Protecting Qutrit-Qutrit Entanglement Under the Generalized Amplitude Decoherence of the Finite Temperature

We investigate the dynamics and protection of quantum entanglement of a qutrit-qutrit system under local amplitude damping channels with finite temperature. We consider two different initial states. We find that the qutrit-qutrit entanglement decays monotonically as the decoherence strength increases, and may go through entanglement sudden death at higher temperature. Special attention is paid to how to protect the quantum entanglement from decoherence by weak measurement and quantum measurement reversal. Our results show that the entanglement increases with the increase of weak measurement strength when the temperature is lower. However, the protections of entanglement by weak measurement and quantum measurement reversal are almost failed and the decays of entanglement goes up with the increase of weak measurement strength for different decoherence strength when the temperature is higher, even entanglement suffers sudden death.

     

噪声对一种三粒子量子探针态的影响

量子度量学是研究量子测量与统计推断的一门学科,主要利用量子手段来提高参数估计的精度,在量子信息处理与测量中起到关键作用.量子参数估计的一般过程包含四个步骤:探针态的制备、参数化过程、对参数化后的输出态进行测量以及根据测量结果估计待测参数.其中探针态的选取对测量精度起着至关重要的作用.然而在实际的量子探针态的制备过程中,初始探针态会受到环境噪声的影响.目前人们已经研究了W态与Greenberger-Horne-Zeilinger(GHZ)态的量子Fisher信息(QFI)在典型噪声通道下的变化行为.由于W态与GHZ态有着不同的纠缠性质,对于W态与GHZ态的叠加态的QFI动力学研究具有重要的实际意义.故此,本文主要研究典型噪声通道对这两种状态的叠加态的QFI动力学行为的影响,得出了QFI随噪声参数的变化行为.结果表明,叠加态中W态组分可明显对抗相位阻尼噪声对探针态的QFI的影响,而其中的GHZ态组分可明显对抗振幅阻尼噪声的影响,从而为在实际环境中选取高精度的参数估计过程提供参考.     

Geometric Quantum Discord of a Two-Qutrit System Under Decoherence at Finite Temperature

The dynamics and protection of geometric quantum discord (GQD) for a two-qutrit system under amplitude damping channel with finite temperature have been studied in detail. By using of a lower bound of GQD, numerical results show that the GQD dynamics suffering from amplitude damping channels is more robust against the decoherence at lower temperature. Moreover, by combining weak measurement with measurement reversal, we have also investigated the protecting of the GDQ for a two-qutrit system under decoherence. It is found that the measurement technique can effectively protect the GQD against decoherence at lower temperature, but fails to protect GQD at higher temperature of channel.     

Weak Measurement-Based Entanglement Protection of Two-Qubit X-States from Amplitude Damping Decoherence

Considering X-states the density matrixes of which look like the letter X, we propose a weak measurement-based entanglement protection protocol of two-qubit X-states under local amplitude damping channels using weak measurement and reversal operation. It is shown that, with increase of the decoherence parameter, the entanglement attenuates rapidly owing to the amplitude damping noise and even experiences entanglement sudden death (ESD). However, the entanglement under the weak measurement and reversal operation is always much stronger than the entanglement undergoing the amplitude damping decoherence. These results reflect that entanglement of two-qubit X-states from amplitude damping decoherence can be protected, and ESD can be circumvented by increasing the weak measurement strength.     

利用弱测量保护两个三能级原子系统的束缚纠缠

高维量子系统的纠缠态因其诸多的优点而受到广泛的关注。目前,肖兴等人[Eur.Phys.J.D.(2013)67:204]研究了两个V-型三能级原子系统的演化动力学,得到了弱测量方案能保护系统自由纠缠的结论。本文研究了在振幅阻尼噪声中两个全同三能级原子系统束缚纠缠的演化动力学。在振幅阻尼通道中,前置弱测量和后置弱测量反转操作,实现了对系统束缚纠缠的保护。束缚纠缠保持的时间受量子态参数和弱测量强度的影响。相应的物理原因也得到了合理的解释。对于两个非全同三能级原子的情况,此结论依旧成立。另外,弱测量方案并不是对所有类型的束缚纠缠态都适用,有一定的局限性。     

Enhancing robustness of multiparty quantum correlations using weak measurement

Multipartite quantum correlations are important resources for the development of quantum information and computation protocols. However, the resourcefulness of multipartite quantum correlations in practical settings is limited by its fragility under decoherence due to environmental interactions. Though there exist protocols to protect bipartite entanglement under decoherence, the implementation of such protocols for multipartite quantum correlations has not been sufficiently explored. Here, we study the effect of local amplitude damping channel on the generalized Greenberger–Horne–Zeilinger state, and use a protocol of optimal reversal quantum weak measurement to protect the multipartite quantum correlations. We observe that the weak measurement reversal protocol enhances the robustness of multipartite quantum correlations. Further it increases the critical damping value that corresponds to entanglement sudden death. To emphasize the efficacy of the technique in protection of multipartite quantum correlation, we investigate two proximately related quantum communication tasks, namely, quantum teleportation in a one sender, many receivers setting and multiparty quantum information splitting, through a local amplitude damping channel. We observe an increase in the average fidelity of both the quantum communication tasks under the weak measurement reversal protocol. The method may prove beneficial, for combating external interactions, in other quantum information tasks using multipartite resources.     

Decoherence Effects on Multiplayer Cooperative Quantum Games

We study the behavior of cooperative multiplayer quantum games [Q. Chen, Y. Wang, J.T. Liu, and K.L. Wang, Phys. Lett. A 327 (2004) 98; A.P. Flitney and L.C.L. Hollenberg, Quantum Inf. Comput. 7 (2007) 111] in the presence of decoherence using different quantum channels such as amplitude damping, depolarizing and phase damping. It is seen that the outcomes of the games for the two damping channels with maximum values of decoherence reduce to same value. However, in comparison to phase damping channel, the payoffs of cooperators are strongly damped under the influence amplitude damping channel for the lower values of decoherence parameter. In the case of depolarizing channel, the game is a no-payoff game irrespective of the degree of entanglement in the initial state for the larger values of decoherence parameter. The decoherence gets the cooperators worse off.     

Decoherence suppression for three-qubit W-like state using weak measurement and iteration method

Multi-qubit entanglement states are the key resources for various multipartite quantum communication tasks. For a class of generalized three-qubit quantum entanglement, W-like state, we demonstrate that the weak measurement and the reversal measurement are capable of suppressing the amplitude damping decoherence by reducing the initial damping factor into a smaller equivalent damping factor. Furthermore, we propose an iteration method in the weak measurement and the reversal measurement to enhance the success probability of the total measurements. Finally, we discuss how the number of the iterations influences the overall effect of decoherence suppression, and find that the "half iteration" method is a better option that has more practical value.     

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.     

Enhancing Robustness of Entanglement in Finite Temperature Environment Using Quantum Measurement Reversal

We demonstrate methods of enhancing robustness of entanglement of two-qubit systems undergoing generalized amplitude damping decoherence using weak measurement and measurement reversal. The results show that the local action of generalized amplitude damping noise can cause sudden death of entanglement, and the weak measurement and measurement reversal is useful for combating generalized amplitude damping decoherence and recovering the entanglement of two entangled qubits. In addition, the results indicate that it would be much more easily implemented by applying quantum measurement reversal on a single-qubit to enhance robustness of entanglement in finite temperature environment, than on both qubits.     

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.     

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 nonorthogonal states effectively, and find that projective measurement with unbiased 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.     

Quantum Monty Hall Problem under Decoherence

We study the effect of decoherence on quantum Monty Hall problem under theinfluence of amplitude damping, depolarizing, and dephasing channels. It isshown that under the effect of decoherence, there is a Nash equilibrium ofthe game in case of depolarizing channel for Alice's quantum strategy.Whereas in case of dephasing noise, the game is not influenced by thequantum channel. For amplitude damping channel, Bob's payoffs are foundsymmetrical about a decoherence of 50% and the maximum occurs at this value of decoherence for his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob's classical strategy remains always dominant against any choice of Alice's strategy.     

Dynamics of Measurement-Induced Disturbance for a Qubit-Qutrit System in Noninertial Frames

We investigate the dynamics of measurement-induced disturbance(MID) for a qubit-qutrit system in noninertial frames under various multi-local decoherence channels(i.e.,dephasing,phase-flip,bit-(trit-) flip,bit-(trit-) phase-flip,and depolarizing channels).We find that,for any acceleration,the MID can decay in a monotonic way to zero or to a nonzero steady value(i.e.,residual MID exists).Consequently,no sudden death of the MID occurs,which is different from entanglement.     

Protecting Distribution Entanglement for Two-Qubit State Using Weak Measurement and Reversal

Protection of entanglement from disturbance of the environment is an essential task in quantum information processing. We investigate the effect of the weak measurement and reversal (WMR) on the protection of the entanglement for an arbitrarily entangled two-qubit pure state from these three typical quantum noisy channels, i.e., amplitude damping channel, phase damping channel and depolarizing quantum channel. Given the parameters of the Bell-like initial qubits’ state |ψ〉 = a|00〉 + d|11〉, it is found that the WMR operation indeed helps for protecting distributed entanglement from the above three noisy quantum channels. But for the Bell-like initial qubits’ state |?〉 = b|01〉 + c|10〉, the WMR operation only protects entanglement in the amplitude damping channel, not for the phase damping and depolarizing quantum channels. In addition, we discuss how the concurrence and the success probability behave with adjusting the weak or the reversal weak measurement strength.     

Quantum Parrondo’s Games Under Decoherence

We study the effect of quantum noise on history dependent quantum Parrondo’s games by taking into account different noise channels. Our calculations show that entanglement can play a crucial role in quantum Parrondo’s games. It is seen that for the maximally entangled initial state in the presence of decoherence, the quantum phases strongly influence the payoffs for various sequences of the game. The effect of amplitude damping channel leads to winning payoffs. Whereas the depolarizing and phase damping channels lead to the losing payoffs. In case of amplitude damping channel, the payoffs are enhanced in the presence of decoherence for the sequence AAB. This is because the quantum phases interfere constructively which leads to the quantum enhancement of the payoffs in comparison to the undecohered case. It is also seen that the quantum phase angles damp the payoffs significantly in the presence of decoherence. Furthermore, it is seen that for multiple games of sequence AAB, under the influence of amplitude damping channel, the game still remains a winning game. However, the quantum enhancement reduces in comparison to the single game of sequence AAB because of the destructive interference of phase dependent terms. In case of depolarizing channel, the game becomes a loosing game. It is seen that for the game sequence B the game is loosing one and the behavior of sequences B and BB is similar for amplitude damping and depolarizing channels. In addition, the repeated games of A are only influenced by the amplitude damping channel and the game remains a losing game. Furthermore, it is also seen that for any sequence when played in series, the phase damping channel does not influence the game.     

Protecting qutrit-qutrit entanglement by weak measurement and reversal

Entangled states in high dimensional systems are of great interest due to the extended possibilities they provide in quantum information processing. Recently, Sun et al. [Phys. Rev. A 82, 052323 (2010)] and Kim et al. [Nat. Phys. 8, 117 (2012)] pointed out that weak measurement and quantum weak measurement reversal can actively combat decoherence. We generalize their studies from qubits to qutrits under amplitude damping decoherence. We find that the qutrit-qutrit entanglement can be partially retrieved for certain initial states when only weak measurement reversals are performed. However, we can completely defeat amplitude damping decoherence for any initial states by the combination of prior weak measurements and post optimal weak measurement reversals. The experimental feasibility of our schemes is also discussed.     

Simulating the effect of weak measurements by a phase damping channel and determining different measures of bipartite correlations in nuclear magnetic resonance

Quantum discord is a measure based on local projective measurements which captures quantum correlations that may not be fully captured by entanglement. A change in the measurement process, achieved by replacing rank-one projectors with a weak positive operator-valued measure (POVM), allows one to define weak variants of quantum discord. In this work, we experimentally simulate the effect of a weak POVM on a nuclear magnetic resonance quantum information processor. The two-qubit system under investigation is part of a three-qubit system, where one of the qubits is used as an ancillary to implement the phase damping channel. The strength of the weak POVM is controlled by varying the strength of the phase damping channel. We experimentally observed two weak variants of quantum discord namely, super quantum discord and weak quantum discord, in two-qubit Werner and Bell-diagonal states. The resultant dynamics of the states is investigated as a function of the measurement strength.     

弱测量对四个量子比特量子态的保护

廖湘萍等(Chin.Phys.B 23 020304,2014)指出弱测量和弱测量反转操作可以保护三个量子比特的纠缠,提高保真度.本文将弱测量方法推广至四个量子比特的情况,研究了几种典型四个量子比特量子态的演化.结果表明:在振幅阻尼通道中,弱测量方法能够有效地提高系统量子态的保真度.分析了影响量子态保真度的各种因素,对比了不同量子态的演化特征,划分了量子态保真度提高的敏感区域.最后,对弱测量方法抑制量子态衰减的内在机制做了合理的物理解释.     

LMG model: Markovian evolution of classical and quantum correlations under decoherence

We have investigated the quantum phase transition in the ground state of collective Lipkin-Meshkov-Glick model (LMG model) subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. We discuss the behavior of quantum and classical pair wise correlations in the system, with the quantumness of correlations measured by quantum discord (QD), entanglement of formation (EOF), measurement-induced disturbance (MID) and the Clauser-Horne-Shimony-Holt-Bell function (CHSH-Bell function). The time evolution established by system-environment interactions is assumed to be Markovian in nature and the quantum channels studied include the amplitude damping (AD), phase damping (PD), bit-flip (BF), phase-flip (PF), and bit-phase-flip (BPF) channels. One can identify appropriate quantities associated with the dynamics of quantum correlations signifying quantum phase transition in the model. Surprisingly, the CHSH-Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.