M. Ricci, F. De Martini, N. J. Cerf, R. Filip, J. Fiurasek, C. Macchiavello
We report the experimental realization of the purification protocol for single qubits sent through a depolarization channel. The qubits are associated with polarization encoded photon particles and the protocol is achieved by means of passive linear optical elements. The present approach may represent a convenient alternative to the distillation and error correction protocols of quantum information.
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
We show an efficient purification protocol in solid-state qubits by replacing the usual bilateral CNOT gate by the bilateral iSWAP gate. We also show that this replacement can be applied to breeding and hashing protocols, which are useful for quantum state purification. These replacements reduce the number of fragile and cumbersome two-qubit operations, making more feasible quantum-information-processing with solid-state qubits. As examples, we also present quantitative analyses for the required time to perform state purification using either superconducting or semiconducting qubits.
We introduce a new decomposition of the multiqubit states of the form $ρ^{\otimes N}$ and employ it to construct the optimal single qubit purification procedure. The same decomposition allows us to study optimal quantum cloning and state estimation of mixed states.
We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of $n$ copies of a two-qubit state.
We investigate the time-optimal control of the purification of a qubit interacting with a structured environment, consisting of a strongly coupled two-level defect in interaction with a thermal bath. On the basis of a geometric analysis, we show for weak and strong interaction strengths that the optimal control strategy corresponds to a qubit in resonance with the reservoir mode. We investigate when qubit coherence and correlation between the qubit and the environment speed-up the control process.
A novel method of purification, purification through Zeno-like measurements [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003)], is discussed extensively and applied to a few simple qubit systems. It is explicitly demonstrated how it works and how it is optimized. As possible applications, schemes for initialization of multiple qubits and entanglement purification are presented, and their efficiency is investigated in detail. Simplicity and flexibility of the idea allow us to apply it to various kinds of settings in quantum information and computation, and would provid…
We propose an entanglement purification scheme based on material qubits and ancillary coherent multiphoton states. We consider a typical QED scenario where material qubits implemented by two-level atoms fly sequentially through a cavity and interact resonantly with a single mode of the radiation field. We explore the theoretical possibilities of realizing a high-fidelity two-qubit quantum operation necessary for the purification protocol with the help of a postselective balanced homodyne photodetection. We demonstrate that the obtained probabilistic quantum operation can be used as a bilateral…
This paper reconsiders the claimed rapidity of a scheme for the purification of the quantum state of a qubit, proposed recently in Jacobs 2003 Phys. Rev. A67 030301(R). The qubit starts in a completely mixed state, and information is obtained by a continuous measurement. Jacobs' rapid purification protocol uses Hamiltonian feedback control to maximise the average purity of the qubit for a given time, with a factor of two increase in the purification rate over the no-feedback protocol. However, by re-examining the latter approach, we show that it mininises the average time taken for a qubit to …
Selection of an ensemble of equally prepared quantum systems, based on measurements on it, is a basic step in quantum state purification. For an ensemble of single qubits, iterative application of selective dynamics has been shown to lead to complex chaos, which is a novel form of quantum chaos with true sensitivity to the initial conditions. The Julia set of initial valuse with no convergence shows a complicated structre on the complex plane. The shape of the Julia set varies with the parameter of the dynamics. We present here results for the two qubit case demonstrating how a purification pr…
We propose schemes for entanglement concentration and purification for qubit systems encoded in flying atomic pairs. We use a cavity-quantum electrodynamics setting as the paradigmatic scenario within which our proposals can be implemented. Maximally entangled pure states of qubits can be produced as a result of our protocols. In particular, the concentration protocol yields Bell states with the largest achievable theoretical probability while the purification scheme produces arbitrarily pure Bell states. The requirements for the implementation of these protocols are modest, within the state o…
Purification of mixed states in Quantum Mechanics, by which we mean the transformation into pure states, has been viewed as an {\it Operation} in the sense of Kraus et al and explicit {\it Kraus Operators} \cite{kra1,kra2,kra3} have been constructed for two seperate purification protocols. The first one, initially due to Schrodinger \cite{sch} and subsequently elaborated by Sudarshan et al \cite{sudar}, is based on the {\it preservation of probabilities}. We have constructed a second protocol here based on {\it optimization of fidelities}. Both purification protocols have been implemented on a…
Recently, the theoretical work of Fröwis and W. Dür (Phys. Rev. Lett. \textbf{106}, 110402 (2011)) and the experiment of Lu \emph{et al.} (Nat. Photon. \textbf{8}, 364 (2014)) both showed that the logic-qubit entanglement has its potential application in future quantum communication and quantum network. However, the entanglement will suffer from the noise and decoherence. In this paper, we will investigate the entanglement purification for logic-qubit entanglement. We show that both the bit-flip error and phase-flip error in logic-qubit entanglement can be well purified. Moreover, the bit-flip…
Recently two papers [K. Jacobs, Phys. Rev. A {\bf 67}, 030301(R) (2003); H. M. Wiseman and J. F. Ralph, New J. Physics {\bf 8}, 90 (2006)] have derived control strategies for rapid purification of qubits, optimized with respect to various goals. In the former paper the proof of optimality was not mathematically rigorous, while the latter gave only heuristic arguments for optimality. In this paper we provide rigorous proofs of optimality in all cases, by applying simple concepts from optimal control theory, including Bellman equations and verification theorems.
We consider qubit purification under simultaneous continuous measurement of the three non-commuting qubit operators σ_x, σ_y, σ_z. The purification dynamics is quantified by (i) the average purification rate, and (ii) the mean time of reaching given level of purity, (1-ε). Under ideal measurements (detector efficiency η=1), we show in the first case an asymptotic mean purification speed-up of 4 as compared to a standard (classical) single-detector measurement. However by the second measure --- the mean time of first passage T(ε) of the purity --- the corresponding speed-up is only 2. We explai…
We present the convergence study of a recurrence entanglement purification protocol using arbitrary two-qubit initial states. The protocol is based on a rank two projector in the Bell basis which serves as a two-qubit operation replacing the usual controlled-NOT gate. We show that the whole space of two-qubit density matrices is mapped onto an invariant subspace characterized by seven real parameters. By analyzing this type of density matrices we are able to find general conditions for entanglement purification in the form of two inequalities between pairs of diagonal elements and pairs of coh…
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…
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…
Optimal two-qubit gates in recurrence protocols of entanglement purification
本研究提出一种借助拟牛顿算法在SU(4)矩阵集搜索的方法，用于优化纠缠纯化递推协议，发现最优协议不必依赖双侧controlled-NOT门，为实验实现提供了灵活性。
Quantum control is an essential tool for the operation of quantum technologies such as quantum computers, simulators, and sensors. Although there are sophisticated theoretical tools for developing quantum control protocols, formulating optimal protocols while incorporating experimental conditions remains a challenge. In this paper, motivated by recent advances in realization of real-time feedback control in circuit quantum electrodynamics systems, we study the effect of experimental imperfections on the optimality of qubit purification protocols. Specifically, we find that the optimal control …
In this paper we consider feedback control algorithms for the rapid purification of a bipartite state consisting of two qubits, when the observer has access to only one of the qubits. We show 1) that the algorithm that maximizes the average purification rate is not the same as that that for a single qubit, and 2) that it is always possible to construct an algorithm that generates a deterministic rate of purification for {\em both} qubits. We also reveal a key difference between projective and continuous measurements with regard to state-purification.
Recently, two-photon six-qubit hyperentangled states were produced in experiment and they can improve the channel capacity of quantum communication largely. Here we present a scheme for the hyperentanglement purification of nonlocal two-photon systems in three degrees of freedom (DOFs), including the polarization, the first-longitudinal-momentum, and the second longitudinal momentum DOFs. Our hyperentanglement purification protocol (hyper-EPP) is constructed with two steps resorting to parity-check quantum nondemolition measurement on the three DOFs and SWAP gates, respectively. With these two…
A geometric Fano--Procrustes framework for purification-based distances and quantum channels analysis
本文提出了一种基于净化的几何框架，用于分析混合的双量子比特态和量子通道，通过Fano表示法将净化过程参数化为Bloch矢量、辅助系统Bloch矢量和相关矩阵，并将净化优化问题转化为在SO(3)李群上的正交Procrustes问题，从而得到最大净化重叠和最优旋转，定义了净化偏移角Θ，提供几何信息。
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.
This work provides a parametrization of the set of purifications of a 2x2 mixed state, and joint purifications (if any) of a given pair of mixed 2x2 states. The former is parametrized by SO(3, R), while the latter is parametrized by SO(2,R), except when the 2x2 state is pure. Using this parametrization some quantum information measures are obtained. In the process it is shown how to solve one variation of the classical Procustes problem. The appendix is devoted to the first step in extending this work to higher dimensions.
Scaling-optimal purification of noisy qubit unitary channels
针对带噪声的量子比特酉通道，提出基于纠缠辅助量子纠错码的U(2)-协变并行协议，实现噪声强度O(1/n)抑制，并证明在低噪声区域渐近最优。
Carrier-Assisted Entanglement Purification
提出一种利用单拷贝纠缠态量子存储器和传输单量子比特的载子辅助纠缠提纯协议，通过分析噪声信道条件并采用多载子方案，使固定点保真度趋近于1，显著降低实验开销。
A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However existing results suggest that such an enhancement is only possible when the measurement efficiency exceeds 0.5, which is difficult to achieve experimentally. We address the task of finding the global optimal feedback control for purifying a single qubit in the presence of measurement inefficiency. We use the Bloch vector length, a more physical and practical quantity than purity, to assess the quality of the state, and employ a backward iteratio…
Logic-qubit entanglement is a promising resource in quantum information processing, especially in future large-scale quantum networks. In the paper, we put forward an efficient entanglement purification protocol (EPP) for nonlocal mixed logic entangled states with the bit-flip error in the logic qubits of the logic Bell state, resorting to the photon-atom interaction in low-quality (Q) cavity and atomic state measurement. Different from existing EPPs, this protocol can also purify the logic phase-flip error, and the bit-flip error and the phase-flip error in physic qubit. During the protocol, …
Entanglement purification allows the creation of qubit pairs of arbitrarily high fidelity with respect to a maximally entangled state, starting from a larger number of low-fidelity pairs. Purification requires quantum memory, a role for which electron spins are well suited. However, using existing recurrence protocols involving symmetric local two-qubit operations for spin qubits turns out to be rather unpractical. We present an efficient purification protocol requiring only a single pulsed Heisenberg- or XY-type exchange interaction between two qubit pairs. In contrast to known protocols, we …
We propose the manipulation of an isolated qubit by a simple instantaneous closed-loop feedback scheme in which a time-dependent electronic detector current is directly back-coupled into qubit parameters. As specific detector model we employ a capacitively coupled single-electron transistor. We demonstrate the stabilization of pure delocalized qubit states above a critical detector-qubit coupling. This electronic purification is independent of the initial qubit state and is accomplished after few electron jumps through the detector. Our simple scheme can be used for the efficient and robust in…
We present a method for multipartite entanglement purification of any stabilizer state shared by several parties. In our protocol each party measures the stabilizer operators of a quantum error-correcting code on his or her qubits. The parties exchange their measurement results, detect or correct errors, and decode the desired purified state. We give sufficient conditions on the stabilizer codes that may be used in this procedure and find that Steane's seven-qubit code is the smallest error-correcting code sufficient to purify any stabilizer state. An error-detecting code that encodes two qubi…
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。
Security of One-Way Entanglement Purification with Quantum Sampling Against a Restricted Adversary
针对受限为单量子比特泡利门的对手，提出基于量子采样的单向纠缠纯化协议，利用与纠错码的等价性估计汉明重量并纠错，实现安全纯化。
Pursuit and Review of Magnetic Resonance Imaging (MRI) based Quantum Computing -- Qubit Generation, Spin Purification, Tailored RF Pulses and MRI Sequences for Quantum Computing
本研究提出一种基于MRI技术、利用水质子NMR生成多量子比特的新方法，结合局部反向梯度实现高均匀场单频量子比特，可室温运行并复用MRI现有软硬件，能为量子计算提供复杂信号处理能力。
We show that thresholds for fault-tolerant quantum computation are solely determined by the quality of single-system operations if one allows for d-dimensional systems with $8 \leq d \leq 32$. Each system serves to store one logical qubit and additional auxiliary dimensions are used to create and purify entanglement between systems. Physical, possibly probabilistic two-system operations with error rates up to 2/3 are still tolerable to realize deterministic high quality two-qubit gates on the logical qubits. The achievable error rate is of the same order of magnitude as of the single-system op…
Statistical evaluation and optimization of entanglement purification protocols
本文利用并发度和命中即跑算法统计评估双量子比特纠缠纯化协议，提出变分优化协议，在减少纠缠态浪费的同时提升输出并发度，超越已有方案。
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…
Purification enables an unbounded query separation in sequential quantum channel discrimination
本文证明在顺序量子信道鉴别中，利用纯化资源（即使环境参考系未知）能严格提升成功概率，优于裸访问和平行策略，并给出具体信道实例验证该优势。
Pure dephasing processes limit the fidelities achievable in driven-dissipative schemes for stabilization of entangled states of qubits. We propose a scheme which, combined with already existing entangling methods, purifies the desired entangled state by driving out of equilibrium auxiliary dissipative cavity modes coupled to the qubits. We lay out the specifics of our scheme and compute its efficiency in the particular context of two superconducting qubits in a cavity-QED architecture, where the strongly coupled auxiliary modes provided by collective cavity excitations can drive and sustain th…
It was first shown by Jacobs, in 2003, that the process of qubit state purification by continuous measurement of one observable can be enhanced, on average, by unitary feedback control. Here, we quantify this by the reduction in any one of the family of Rényi entropies $S_α$, with $0< α< \infty$, at some terminal time, revealing the rich structure of stochastic quantum control even for this simple problem. We generalize Jacobs' original argument, which was for (the unique) impurity measure with a linear evolution map under his protocol, by replacing linearity with convexity, thereby making it …
As the hyperentanglement of photon systems presents lots of unique opportunities in high-capacity quantum networking, the hyperentanglement purification protocol (hyper-EPP) becomes a vital project work and the quality of its accomplishment attracts much attention recently. Here we present the first theoretical scheme of faithful hyper-EPP for nonlocal two-photon systems in two degrees of freedom (DOFs) by constructing several fidelity-robust quantum circuits for hyper-encoded photons. With this faithful hyper-EPP, the bit-flip errors in both the polarization and spatial-mode DOFs can be effic…
We propose a scheme to evaluate the amount of quantum discord and entanglement of formation for mixed states, and reveal their ordering relation via an intrinsic relationship between the two quantities distributed in different partners of the associated purification. This approach enables us to achieve analytical expressions of the two measures for a sort of quantum states, such as an arbitrary two-qubit density matrix reduced from pure three-qubit states and a class of rank-2 mixed states of 4\times 2 systems. Moreover, we apply the scheme to characterize fully the dynamical behavior of quant…
In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be subject to less than 5.3% error. An existing proof that purification is equivalent to error correction is used to show that this bound can also be applied to concatenated error correcting codes in the presence of noisy gates, and hence gives a limit to the tolerable error rate for a fault-tolerant quantum computer formed by concatenation. This is shown to ap…
Purification of a monitored qubit: exact path-integral solution
研究连续时间监控下单量子比特纯化动力学，通过碰撞模型框架描述密度矩阵的条件演化，推导出纯度参数的朗之万方程，并利用路径积分法求解，揭示纯化过程中从扩散主导到测量主导的动态相变。
Given an ensemble of mixed qubit states, it is possible to increase the purity of the constituent states using a procedure known as state purification. The reverse operation, which we refer to as dilution, reduces the level of purity present in the constituent states. In this paper we find asymptotically optimal procedures for purification and dilution of an ensemble of i.i.d. mixed qubit states, for some given input and output purities and an asymptotic output rate. Our solution involves using the statistical tool of local asymptotic normality, which recasts the qubit problem in terms of atte…
Generic eigenstate preparation via measurement-based purification
本文提出通过辅助量子比特的重复投影测量实现任意本征态制备的通用量子控制框架，并展示了其在纠缠纯化和加速受激拉曼绝热通道中的应用。
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…
Entanglement Cost of Optimal Distributed Quantum State Purification
本文确定了去极化噪声下任意二分纯态最优两拷贝纯化所需预共享纠缠：一ebit最大纠缠对足够，且任何达到最优的资源态形成纠缠至少一ebit，为量子网络噪声管理提供纠缠需求基准。
Virtual Channel Purification
本文提出虚拟信道纯化（VCP）协议，结合旗标容错与虚拟态纯化思想，在无需目标态和噪声模型知识的情况下实现强误差抑制，并衍生出虚拟误差校正（VEC）协议，以低采样成本实现QEC级保护，适用于量子网络任务。
Locally maximally entangleable states (LMESs) constitute a large set of multipartite states, containing for instance all stabilizer states. LMESs are uniquely characterized by (2n-1) phases, where n denotes the number of qubits. We consider here those LMES whose phases are either 0 or π and present a multipartite entanglement purification protocol for arbitrary such states. In contrast to all previously known recurrence protocols this protocol uses a novel ingredient, which is required due to the quantum correlations contained in the various LMESs. We compare this scheme to previously known en…
Distilling Qubit Unitary Operations: A No-Go Theorem and Minimal Realization
本文研究通用酉净化任务，证明在不定因果序框架下无平凡2槽高阶操作可通用净化单比特酉，并发现3槽并行架构是实现非平凡净化的最小方案，通过辅助量子比特吸收误差达到最优平均保真度。
We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble in an explicit and controlled way, thereby reducing the amount of noise in the ensemble and purifying the remaining states. This allows us to design entanglement purification protocols for any number of copies that work particularly well for a small number of expected errors, i.e. high fidelity of initial states. The main tool is a counter gate with which the required non-local information ca…
We study 12 parameter families of two qubit density matrices, arising from a special class of two-fermion systems with four single particle states or alternatively from a four-qubit state with amplitudes arranged in an antisymmetric matrix. We calculate the Wooters concurrences and the negativities in a closed form and study their behavior. We use these results to show that the relevant entanglement measures satisfy the generalized Coffman-Kundu-Wootters formula of distributed entanglement. An explicit formula for the residual tangle is also given. The geometry of such density matrices is elab…
We investigate novel protocols for entanglement purification of qubit Bell pairs. Employing genetic algorithms for the design of the purification circuit, we obtain shorter circuits achieving higher success rates and better final fidelities than what is currently available in the literature. We provide a software tool for analytical and numerical study of the generated purification circuits, under customizable error models. These new purification protocols pave the way to practical implementations of modular quantum computers and quantum repeaters. Our approach is particularly attentive to the…
We present an entanglement purification protocol for a mixture of a pure entangled state and a pure product state, which are orthogonal to each other. The protocol is combination of bisection method and one-way hashing protocol. We give recursive formula for the rate of the protocol for different states, i.e. the number of maximally entangled two-qubit pairs obtained with the protocol per a single copy of the initial state. We also calculate numerically the rate for some states.
The deterministic quantum computation with one qubit (DQC1) model is a restricted model of quantum computing able to calculate efficiently the normalized trace of a unitary matrix. In this work we analyse the quantum correlations named entanglement, Bell's nonlocality, quantum discord, and coherence generated by the DQC1 circuit considering only two qubits (auxiliary and control). For the standard DQC1 model only quantum discord and coherence appear. By introducing a filter in the circuit we purify the auxiliary qubit taking it out from the totally mixed state and consequently promoting other …
Purification of Noisy Measurements and Faithful Distillation of Entanglement
本文提出一种在噪声测量条件下纯化量子测量并实现纠缠蒸馏的协议，每方仅需额外一个量子比特，具有资源高效性和现有技术可行性。
We present a number of rapid-purification feedback protocols for optical homodyne detection of a single optical qubit. We derive first a protocol that speeds up the rate of increase of the average purity of the system, and find that like the equivalent protocol for a non-disspative measurement, this generates a deterministic evolution for the purity in the limit of strong feedback. We also consider two analogues of the Wiseman-Ralph rapid-purification protocol in this setting, and show that like that protocol they speed up the average time taken to reach a fixed level of purity. We also examin…
We discuss the problem of transfering a qubit from Alice to Bob using a noisy quantum channel and only finite resources. As the basic protocol for the transfer we apply quantum teleportation. It turns out that for a certain quality of the channel direct teleportation combined with qubit purification is superior to entanglement purification of the channel. If, however, the quality of the channel is rather low one should simply apply an estimation-preparation scheme.
Developing universal logical state-purification strategy for quantum error correcting codes
提出一种基于测量的协议，通过工程化哈密顿量时间演化、投影测量与后选择，从任意热态以单位保真度纯化量子纠错码的任意逻辑态，并验证了其鲁棒性与可行性。
Global unitary transformations (OPTSWAPS) that optimally increase the bias of any mixed computation qubit in a quantum system -- represented by a diagonal density matrix -- towards a particular state of the computational basis which, in effect, increases its purity are presented. Quantum circuits that achieve this by implementing the above data compression technique -- a generalization of the 3B-Comp used before -- are described. These circuits enable purity increment in the computation qubit by maximally transferring part of its von Neumann or Shannon entropy to any number of surrounding qubi…
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。