Preserving entanglement and the fidelity of three-qubit quantum states undergoing decoherence using weak measurement

We demonstrate a method to preserve entanglement and improve fidelity of three-qubit quantum states undergoing amplitude-damping decoherence using weak measurement and quantum measurement reversal. It is shown that we are able to enhance entanglement to the greatest extent, and to circumvent entanglement sudden death by increasing the weak measurement strength both for the GHZ state and the W state. The weak measurement technique can also enhance the fidelity to the quantum region and even close to 1 for the whole range of the decoherence parameter in both of the two cases. In addition, the W state can maintain more fidelity than the GHZ state in the protection protocol. However, the GHZ state has a higher success probability than the W state.

Protecting the entanglement of two-qubit over quantum channels with memory via weak measurement and quantum measurement reversal

Based on the quantum technique of the weak measurement and quantum measurement reversal(WMR),we propose a scheme to protect entanglement for an entangled two-qubit pure state from four typical quantum noise channels with memory,i.e.,the amplitude damping channel,the phase damping channel,the bit flip channel,and the depolarizing channel.For a given initial state |Ψ>=a |00>+d|11>,it is found that the WMR operation indeed helps to protect entanglement from the above four quantum channels with memory,and the protection effect of WMR scheme is better when the coefficient a is small.For the other initial state |φ>=b|01>+c|10>,the effect of the protection scheme is the same regardless of the coefficient b and the WMR operation can protect entanglement in the amplitude damping channel with memory.Moreover,the protection of entanglement in quantum noise channels without memory in contrast to the results of the channels with memory is more effective.For |Ψ> or |φ>,we also find that the memory parameters play a significant role in the suppression of entanglement sudden death and the initial entanglement can be drastically amplified.Another more important result is that the relationship between the concurrence,the memory parameter,the weak measurement strength,and quantum measurement reversal strength is found through calculation and discussion.It provides a strong basis for the system to maintain maximum entanglement in the nosie channel.

Optimizing quantum correlation dynamics by weak measurement in dissipative environment

We investigate the protection of quantum correlations of two qubits in independent vacuum reservoirs by means of weak measurements. It is found that the weak measurement can reduce the amount of quantum correlation for one type of initial state at the beginning in a non-Markovian environment and meanwhile it can reduce the occurrence time of entanglement sudden death （ESD） in the process of time evolution. In a Markovian environment, the quantum entanglements of the two kinds of initial states decay rapidly and the weak measurement can further weaken the quantum entanglement, therefore in this case the entanglement cannot be optimized in the evolution process.

Protected simultaneous quantum remote state preparation scheme by weak and reversal measurements in noisy environments

We discuss a quantum remote state preparation protocol by which two parties, Alice and Candy, prepare a single-qubit and a two-qubit state, respectively, at the site of the receiver Bob. The single-qubit state is known to Alice while the two-qubit state which is a non-maximally entangled Bell state is known to Candy. The three parties are connected through a single entangled state which acts as a quantum channel. We first describe the protocol in the ideal case when the entangled channel under use is in a pure state. After that, we consider the effect of amplitude damping(AD) noise on the quantum channel and describe the protocol executed through the noisy channel. The decrement of the fidelity is shown to occur with the increment in the noise parameter. This is shown by numerical computation in specific examples of the states to be created. Finally, we show that it is possible to maintain the label of fidelity to some extent and hence to decrease the effect of noise by the application of weak and reversal measurements. We also present a scheme for the generation of the five-qubit entangled resource which we require as a quantum channel. The generation scheme is run on the IBMQ platform.

A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement

Fidelity plays an important role in quantum information processing,which provides a basic scale for comparing two quantum states.At present,one of the most commonly used fidelities is Uhlmann-Jozsa(U-J)fidelity.However,U-J fidelity needs to calculate the square root of the matrix,which is not trivial in the case of large or infinite density matrices.Moreover,U-J fidelity is a measure of overlap,which has limitations in some cases and cannot reflect the similarity between quantum states well.Therefore,a novel quantum fidelity measure called quantum Tanimoto coefficient(QTC)fidelity is proposed in this paper.Unlike other existing fidelities,QTC fidelity not only considers the overlap between quantum states,but also takes into account the separation between quantum states for the first time,which leads to a better performance of measure.Specifically,we discuss the properties of the proposed QTC fidelity.QTC fidelity is compared with some existing fidelities through specific examples,which reflects the effectiveness and advantages of QTC fidelity.In addition,based on the QTC fidelity,three discrimination coefficients d_(1)^(QTC),d_(2)^(QTC),and d_^(3)^(QTC)are defined to measure the difference between quantum states.It is proved that the discrimination coefficient d_(3)^(QTC)is a true metric.Finally,we apply the proposed QTC fidelity-based discrimination coefficients to measure the entanglement of quantum states to show their practicability.

Protecting Distribution Entanglement by Weak Measurement and Reversal under Various Decoherence Sources

Protection of entanglement from disturbance of the environment is an essential task marion processing. We examine the validity and limitation of the weak measurement and reversal in quantum infor- （WMR） operation in the protection of distributed entanglement from various decoherence sources. Since the entanglement variation can be investigated analytically for an arbitrarily entangled bipartite pure state under three kinds of typical noisy quantum channels, we show explicitly that the WMR operation indeed helps for protecting distributed entanglement from ampli- tude damping and phase damping, but not for depolarizing. Bxperimental feasibility for testing our results is discussed using current laboratory techniques.

Reversion of weak-measured quantum entanglement state

We theoretically study the reversible process of quantum entanglement state by means of weak measurement and corresponding reversible operation.We present a protocol of the reversion operation in two bodies based on the theory of reversion of single photon and then expend it in quantum communication channels.The theoretical results demonstrate that the protocol does not break the information transmission after a weak measurement and a reversible measurement with the subsequent process in the transmission path.It can reverse the perturbed entanglement intensity evolution to its original state.Under the condition of different weak measurement intensity the protocol can reverse the perturbed quantum entanglement system perfectly.In the process we can get the classical information described by information gain from the quantum system through weak measurement operation.On the other hand,in order to realize complete reversibility,the classical information of the quantum entanglement system must obey a limited range we present in this paper in the reverse process.

Atom interferometers with weak-measurement path detectors and their quantum mechanical analysis

According to the orthodox interpretation of quantum physics, wave-particle duality(WPD) is the intrinsic property of all massive microscopic particles. All gedanken or realistic experiments based on atom interferometers(AI) have so far upheld the principle of WPD, either by the mechanism of the Heisenberg’s position-momentum uncertainty relation or by quantum entanglement. In this paper, we propose and make a systematic quantum mechanical analysis of several schemes of weak-measurement atom interferometer(WM-AI) and compare them with the historical schemes of strongmeasurement atom interferometer(SM-AI), such as Einstein’s recoiling slit and Feynman’s light microscope. As the critical part of these WM-AI setups, a weak-measurement path detector(WM-PD) deliberately interacting with the atomic internal electronic quantum states is designed and used to probe the which-path information of the atom, while only inducing negligible perturbation of the atomic center-of-mass motion. Another instrument that is used to directly interact with the atomic center-of-mass while being insensitive to the internal electronic quantum states is used to monitor the atomic centerof-mass interference pattern. Two typical schemes of WM-PD are considered. The first is the micromaser-cavity path detector, which allows us to probe the spontaneously emitted microwave photon from the incoming Rydberg atom in its excited electronic state and record unanimously the which-path information of the atom. The second is the optical-lattice Bragg-grating path detector, which can split the incoming atom beam into two different directions as determined by the internal electronic state and thus encode the which-path information of the atom into the internal states of the atom. We have used standard quantum mechanics to analyze the evolution of the atomic center-of-mass and internal electronic state wave function by directly solving Schr¨odinger’s equation for the composite atom-electron-photon system in these WM-AIs. We have also compared our analysis with the theoretical and experimental studies that have been presented in the previous literature. The results show that the two sets of instruments can work separately, collectively, and without mutual exclusion to enable simultaneous observation of both wave and particle nature of the atoms to a much higher level than the historical SM-AIs, while avoiding degradation from Heisenberg’s uncertainty relation and quantum entanglement. We have further investigated the space–time evolution of the internal electronic quantum state, as well as the combined atom–detector system and identified the microscopic origin and role of quantum entanglement, as emphasized in numerous previous studies. Based on these physics insights and theoretical analyses, we have proposed several new WM-AI schemes that can help to elucidate the puzzling physics of the WPD of the atoms. The principle of WM-AI scheme and quantum mechanical analyses made in this work can be directly extended to examine the principle of WPD for other massive particles.

Promote entanglement trapping in photonic band gaps

We study the entanglement trapping of two entangled qubits, each of which is in its own photonic band gap, based on the weak measurement and quantum measurement reversal. An almost maximal entanglement of the two-qubit system can be trapped by using a certain weak measurement strength. Furthermore, we find that the optimal entanglement enhancing is not only dependent on the weak measurement strength but also on the different initial states. The outcomes in our scheme are completely different from that without any measurement on the studied system.

记忆幅值阻尼噪声下带有弱测量与恢复测量的量子隐形传态

认识并降低噪声对传输粒子保真度的影响,是量子隐形传态重要的研究方向之一。不同于以前的独立噪声和带记忆的Pauli噪声,研究了记忆幅值阻尼噪声对保真度的影响,并给出了一个抵抗该噪声信道的方案。该方案通过让参与者在粒子分发前实施弱测量而粒子接收后实施恢复测量的方式提高保真度。研究结果表明,记忆幅值阻尼信道的记忆因子强度与保真度大小呈正相关,并且在部分记忆信道与全记忆信道下弱测量与恢复测量方法也能一定程度上提高传输粒子的保真度。

Quantum State Preparation and Protection by Measurement-Based Feedback Control Against Decoherence

We consider an open quantum system subjected to a noise channel under measurement-based feedback control and two prototypical classes of decoherence channels are considered： phase damping and generalized amplitude damping. Based on quantum trajectory theory, we obtain an extended master equation for the dynamics of the reduced system in the presence of feedback control. For a qubit system we analytically solve this master equation and obtain the solution of the state vector dynamics. Then we propose an effective feedback control scheme for preparing an arbitrary quantum pure state. We also study how to protect two nonorthogonai states effectively, and find that projective measurement with unbiazed basis is not optimal for this task, while weak measurement with biased basis could realize the best protection of two nonorthogonal states. Furthermore, the inefficiencies in the feedback process are also discussed

降雨环境下星地双向受控量子隐形传态方法研究

为解决降雨环境下星地双向受控量子隐形传态质量下降的问题。首先提出一种基于十粒子纠缠态的星地双向受控量子隐形传态方案,其中通信方Alice和Bob在位于卫星的控制方Charlie允许的情况下可以同时双向传输任意二粒子量子态。进一步地,为研究降雨环境对该隐形传态方案性能的影响,以幅值阻尼噪声信道为例,分析了星地双向受控量子隐形传态的保真度及其影响因素。最后,为克服降雨环境的影响,利用弱测量和反转测量保护量子纠缠。理论分析与仿真结果表明,弱测量和反转测量操作可以有效提高星地隐形传态的保真度,因此,本方法对于提升降雨环境下的星地受控隐形传态质量具有一定的参考价值。

利用弱测量和量子测量翻转方法克服纠缠退相干

纠缠态是量子信息处理中的一种重要的物理资源,量子态在传输过程中会与环境产生不可避免的退相干。本文我们通过弱测量和量子测量翻转方法,来保护纠缠态免受振幅阻尼退相干信道的影响。以三体Wigner的朋友实验中的三量子比特态作为研究对象,计算不同退相干强度以及弱测量强度下,弱测量和量子测量翻转前后量子系统纠缠态的纠缠度与保真度。结果表明,量子态的纠缠度和保真度随弱测量强度变化,弱测量强度越大,保真度与纠缠度越大,甚至当弱测量强度足够大时,纠缠度和保真度可恢复至原值。可知弱测量和量子测量翻转方法确实有助于减轻或避免振幅阻尼量子信道中的退相干。

级联环境下三量子比特量子关联动力学研究

基于与各自的级联环境相互耦合的三个独立的量子比特系统,详细考察了强、弱耦合体系下腔-腔耦合强度Ω和腔衰减率Γ1对负性纠缠度、Bell非定域性和纠缠目击的影响.结果表明:Bell非定域性和纠缠目击都可以出现猝死和猝生现象;Γ1=0时,随着W的增加,三者在历经短时阻尼振荡后,均会随时间达到各自的稳定值,且该稳定值随着Ω的增大而增大.同时,三者在弱耦合体系的量值或存活时间都优于强耦合体系.此外,非零Γ1对量子关联有着很大的负面效应.于是,为了更好地抑制量子关联损失,进一步分析了弱测量和测量反转操作的有效调控作用,得到一些有趣的结果.

多粒子纠缠的保护方案

量子纠缠是量子信息的重要物理资源.然而当量子系统与环境相互作用时,会不可避免地产生消相干导致纠缠下降,因此保护纠缠不受环境的影响具有重要意义.振幅衰减是一种典型的衰减机制.如果探测环境保证没有激发从系统中流出,即视为对系统的一种弱测量.本文基于局域脉冲序列和弱测量,提出了一种可以保护多粒子纠缠不受振幅衰减影响的有效物理方案,保护的对象是在量子通信和量子计算中发挥重要作用的Cluster态和maximal slice态.

2种量子测量方案对非最大纠缠相干态隐形传态平均保真度的影响

在纠缠相干态的隐形传态过程中,使用双模光子数测量和奇偶态测量2种粒子数测量方案,得到的平均保真度存在较大差异.据此对使用非最大纠缠相干态作为量子信道时,2种测量方法得到的平均保真度进行了对比.结果显示:相较于双光子数测量,用奇偶态粒子数测量方案时,隐形传态的平均保重度有了较大提高.

弱测量理论对三能级量子态共享的保真度分析

量子态共享是量子密码学研究中的一个重要分支,而纠缠态分发是实现量子态共享方案的必要手段.噪声环境会导致量子纠缠态产生退相干,从而降低量子态共享方案的性能甚至出现失败的情况.基于三能级量子系统下三方量子态共享方案,研究了振幅阻尼信道在4种不同配置下量子态共享的保真度问题.为提升共享量子态的保真度,采用量子弱测量方法对振幅阻尼噪声信道中纠缠态的分发进行保护,得到在量子弱测量方法辅助下振幅阻尼信道中量子态共享的保真度.最后,以特定形式的量子态为例,分析了在4种不同配置的振幅阻尼信道中量子弱测量方法对共享量子态保真度的改善效果.通过仿真实验表明,量子弱测量方法只对振幅阻尼信道中2种不同配置下的量子态共享保真度有改善作用,而对其他2种配置下量子态共享的保真度没有明显的改善效果,甚至会产生相反的效果.

弱测量对多体簇态纠缠和保真度的保护

研究了在振幅阻尼通道中,利用弱测量来保护簇态的纠缠和保真度。通过前置弱测量和后置弱测量反转操作,系统的退相干能够得到有效抑制,保真度明显提高。另外,系统的纠缠和保真度演化与弱测量强度P的取值有关,在选择适当的P值时,系统的纠缠和保真度能得到最佳的保护。

基于弱测量操作下的量子关联动力学及关联转移

利用弱测量技术研究两量子比特的量子关联动力学演化和转移。有纠缠突然死亡现象产生的非最大纠缠初态经前选择测量操作后,在演化过程中不但能够提高量子关联强度,而且能够缩短甚至消除量子比特纠缠的突然死亡区域;而对于演化中无纠缠突然死亡的非最大纠缠初态,弱测量操作则会降低量子比特间关联强度。对初始处于最大纠缠态的粒子,弱测量操作不能增强粒子间的纠缠但可以优化量子关联中的量子失谐。弱测量在实现量子关联转移时的破坏极小,能够延迟纠缠的衰减,并可使量子纠缠的转移时间提前。另外腔场与量子比特间的耦合强度与系统耗散率的关系决定纠缠原子在腔中动力学演化,表现为马尔可夫和非马尔可夫过程。

基于十粒子Cluster态的受控双向量子隐形传态在噪声背景下的纠缠特性及保真度优化方法

本文提出了一种利用弱测量进行纠缠预补偿的方法。首先分析了十粒子Cluster态的受控双向量子隐形传态的传输过程，通过理论推导给出了不同测量基下相应的幺正变换，成功得到对方待传的未知量子态。在此基础上重点研究了振幅阻尼噪声对量子隐形传态纠缠保真度的影响，并根据弱测量和反馈测量对量子传输信道的调控特性，提出了预补偿的纠缠优化方法。理论分析与性能仿真结果表明，相比于现有纠缠优化方法，本方法不需要引入任何辅助粒子和复杂的系统操作就能获得更高的隐形传态保真度，对克服纠缠退相干带来的隐形传态质量下降具有一定意义。