Sufficient Conditions of the Same State Order Induced by Coherence

In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and l₁ norm of coherence, and give the sufficient conditions of the same state order induced by above coherence measures. First, we show that the above measures give the same ordering for single-qubit states in some special cases. Second, we consider some special states in a d-dimensional quantum system. We show that the above measures generate the same ordering for these special states. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find amplitude damping channel changes the coherence-induced ordering even though for single-qubit states with fixed mixedness.     

Sufficient Conditions of the Same State Order Induced by Coherence

In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and l1 norm of coherence, and give the sufficient conditions of the same state order induced by above coherence measures. First, we show that the above measures give the same ordering for single-qubit states in some special cases. Second, we consider some special states in a d-dimensional quantum system. We show that the above measures generate the same ordering for these special states. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find amplitude damping channel changes the coherence-induced ordering even though for single-qubit states with fixed mixedness.     

利用量子相干性判定开放二能级系统中非马尔可夫性

从量子相干性包括l₁ norm相干性和量子相对熵相干性的角度建立了判定开放量子系统中非马尔可夫过程的方法, 并给出了相应的判别条件. 作为它们的具体应用, 研究了一个两能级系统分别经历相位衰减通道、 随机幺正通道和振幅耗散通道作用时对应的非马尔可夫过程发生必须满足的条件. 对于三种通道模型, 得到了l₁ norm相干性对系统任意态非马尔可夫过程发生的判别条件, 并发现在相位衰减通道和振幅耗散通道中其非马尔可夫过程发生 的条件与用其他方式如信息回流、可分性和量子互熵给出的条件是相同的, 而在随机幺正通道中给出了一个新的且不完全等价于基于信息回流和可分性对应的条件. 至于量子相对熵相干性, 在相位衰减通道中得到了对系统任意态的非马尔可夫过程发生的具体条件, 并发现该条件也等同于基于信息回流、可分性和量子互熵给出的条件. 而在随机幺正通道和振幅耗散通道中得到了系统最大相干态对应的非马尔可夫过程发生的条件.     

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.     

Properties on the distant distribution of entanglement for arbitrary two-qubit pure states via noisy quantum channels

This paper investigates the change of entanglement for transmitting an arbitrarily entangled two-qubit pure state via one of three typical kinds of noisy quantum channels: amplitude damping quantum channel, phase damping quantum channel and depolarizing quantum channel. It finds, in all these three cases, that the output distant entanglement (measured by concurrence) reduces proportionately with respect to its initial amount, and the decaying ratio is determined only by the noisy characteristics of quantum channels and independent of the form of initial input state.     

Entanglement Dynamics of Two-Qubit System in Different Types of Noisy Channels

In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally, interacting with independent noisy channels, i.e., amplitude damping, phase damping, and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death （ESD） and/or be decreased for the critical probability at which the entanglement disappear.     

Decay Rate of the l1 Norm Coherence in Single-Qubit Systems

We examine to what extent the l₁ norm of coherence through an open quantum system is affected by noise. To discuss the effect of the noise, we give a definition of the decay rate of the l₁ norm of coherence, i.e., the value of the coherence of initial states divided by the coherence of final states. Then we use the measure of the decay of coherence to discuss to what extent several noisy channels affects the coherence. We find that the decay rate is independent of the initial state parameters but only related to parameters of the phase flip channels, the depolarizing channels, and the amplitude channels. However, the decay rate is related to the initial state parameters and parameters of the bit flip channels. Contrary to the view at first glance, we find that the bit flip channels even have cohering power.

     

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.     

Dynamics of Quantum Coherence in Bell-Diagonal States under Markovian Channels

We study the curves of coherence for the Bell-diagonal states including l_1-norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase flip channel, we find frozen coherence under l_1 norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. Also, we study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem n times and find that coherence under depolarizing channel decreases initially then increases for small n and tends to zero for large n. The dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels is discussed.     

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.     

Coherence migration in high-dimensional bipartite systems

The conservation law for first-order coherence and mutual correlation of a bipartite qubit state was firstly proposed by Svozilík et al., and their theories laid the foundation for the study of coherence migration under unitary transformations. In this paper, we generalize the framework of first-order coherence and mutual correlation to an arbitrary (m $\otimes$ n)-dimensional bipartite composite state by introducing an extended Bloch decomposition form of the state. We also generalize two kinds of unitary operators in high-dimensional systems, which can bring about coherence migration and help to obtain the maximum or minimum first-order coherence. Meanwhile, the coherence migration in open quantum systems is investigated. We take depolarizing channels as examples and establish that the reduced first-order coherence of the principal system over time is completely transformed into mutual correlation of the (2 $\otimes$ 4)-dimensional system-environment bipartite composite state. It is expected that our results may provide a valuable idea or method for controlling the quantum resource such as coherence and quantum correlations.     

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.     

Robustness of two-qubit and three-qubit states in correlated quantum channels

We investigate how the correlated actions of quantum channels affect the robustness of entangled states. We consider the Bell-like state and random two-qubit pure states in the correlated depolarizing, bit flip, bit-phase flip, and phase flip channels. It is found that the robustness of two-qubit pure states can be noticeably enhanced due to the correlations between consecutive actions of these noisy channels, and the Bell-like state is always the most robust one. We also consider the robustness of three-qubit pure states in correlated noisy channels. For the correlated bit flip and phase flip channels, the result shows that although the most robust and most fragile states are locally unitary equivalent, they exhibit different robustness in different correlated channels, and the effect of channel correlations on them is also significantly different. However, for the correlated depolarizing and bit-phase flip channels, the robustness of two special three-qubit pure states is exactly the same. Moreover, compared with the random three-qubit pure states, they are neither the most robust states nor the most fragile states.     

Relativistic Quantum Bayesian Game Under Decoherence

We study how Unruh effect and quantum noise affect the payoffs of a quantum conflicting interest Bayesian game. Three types of noisy channels, i.e., the amplitude damping channel, the depolarizing channel and the phase damping channel, are employed to model the decoherence processes. We find that Unruh effect weakens the payoffs in the quantum game and the quantum payoffs are lower than the classical payoffs when the acceleration parameter is large enough. However, the variation of the payoffs with the decoherence parameter is not always monotonic. Sometimes more decoherence may lead to higher payoffs.     

Degradation of Grover’s search under collective phase flips in queries to the oracle

We address the case in which querying the oracle in Grover’s algorithm is exposed to noise including phase distortions. The oracle-box wires can be altered by an opposing party that tries to prevent reception of correct data from the oracle. This situation reflects an experienced truth that any access to prophetic knowledge cannot be common and direct. To study this problem, we introduce a simple model of collective phase distortions on the basis of a phase-damping channel. In the model, the probability of success is not altered via the oracle-box wires per se. Phase distortions of the considered type can hardly be detected via any one-time query to the oracle. However, the probability of success is significantly changed when such errors are introduced as an intermediate step in the Grover iteration. We investigate the probability of success with respect to variations of the parameter that characterizes the amount of phase errors. It turns out that the probability of success decreases significantly even if the error is not very high. Moreover, this probability quickly reduces to the value of one half, which corresponds to the completely mixed state. We also study trade-off relations between quantum coherence and the probability of success in the presence of noise of the considered type.     

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.     

Mutual Information of Pauli Channels with Correlated Noise

A general formula for the mutual information of the Paufi channels with memory modelled by correlated noise is derived. It is shown that the mutual information depends on the channel shrinking factor, the input state parameter and the channel memory coefficient. The analyses based on the general formula reveal that the entanglement is always a useful resource to enhance the mutual information of some Pauli channels, such as the bit flip channel and the bit-phase flip channel. Our analyses also show that the entanglement is not advantageous to the reliable transmission of classical information for some Pauli channels at any time, such as the phase flip channel and the phase damping channel.     

Dense coding capacity in correlated noisy channels with weak measurement

Capacity of dense coding via correlated noisy channel is greater than that via uncorrelated noisy channel. It is shown that the weak measurement and reversal measurement need to further improve their quantum dense coding capacity in correlated amplitude damping channel, but this improvement is very small in correlated phase damping channel and correlated depolarizing channel.     

与XY双自旋链耦合的双量子比特系统的关联性与相干性

研究了双量子比特系统中在具有Dzyaloshinsky-Moriya相互作用的独立XY自旋链环境下的相干性与关联性动力学.推导出相干性与关联性的演化规律.发现在自旋链的临界点附近,当tt_0时,系统相干性的演化与经典关联完全相同;而在tt_0时,则与量子关联完全相同;在t_0时刻,量子关联突变为经典关联.     

Dynamics of entanglement under decoherence in noninertial frames

In this paper,we investigate the entanglement dynamics of a two-qubit entangled state coupled with its noisy environment,and plan to utilize weak measurement and quantum reversal measurement to study the entanglement dynamics under different decoherence channels in noninertial frames.Through the calculations and analyses,it is shown that the weak measurement can prevent entanglement from coupling to the amplitude damping channel,while the system is under the phase damping and flip channels.This protection protocol cannot prevent entanglement but will accelerate the death of entanglement.In addition,if the system is in the noninertial reference frame,then the effect of weak measurement will be weakened for the amplitude damping channel.Nevertheless,for other decoherence channels,the Unruh effect does not affect the quantum weak measurement,the only exception is that the maximum value of entanglement is reduced to√2/2of the original value in the inertial frames.