Hans Maassen, Burkhard Kümmerer
We prove that the quantum trajectory of repeated perfect measurement on a finite quantum system either asymptotically purifies, or hits upon a family of `dark' subspaces, where the time evolution is unitary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Purification of quantum trajectories in infinite dimensions
本文展示了一类例子，证明基于“暗”子空间的量子轨迹纯化刻画在无限维系统中失效，并指出该现象源于正交投影集非序列紧性，同时证明了有限维结果可推广至一类无限维模型。
Asymptotic Purification of Quantum Trajectories under Random Generalized Measurements
本文开发通用框架研究平稳噪声下重复随机测量的量子轨迹，推广Kümmerer和Maassen的结果，阐明无序场景暗子空间概念，证明其为空等价于渐近纯化，并给出例子。
The rate of purification of quantum trajectories
本文通过李雅普诺夫方法证明了量子轨迹净化的指数速率，并量化了测量过程揭示信息的速率。
We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied. Several applications of entanglement purification in quantum communication and computation are presented, w…
We introduce a quantity called the coherence of purification which can be a measure of total quantumness for a single system. We prove that coherence of purification is always more than the coherence of the system. For a pure state, the coherence of purification is same as the relative entropy of coherence. Furthermore, we show that the difference in the coherence of purification of a quantum state before and after the dephasing can capture residual quantumness. In addition, we show that the entanglement of purification that can be created by incoherent operation between two subsystems is uppe…
We investigate the dynamics of quantum discord during the purification process. In the case of Werner states, it is shown that quantum discord is increased after a round of purification protocol. Furthermore, quantum mutual information and classical correlation is also increased during this process.Wealso give an analytic expression for a class of higher dimensional states which have additive quantum discord.
We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a pure state in a higher-dimensional Hilbert space, the reduced density matrix of which is identical to the original state. We characterize all sets of mixed quantum states, for which perfect purification is possible. Surprisingly, some sets of two non-commuting states are among them. Furthermore, we investigate the possibility of performing an imperfect purific…
A new purification scheme is proposed which applies to arbitrary dimensional bipartite quantum systems. It is based on the repeated application of a special class of nonlinear quantum maps and a single, local unitary operation. This special class of nonlinear quantum maps is generated in a natural way by a hermitian generalized XOR-gate. The proposed purification scheme offers two major advantages, namely it does not require local depolarization operations at each step of the purification procedure and it purifies more efficiently than other know purification schemes.
An iterative random procedure is considered allowing an entanglement purification of a class of multi-mode quantum states. In certain cases, a complete purification may be achieved using only a single signal state preparation. A physical implementation based on beam splitter arrays and non-linear elements is suggested. The influence of loss is analyzed in the example of a purification of entangled N-mode coherent states.
We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. In the security regime, the purification process factorises the overall initial state into a tensor-product state of Alice and Bob, on one side, and Eve on the other side, thus establishing a completely private, albeit noisy, quantum communication channel between Alice and Bob. The security regime is found to coincide for all practical purposes with the purification regime of a two-way recurrence protocol. This makes two-way entanglement …
Universal quantum state purification under energy-preserving constraints
本文提出在能量守恒约束下实现通用态净化的框架，推导了无通用能量守恒净化的必要条件，并分析了最优性能及协议，展示了如何通过能量守恒操作系统实现最优协议。
We present a novel procedure to purify quantum states, i.e., purification through Zeno-like measurements. By simply repeating one and the same measurement on a quantum system, one can purify another system in interaction with the former. The conditions for the (efficient) purification are specified on a rather general setting, and the framework of the method possesses wide applicability. It is explicitly demonstrated on a specific setup that the purification becomes very efficient by tuning relevant parameters.
A generalization of the quantum XOR-gate is presented which operates in arbitrary dimensional Hilbert spaces. Together with one-particle Fourier transforms this gate is capable of performing a variety of tasks which are important for quantum information processing in arbitrary dimensional Hilbert spaces. Among these tasks are the preparation of Bell states, quantum teleportation and quantum state purification. A physical realization of this generalized XOR-gate is proposed which is based on non-linear optical elements.
Joint Optimization of Routing and Purification to Meet Fidelity Targets in Quantum Networks
本文提出一种联合优化路由与净化的方案，通过智能调度减少量子网络延迟并提升成功率。
We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. Our proof applies to all possible attacks (individual and coherent). Due to the quantum nature of the entanglement purification protocol, it is also possible to use the obtained quantum channel for secure transmission of quantum information.
In this work we study the properties of an purification-based entropic metric for measuring the distance between both quantum states and quantum processes. This metric is defined as the square root of the entropy of the average of two purifications of mixed quantum states which maximize the overlap between the purified states. We analyze this metric and show that it satisfies many appealing properties, which suggest this metric is an interesting proposal for theoretical and experimental applications of quantum information.
Recently, Briegel et al. present a quantum repeaters protocol using nest entanglement purification for long distance quantum communication(Physical Review Letters \textbf{81},5932). In this paper we present a modified scheme for constructing an optimal quantum repeater using doubly entangled photon pairs that overcomes the limitations of quantum communication via noisy channels. Based on the imperfect quantum operations and classical communications, the polarization entangled quantum channels can be built with a better efficiency.
We analyze the estimation of a finite ensemble of quantum bits which have been sent through a depolarizing channel. Instead of using the depolarized qubits directly, we first apply a purification step and show that this improves the fidelity of subsequent quantum estimation. Even though we lose some qubits of our finite ensemble the information is concentrated in the remaining purified ones.
We have applied an entanglement purification protocol to produce a single entangled pair of photons capable of violating a CHSH Bell inequality from two pairs that individually could not. The initial poorly-entangled photons were created by a controllable decoherence that introduced complex errors. All of the states were reconstructed using quantum state tomography which allowed for a quantitative description of the improvement of the state after purification.
A Nonstabilizerness Resource Law for Universal Quantum State Purification
研究通用量子态纯化，通过证明奇数维线性魔力定律和多量子比特系统双边线性鲁棒性定律，确定成功纯化映射，建立通用纯化的定量魔法 - 保真度定律，将魔法资源与容错量子信息处理相联系。
No-Go Theorems for Universal Quantum State Purification via Classically Simulable Operations
本文证明仅使用经典可模拟操作无法实现通用量子态纯化，并通过半定规划数值解将不可行定理推广至多副本情形，揭示了非稳定子资源的必要性。
Pure states are fundamental for the implementation of quantum technologies, and several methods for the purification of the state of a quantum system S have been developed in the past years. In this letter we present a new approach, based on the interaction of S with an auxiliary system P, having a wide range of applicability. Considering two-level systems S and P and assuming a particular interaction between them, we prove that complete purifications can be obtained under suitable conditions on the parameters characterizing P. Using analytical and numerical tools, we show that the purificatio…
Integrating Entanglement Purification into All-Photonic Quantum Repeaters
该研究提出了一种基于RGS框架的全光量子中继方案，利用半RGS构建块实现长距离纠缠纯化，有效降低开销并保持通信延迟可控。
Hyperentanglement is a promising resource in quantum information processing, especially for increasing the channel capacity of long-distance quantum communication. Hyperentanglement purification is an important method to obtain high-fidelity nonlocal hyperentangled states from mixed hyperentangled states in a long-distance quantum communication process with noisy channels. Here, we present a two-step hyperentanglement purification protocol for nonlocal mixed hyperentangled states with polarization bit-flip errors and spatial-mode phase-flip errors, resorting to polarization-spatial phase-check…
The distribution of entangled states between distant locations will be essential for the future large scale realization of quantum communication schemes such as quantum cryptography and quantum teleportation. Because of the unavoidable noise in the quantum communication channel, the entanglement between two particles is more and more degraded the further they propagate. Entanglement purification is thus essential to distill highly entangled states from less entangled ones. Existing general purification protocols are based on the quantum controlled-NOT (CNOT) or similar quantum logic operations…
Quantum error mitigation is essential for computing on the noisy quantum computer with a limited number of qubits. In this paper, we propose a practical protocol of error mitigation by virtually purifying the quantum state without qubit overhead or requiring only one ancillary qubit. In dual-state purification, we effectively generate a purified state with increased fidelity using the erroneous state and its dual state, respectively, prepared with the noisy quantum circuit and the dual map of its inverse circuit. Combined with tomography purification, we can make sure that the final estimate o…
Advances in quantum entanglement purification
本文综述量子纠缠纯化的理论、协议类型与线性光学实验进展，并展望其在长距离量子通信和量子网络中的应用前景。
Quantum communication is a secure way to transfer quantum information and to communicate with legitimate parties over distant places in a network. Although communication over a long distance has already been attained, technical problem arises due to unavoidable loss of information through the transmission channel. Quantum repeaters can extend the distance scale using entanglement swapping and purification scheme. Here we demonstrate the working of a quantum repeater by the above two processes. We use IBM's real quantum processor `ibmqx4' to create two pair of entangled qubits and design an equ…
Chip-to-chip hyperentanglement distribution and entanglement purification using silicon integrated photonics
该研究首次在集成硅芯片间实现偏振-空间超纠缠分发，并通过消耗空间自由度完成纠缠纯化，弥补了片上量子中继器的关键环节。
We describe an entanglement purification protocol to generate maximally entangled states with high efficiencies from two-mode squeezed states or from mixed Gaussian continuous entangled states. The protocol relies on a local quantum non-demolition measurement of the total excitation number of several continuous variable entangled pairs. We propose an optical scheme to do this kind of measurement using cavity enhanced cross--Kerr interactions.
Power and limitations of distributed quantum state purification
本文研究了分布式量子系统中通过LOCC实现态纯化的功效与局限性，证明了针对特定态的纯化在去极化噪声下可行，并提出了一种优化算法设计纯化协议。
We study the stability under quantum noise effects of the quantum privacy amplification protocol for the purification of entanglement in quantum cryptography. We assume that the E91 protocol is used by two communicating parties (Alice and Bob) and that the eavesdropper Eve uses the isotropic Bužek-Hillery quantum copying machine to extract information. Entanglement purification is then operated by Alice and Bob by means of the quantum privacy amplification protocol and we present a systematic numerical study of the impact of all possible single-qubit noise channels on this protocol. We find th…
We present a nondestructive parity-check detector (PCD) scheme for two single-electron quantum dots embedded in double-sided optical microcavities. Using a polarization-entangled photon pair, the PCD works in a parallel style and is robust to the phase fluctuation of the optical path length. In addition, we present an economic entanglement purification protocol for electron pairs with our nondestructive PCD. The parties in quantum communication can increase the purification efficiency and simultaneously decrease the quantum source consumed for some particular fidelity thresholds. Therefore, ou…
We present an improved protocol for entanglement purification of bipartite mixed states. The protocol requires two-way classical communication and hence implies an improved lower bound on the quantum capacity with two-way classical communication of the quantum depolarizing channel.
Quantum Purification for Amplitude Damping Noise
本文提出一种针对振幅阻尼噪声的量子纯化新方法，仅需少量辅助比特和克利福德门，即可显著提升态或信道的保真度，且成功概率较高，为实际量子系统提供了可扩展的噪声缓解方案。
Error-mitigated quantum metrology via enhanced virtual purification
本文提出增强虚拟通道净化方法，通过提升虚拟态净化效果，提高量子计量的精度和鲁棒性，适用于单参数和多参数任务，并拓展至更广泛的量子信息领域。
We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is however possible to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An impor…
We present an approach to purification and entanglement routing on complex quantum network architectures, that is, how a quantum network equipped with imperfect channel fidelities and limited memory storage time can distribute entanglement between users. We explore how network parameters influence the performance of path-finding algorithms necessary for optimizing routing and, in particular, we explore the interplay between the bandwidth of a quantum channels and the choice of purification protocol. Finally, we demonstrate multi-path routing on various network topologies with resource constrai…
We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to the entanglement cost of creating a state $ρ$ asymptotically from maximally entangled states, with negligible communication. We prove that the classical mutual information and the quantum mutual information divided by two are lower bounds for the regularized entanglement of purification. We present numerical results of the entanglement of purification for Werner states in ${\cal H}_2 \otimes {\cal …
To Purify or Not to Purify: Entanglement Purification under Input Fidelity Asymmetry in Quantum Networks
研究探讨了在量子网络中因输入保真度不对称而进行纠缠净化的必要性，推导了保真度不对称容忍度公式，并提出DeltaPurify策略以优化净化决策。
To achieve the practical applications of near-term noisy quantum devices, low-cost ways to mitigate the noise damages in the devices are essential. In many applications, the noiseless state we want to prepare is often a pure state, which has recently inspired a range of purification-based quantum error mitigation proposals. The existing proposals either are limited to the suppressions of only the leading-order state preparation errors, or require a large number of long-range gates that might be challenging to implement depending on the qubit architecture. This article will provide an overview …
The entanglement resource required for quantum information processing comes in a variety of forms, from Bell states to multipartite GHZ states or cluster states. Purifying these resources after their imperfect generation is an indispensable step towards using them in quantum architectures. While this challenge, both in the case of Bell pairs and more general multipartite entangled states, is mostly overcome in the presence of perfect local quantum hardware with unconstrained qubit register sizes, devising optimal purification strategies for finite-size realistic noisy hardware has remained elu…
Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we investigate a scenario that interpolates between these two extremes. We search for the optimal physical process that generates $M$ approximate copies of pure and amplified coherent state, starting from $N$ copies of a noisy coherent state with Gaussian modulation. We prove that the optimal deterministic processes are always Gaussian, whereas non-Gaussianity powers…
High-fidelity quantum entanglement is a key resource for quantum communication and distributed quantum computing, enabling quantum state teleportation, dense coding, and quantum encryption. Any sources of decoherence in the communication channel however degrade entanglement fidelity, thereby increasing the error rates of entangled state protocols. Entanglement purification provides a method to alleviate these non-idealities, by distilling impure states into higher-fidelity entangled states. Here we demonstrate the entanglement purification of Bell pairs shared between two remote superconductin…
Localized Entanglement Purification
本文提出局部纠缠纯化方法，通过利用空间噪声不对称性，减少资源消耗，实现更大量子系统的可扩展纯化策略。
We consider the problem of improving noisy quantum measurements by suitable preprocessing strategies making many noisy detectors equivalent to a single ideal detector. For observables pertaining to finite-dimensional systems (e.g. qubits or spins) we consider preprocessing strategies that are reminiscent of quantum error correction procedures and allows one to perfectly measure an observable on a single quantum system for increasing number of inefficient detectors. For measurements of observables with unbounded spectrum (e.g. photon number, homodyne and heterodyne detection), the purification …
No Universal Purification in Quantum Mechanics
本文证明量子力学的线性和正性对纯化施加了普遍限制，排除了未知量子态或信道的精确通用纯化，并给出了近似纯化的样本复杂度下界，揭示了纯化与量子学习之间的深层联系。
Exponential Separations between Quantum Learning with and without Purification
本研究证明访问目标混合态的纯化可实现量子学习任务中统计复杂度的指数级降低，仅需常数辅助比特和样本，而无纯化时则需指数级拷贝，并探讨了该优势的来源及应用。
We give a detailed description of the entanglement purification protocol which generates maximally entangled states with high efficiencies from realistic Gaussian continuous variable entangled states. The physical implementation of this protocol is extensively analyzed using high finesse cavities and cavity enhanced cross Kerr nonlinearities. In particular, we take into account many imperfections in the experimental scheme and calculate their influences. Quantitative requirements are given for the relevant experimental parameters.
Experimental Quantum Channel Purification
本研究针对量子网络信道噪声问题，提出利用光子空间与偏振特性、基于双Fredkin门的实验性量子信道纯化方案，实现多类型多水平噪声抑制，在纠缠分发场景下抗噪保纠缠性能优于传统方法。
Capacity Enhancement of n-GHZ State Super-dense Coding Channels by Purification and Quantum Neural Network
提出基于n-GHZ态的超密编码协议，结合纠缠纯化与量子神经网络提升信道容量，实验验证二者叠加增强效果显著。
We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for the maximal achievable average fidelity and we explictly show how to construct a probabilistic operation that achieves this fidelity. We illustrate our method on several examples such as the phase covariant cloning of qubits, cloning of coherent states, and purification of qubits transmitted via depolarizing channel and amplitude damping channel. Our exampl…
We present a protocol based on continuous-variable quantum teleportation and Gaussian post- selection that can be used to correct errors introduced by a lossy channel. We first show that the global transformation enacted by the protocol is equivalent to an effective system composed of a noiseless amplification (or attenuation), and an effective quantum channel, which can in theory have no loss and an amount of thermal noise arbitrarily small, hence tending to an identity channel. An application of our protocol is the probabilistic purification of quantum non-Gaussian states using only Gaussian…
A scheme of three-particle entanglement purification is presented in this work. The physical system undertaken for investigation is dot-like single quantum well excitons independently coupled through a single microcavity mode. The theoretical framework for the proposed scheme is based on the quantum jump approach for analyzing the progress of the trible-exciton entanglement as a series of conditional measurement has been taken on the cavity field state. We first investigate how cavity photon affects the purity of the double-exciton state and the purification efficiency in two-particle protocol…
Entanglement purification is to distill high-quality entangled states from low-quality entangled states. It is a key step in quantum repeaters, determines the efficiency and communication rates of quantum communication protocols, and is hence of central importance in long-distance communications and quantum networks. In this work, we report the first experimental demonstration of deterministic entanglement purification using polarization and spatial mode hyperentanglement. After purification, the fidelity of polarization entanglement arises from $0.268\pm0.002$ to $0.989\pm0.001$. Assisted wit…
High-quality long-distance entanglement is essential for both quantum communication and scalable quantum networks. Entanglement purification is to distill high-quality entanglement from low-quality entanglement in a noisy environment and it plays a key role in quantum repeaters. The previous significant entanglement purification experiments require two pairs of low-quality entangled states and were demonstrated in table-top. Here we propose and report a high-efficiency and long-distance entanglement purification using only one pair of hyperentangled states. We also demonstrate its practical ap…
The need to retain the relative phases in quantum mechanics implies an addition law parametrized by a phase of two density operators required for the purification of a density matrix. This is shown with quantum tomography and the Wigner function. Entanglement is determined in terms of phase dependent multiplication.
Preparing a quantum system in a pure state is ultimately limited by the nature of the system's evolution in the presence of its environment and by the initial state of the environment itself. We show that, when the system and environment are initially uncorrelated and arbitrary joint unitary dynamics is allowed, the system may be purified up to a certain (possibly arbitrarily small) threshold if and only if its environment, either natural or engineered, contains a "virtual subsystem" which has the same dimension and is in a state with the desired purity. Beside providing a unified understandin…
Single photon emitters are indispensable to photonic quantum technologies. Here we demonstrate waveform-controlled high-purity single photons from room-temperature colloidal quantum dots. The purity of the single photons does not vary with the excitation power, thereby allowing the generation rate to be increased without compromising the single-photon quality.
The manipulation of quantum coherence is one of the principal issues in the resource theory of coherence, with two critical topics being the purification and enhancement of coherence. Here, we present two no-go theorems for the deterministic purification of coherence and the probabilistic enhancement of coherence, respectively. Specifically, we prove that a quantum state cannot be deterministically purified if it can be expressed as a convex combination of an incoherent state and a coherent state. Besides, we give an easy-to-verified sufficient and necessary condition to determine whether a st…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。