学分析提供经典方法。
Computing time-dependent reduced models for classical and quantum dynamics
本文提出一种递归算法，构造时间多项式生成元以近似大型系统在固定子空间上的短时动力学，无需弱耦合假设，并在低阶保证完全正迹保持，适用于量子主方程推导。
An example is presented when decoherence and quantum interference gives rise to narrow eigenstates (in coordinate representation) for the reduced density matrix of macroscopic quantum systems. On the basis of modal interpretations this means the emergence of classical properties.
In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. To show that our new formulation can be applied to practic…
We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer--Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity transformed Hamiltonians. The prac…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of lower dimensional surfaces. Such a classical factorization never exists for ergodic eigenstates of a chaotic Hamiltonian. The space of quantum operators corresponds to a double phase space. The various representations of the density operator then result from alternative choices of allowed coordinate planes. In the case of the Wigner function and its Fourier …
We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial state in terms of its quantum discord [H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)]. We prove that initial states that have only classical correlations lead to completely positive reduced dynamics. The induced maps can be not completely positive when quantum correlations including, but not limited to, entanglement are present. We outline t…
Reductions of QAOA Induced by Classical Symmetries: Theoretical Insights and Practical Implications
本文研究了经典对称性如何影响QAOA的结构和训练性，通过固定变量分析MaxCut问题，揭示了DLA维度变化及缩减后的改进效果。
In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces b are rough images of the fundamental {\bf prespace.} Quantum mechanics cannot be reduced to classical one. Both classical and quantum representations induce reductions of prespace information.
Fermionic reduced density low-rank matrix completion, noise filtering, and measurement reduction in quantum simulations
针对量子模拟中2-RDM测量需求大的问题，提出利用低秩矩阵补全从部分信息重构2-RDM的方法，经24个分子体系验证，含噪场景下测量次数可降多个数量级，可适配经典与量子模拟算法。
An exact reduced-density-operator for the output quantum states in time-convolutionless form was derived by solving the quantum Liouville equation which governs the dynamics of a noisy quantum channel by using a projection operator method and both advanced and retarded propagators in time. The formalism developed in this work is general enough to model a noisy quantum channel provided specific forms of the Hamiltonians for the system, reservoir, and the mutual interaction between the system and the reservoir are given. Then, we apply the formulation to model a two-bit quantum gate composed of …
Advances in highly sensitive detection techniques for classical coherent communication systems have reduced the received signal power requirements to a few photons per bit. At this level one can take advantage of the quantum noise to create secure communication, using continuous variable quantum key distribution (CV-QKD). In this work therefore we embed CV-QKD signals within classical signals and transmit classical data and secure keys simultaneously over 25km of optical fibre. This is achieved by using a novel coherent displacement state generator, which has the potential for being used in a …
Patch-Based End-to-End Quantum Learning Network for Reduction and Classification of Classical Data
本文提出一种基于分块的端到端量子学习网络，结合动态量子域数据降维与经典注意力机制，避免传统经典降维的高计算成本，并在Fashion MNIST数据集上以极少的训练参数实现了优异的分类性能。
We show that it is possible to define a Lorentz-covariant reduced spin density matrix for massive particles. Such a matrix allows one to calculate the mean values of observables connected with spin measurements (average polarizations). Moreover, it contains not only information about polarization of the particle but also information about its average kinematical state. We also use our formalism to calculate the correlation function in the Einstein--Podolsky--Rosen--Bohm type experiment with massive relativistic particles.
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These dynamical fluctuations are found to constitute a reliable indicator of the degree of chaos in the quantum dynamics, and are related to stationary features like the eigenvalue and eigenvector distributions of the system under consideration. A brief comparison is made with the evolution of the reduced distribution function in the classical phase space.
Constant-Depth Quantum Imaginary Time Evolution Using Dynamic Fan-out Circuits
本文提出了一种基于动态扇出电路的常深度量子虚时间演化方法，通过减少参数和纠缠生成，提高了基态制备的成功概率，并在硬件上实现了不同变种的对比实验。
The exchange of "information" between a system and its environment based on the reduced dynamics is investigated. The association of trace distance with information cannot be stated, because of lack of symmetry between leakage from the system and absorbability by the environment. A measure of loss for the reduced dynamics is established, which may be seen as a deviation from exact unitary dynamics.
The eigenvalue problem in quantum mechanics is reduced to quantization of the classical action of the physical system. State function of the system, $ψ_0(ϕ)$, is written in the form of superposition of two plane waves in the phase space. Quantization condition is derived from the basic requirements of continuity and finiteness for $ψ_0(ϕ)$ in the whole region.
The problem of classical data compression when the decoder has quantum side information at his disposal is considered. This is a quantum generalization of the classical Slepian-Wolf theorem. The optimal compression rate is found to be reduced from the Shannon entropy of the source by the Holevo information between the source and side information.
The sum of entropic uncertainties for the measurement of two non-commuting observables is not always reduced by the amount of entanglement (quantum memory) between two parties, and in certain cases may be impacted by quantum correlations beyond entanglement (discord). An optimal lower bound of entropic uncertainty in the presence of any correlations may be determined by fine-graining. Here we express the uncertainty relation in a new form where the maximum possible reduction of uncertainty is shown to be given by the extractable classical information. We show that the lower bound of uncertaint…
We use the Koashi-Imoto decomposition of the degrees of freedom of joint system-environment initial states to investigate the reduced dynamics. We show that a subset of joint system-environment initial states guarantees completely positive reduced dynamics, if and only if the system privately owns all quantum degrees of freedom and can locally access the classical degrees of freedom, without disturbing all joint initial states in the given subset. Furthermore, we show that the quantum mutual information for such kinds of states must be independent of the quantum degrees of freedom.
We experimentally explore the state space of three qubits on an NMR quantum information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a non-trivial combination of GHZ and W-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and W states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confir…
This note presents a practical cryptography protocol for transmitting classical and quantum information secretly and directly.
A possibility to detect correlations between two quantum mechanical systems only from the information of a subsystem is investigated. For generic cases, we prove that there exist correlations between two quantum systems if the time-derivative of the reduced purity is not zero. Therefore, an experimentalist can conclude non-zero correlations between his/her system and some environment if he/she finds the time-derivative of the reduced purity is not zero. A quantitative estimation of a time-derivative of the reduced purity with respect to correlations is also given. This clarifies the role of co…
We discuss reduced-scaling strategies employing recently introduced sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to describe many-body systems. These strategies utilize properties of the SES-CC formulations where the equations describing certain classes of sub-systems can be integrated into a computational flows composed coupled eigenvalue problems of reduced dimensionality. Additionally, these flows can be determined at the level of the CC Ansatz by the inclusion of selected classes of cluster amplitudes, which define the wave function "memory" of possible partitioning…
This article has to do with the derivation and solution of the Fokker--Planck equation associated to the momentum-independent Wigner function, of a particle subjected to a harmonic external field and immersed in a ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung and Grabert of interpreting the operators as c-numbers to derive the adjoint equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the in…
Classically Driven Hybrid Quantum Algorithms with Sequential Givens Rotations for Reduced Measurement Cost
本文提出了一种经典驱动的混合量子算法，通过顺序Givens旋转降低测量成本，适用于电子结构模拟。
The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that are essential to calculate the entropy-like quantities that quantify the information. Even in the sparse cases where the spectrum and eigenfunctions are exactly known the entanglement spectrum, {\em i.e.} the spectrum of the reduced density matrices that characterize the problem, must be obtained in an approximate fashion. In this work, we obtain analytically…
More assistance of entanglement, less rounds of classical communication
针对LOCC局域分辨量子态的轮次数问题，本文研究纯两体正交态轮次关系，以d⊗d正交乘积态为例，展示其无纠缠需2d-2轮、1-e比特纠缠辅助降至d且更多纠缠可进一步减少，证明轮次数与纠缠辅助量相关。
In this paper, we reconsider the communication model used in the no-go theorems on the impossibility of quantum bit commitment and oblivious transfer. We state that a macroscopic classical channel may not be replaced with a quantum channel which is used in the reduced model proving the no-go theorems. We show that in some restricted cases, the reduced model is insecure while the original model with a classical channel is secure.
Relativistic effects affect nearly all notions of quantum information theory. The vacuum behaves as a noisy channel, even if the detectors are perfect. The standard definition of a reduced density matrix fails for photon polarization because the transversality condition behaves like a superselection rule. We can however define an effective reduced density matrix which corresponds to a restricted class of positive operator-valued measures. There are no pure photon qubits, and no exactly orthogonal qubit states. Reduced density matrices for the spin of massive particles are well-defined, but are…
In this paper, we calculate the entanglement-assisted classical information capacity of amplitude damping channel and compare it with the particular mutual information which is considered as the entanglement-assisted classical information capacity of this channel in Ref. 6. It is shown that the difference between them is very small. In addition, we point out that using partial symmetry and concavity of mutual information derived from dense coding scheme one can simplify the calculation of entanglement-assisted classical information capacities for non-unitary-covariant quantum noisy channels.
The classical limit of wave quantum mechanics is analyzed. It is shown that the general requirements of continuity and finiteness to the solution $ψ(x)=Ae^{iϕ(x)}+ Be^{-iϕ(x)}$, where $ϕ(x)=\frac 1\hbar W(x)$ and $W(x)$ is the reduced classical action of the physical system, result in the asymptote of the exact solution and general quantization condition for $W(x)$, which yields the exact eigenvalues of the system.
We introduce a framework for the construction of completely positive maps for subsystems of indistinguishable fermionic particles. In this scenario, the initial global state is always correlated, and it is not possible to tell system and environment apart. Nonetheless, a reduced map in the operator sum representation is possible for some sets of states where the only non-classical correlation present is exchange.
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied through the von Neumann entropy of the reduced density matrices. We demonstrate that classical chaos can lead to substantially enhanced entanglement. Conversely, entanglement provides a novel and useful characterization of quantum states in higher dimensional chaotic or complex systems. Information about eigenfunction localization is stored in a graded manner in t…
Reduced-order modeling of two-dimensional turbulent Rayleigh-Bénard flow by hybrid quantum-classical reservoir computing
针对二维湍流Rayleigh-Bénard流动的低阶统计特性复现问题，提出两种混合量子-经典储层计算模型，性能与经典模型相当且储层规模仅为经典的1/4至1/8。
We study the reduced fidelity between local states of lattice systems exhibiting topological order. By exploiting mappings to spin models with classical order, we are able to analytically extract the scaling behavior of the reduced fidelity at the corresponding quantum phase transitions out of the topologically ordered phases. Our results suggest that the reduced fidelity, albeit being a local measure, generically serves as a faithful marker of a topological quantum phase transition.
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self-consistent field theory, which joins the quantum theory and classical field theory, is proposed.
Bounding the forward classical capacity of bipartite quantum channels
本文为二部量子信道提出多种前向经典通信度量，证明其可作为前向经典容量及经典反馈辅助点到点容量的上界，且部分度量可由半定规划计算。
A quantum model can be mapped to a classical model in one higher dimension. Here we introduce a finite-temperature correlation measure based on a reduced density matrix rho_A obtained by cutting the classical system along the imaginary time (inverse temperature) axis. We show that the von-Neumann entropy S_ent of rho_A shares many properties with the mutual information, yet is based on a simpler geometry and is thus easier to calculate. For one-dimensional quantum systems in the thermodynamic limit we proof that S_ent is non-extensive for all temperatures T. For the integrable transverse Ising…
The solution with respect to the reduced action of the one-dimensional stationary quantum Hamilton-Jacobi equation is well known in the literature. The extension to higher dimensions in the separated variable case was proposed in contradictory formulations. In this paper we provide new insights into the construction of the reduced action. In particular, contrary to the classical mechanics case, we analytically show that the reduced action constructed as a sum of one variable functions does not contain a complete information about the quantum motion. In the same context, we also make some obser…
We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases: commuting system and interaction Hamiltonians, the short-time limit, and the Markov approximation.
We studied the Szilard engine under the effect of generalized uncertainty principle (GUP). In the classical Szilard engine, the work done by the engine is reduced by the GUP effect via a modified ideal gas law. In the quantum Szilard engine, the correction comes from the shifted eigen energy due to the nonlinear momentum dependence. We studied its effect on both bosonic and fermionic molecules.
Quantum machine learning for efficient reduced order modelling of turbulent flows
本文提出量子机器学习与降阶建模结合的新框架，实现湍流预测的高效准确建模。
Quantum coherence allows for reduced-memory simulators of classical processes. Using recent results in single-shot quantum thermodynamics, we derive a minimal work cost rate for quantum simulators that is quasistatically attainable in the limit of asymptotically-infinite parallel simulation. Comparing this cost with the classical regime reveals that quantizing classical simulators not only results in memory compression but also in reduced dissipation. We explore this advantage across a suite of representative examples.
Introducing Reduced-Width QNNs, an AI-inspired Ansatz Design Pattern
受QNNs中dropout正则化分析启发，提出一种缩减宽度的电路拟设设计模式，在噪声环境下可显著减少训练时间并保持与全宽度设计相同的结果质量。
New Properties of Intrinsic Information and Their Relation to Bound Secrecy
该研究证明本征信息与约化本征信息的零值等价性，指出有界保密存在性和约化本征信息等于密钥速率这两个猜想必有一错，还给出有界保密候选的信息擦除二值化构造及证明有界保密存在的多种方法。
We study the hybrid classical-quantum version of the channel coding problem for the famous Gel'fand-Pinsker channel. In the classical setting for this channel the conditional distribution of the channel output given the channel input is a function of a random parameter called the channel state. We study this problem when a rate limited version of the channel state is available at the encoder for the classical-quantum Gel'fand-Pinsker channel. We establish the capacity region for this problem in the information-spectrum setting. The capacity region is quantified in terms of spectral-sup classic…
Emergence of Non-Markovian Classical-Quantum Dynamics from Decoherence
研究通过退相干机制展示经典-量子动力学作为全量子系统有效描述的普遍性，提出非马尔可夫性减少动力学的条件及半威格纳算子的正定性要求。
We study the quantum mechanical evolution of the tensor perturbations during inflation with non-linear tensor interactions. We first obtain the Lindblad terms generated by non-linear interactions by tracing out unobservable sub-horizon modes. Then we calculate explicitly the reduced density matrix for the super-horizon modes, and show that the probability of maintaining the unitarity of the squeezed state decreases in time. The decreased probability is transferred to other elements of the reduced density matrix including off-diagonal ones, so the evolution of the reduced density matrix describ…
Contextual Subspace Auxiliary-Field Quantum Monte Carlo: Improved bias with reduced quantum resources
本研究在上下文子空间投影框架下分解试探波函数，提出适配matchgate shadow协议的QC-AFQMC改进算法，以更少量子比特实现更高精度的强关联体系基态能量计算。
We show how to construct hybrid quantum-classical codes from subsystem codes by encoding the classical information into the gauge qudits using gauge fixing. Unlike previous work on hybrid codes, we allow for two separate minimum distances, one for the quantum information and one for the classical information. We give an explicit construction of hybrid codes from two classical linear codes using Bacon-Casaccino subsystem codes, as well as several new examples of good hybrid code.
We present a new approach to calculate real-time quantum dynamics in complex systems. The formalism is based on the partitioning of a system's environment into "core" and "reservoir" modes, with the former to be treated quantum mechanically and the latter classically. The presented method only requires the calculation of the system's reduced density matrix averaged over the quantum core degrees of freedom which is then coupled to a classically evolved reservoir to treat the remaining modes. We demonstrate our approach by applying it to the spin-boson problem using the noninteracting blip appro…
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