Entanglement dynamics of non-inertial observers in a correlated environment

Effect of decoherence and correlated noise on the entanglement of X-type state of the Dirac fields in the non-inertial frame is investigated. A two qubit X-state is considered to be shared between the partners where Alice is in inertial frame and Rob in an accelerated frame. The concurrence is used to quantify the entanglement of the X-state system influenced by time correlated amplitude damping, depolarizing and bit flip channels. It is seen that amplitude damping and bit flip channels heavily influence the entanglement of the system as compared to the depolarizing channel. It is found possible to avoid entanglement sudden death (ESD) for all the channels under consideration for μ > 0.75 for any type of initial state. No ESD behaviour is seen for depolarizing channel in the presence of correlated noise for entire range of decoherence parameter p and Rob’s acceleration r. It is also seen that the effect of environment is much stronger than that of acceleration of the accelerated partner. Furthermore, it is investigated that correlated noise compensates the loss of entanglement caused by the Unruh effect.     

Decoherence and entanglement degradation of a qubit-qutrit system in non-inertial frames

We study the effect of decoherence on a qubit-qutrit system under the influence of global, local and multilocal decoherence in non-inertial frames. We show that the entanglement sudden death can be avoided in non-inertial frames in the presence of amplitude damping, depolarizing and phase damping channels at lower level of decoherence. However, degradation of entanglement is seen due to Unruh effect. It is seen that for lower values of decoherence, the depolarizing channel heavily degrades the entanglement as compared to the amplitude damping and phase damping channels. Entanglement sudden birth is also seen in case of depolarizing channel. However, for higher values of decoherence parameters, amplitude damping channel dominantly degrades the entanglement of the hybrid system. Entanglement sudden death is not seen for any value of acceleration of the accelerated observer “Rob” in case of phase damping channel. Further more, a symmetrical behaviour of negativity is seen for depolarizing channel.     

Distinguishing quantum channels via magic squares game

We study the effect of quantum memory in magic squares game when played in quantum domain. We consider different noisy quantum channels and analyze their influence on the magic squares quantum pseudo-telepathy game. We show that the probability of success can be used to distinguish the quantum channels. It is seen that the mean success probability decreases with increase of quantum noise. Where as the mean success probability increases with increase of quantum memory. It is also seen that the behaviour of amplitude damping and phase damping channels is similar. On the other hand, the behaviour of depolarizing channel is similar to the flipping channels. Therefore, the probability of success of the game can be used to distinguish the quantum channels.     

几种确定型量子程序的可达和终止验证

讨论了单量子比特空间中,比特翻转、相位翻转、去极化、幅值阻尼和相位阻尼等量子信道作为特殊的非确定型量子程序—确定型量子程序,从计算基态运行时程序的可达集合和它们终止及发散的情况。研究表明:这些量子信道从计算基态运行时,有的量子程序的终止和发散与刻画量子信道的参数有紧密的联系,而有的量子程序的终止和发散与刻画量子信道的参数没有联系。     

Quantum discord amplification of fermionic systems in an accelerated frame

Quantum discord of fermionic systems in the relativistic regime, that is, beyond the single-mode approximation (SMA) is investigated. It is shown that quantum discord is amplified for the fermionic system in non-inertial frames irrespective of the choice of state, region and level of mixedness. This ensures that the phenomenon of amplification can actually happen in the relativistic regime. It is seen that quantum discord converges at infinite acceleration limit, which means that it becomes independent of $q_{R}$ (Unruh modes) beyond SMA. This implies that most of the tensor product structures already used in the literature to compute quantum field correlations in relativistic quantum information cannot give rise to physical results. The dynamics of quantum discord is investigated under amplitude damping, depolarizing and flipping channels. The vanishing behavior of quantum discord is seen for higher level of decoherence in the infinite acceleration limit. The depolarizing channel dominantly affects the fermionic quantum discord as compared to the amplitude damping channel. It means that the depolarizing channel has most destructive influence on the discord of the fermionic systems. Moreover, the effect of environment on the discord is much stronger than that of the acceleration of non-inertial frames.     

Decoherence effects in the quantum qubit flip game using Markovian approximation

We are considering a quantum version of the penny flip game, whose implementation is influenced by the environment that causes decoherence of the system. In order to model the decoherence, we assume Markovian approximation of open quantum system dynamics. We focus our attention on the phase damping, amplitude damping and amplitude raising channels. Our results show that the Pauli strategy is no longer a Nash equilibrium under decoherence. We attempt to optimize the players’ control pulses in the aforementioned setup to allow them to achieve higher probability of winning the game compared with the Pauli strategy.     

Dynamics of relative entropy of coherence under Markovian channels

We study the relative entropy of coherence under the effect of certain one-qubit channels that are Markovian and noisy. The cohering power and decohering power of phase damping, amplitude damping, flip and depolarizing channels are analytically calculated. For phase damping channel, the decohering power on the \(x,\ y,\) and z bases is the same. The same phenomenon is observed for the flip and depolarizing channels. Further, we show that weak measurement and its reversal can be employed to suppress the decohering power of the amplitude damping channel.     

Different dynamics of classical and quantum correlations under decoherence

The dynamics of classical and quantum correlations under nondissipative and dissipative decoherences are analytically and numerically investigated with both one-side measures and two-side measures. Specifically, two qubits under local amplitude damping decoherence and depolarizing decoherence channels are considered. We show that, under the action of amplitude damping decoherence, both the entanglement and correlations of the different types of initial states with same initial values, suffer different types of dynamics. Moreover, the transfers of the entanglement and correlations between the system and the environment for different types of initial states are also shown to be different. While for the action of depolarizing decoherence, there does not exist sudden change in the decay rates of both the classical and quantum correlations, which is different from some other nondissipative channels. Furthermore, the quantum dissonance can be found to keep unchanged under the action of depolarizing decoherence. Such different dynamic behaviors of different noisy quantum decoherence channels reveal distinct transmission performance of classical and quantum information.     

Dynamics of measurement-induced nonlocality under decoherence

Measurement-induced nonlocality (MIN)—captures nonlocal effects of a quantum state due to local von Neumann projective measurements, is a bona-fide measure of quantum correlation between constituents of a composite system. In this paper, we study the dynamical behavior of entanglement (measured by concurrence), Hilbert–Schmidt MIN and fidelity-based MIN (F-MIN) under local noisy channels such as hybrid (consists of bit flip, phase flip and bit-phase flip), generalized amplitude damping (GAD) and depolarizing channels for the initial Bell diagonal state. We observed that while sudden death of entanglement occurs in hybrid and GAD channels, MIN and F-MIN are more robust against such noises. Finally, we demonstrate the revival of MIN and F-MIN after a dark point of time against depolarizing noise.     

Multipartite concurrence for X states under decoherence

In this paper, the dynamics evolution of multipartite entanglement for each qubit interacting with a local decoherence channel, such as phase damping, phase flip, bit flip and bit-phase flip channel, is investigated. It is shown that the initial concurrence monotonously decreases much faster with the number of qubit increases and there exists entanglement sudden death (ESD) only for the bit flip channel and bit-phase flip channels. Meanwhile, the time of ESD decreases with the increases of the number of qubit in the multipartite system.     

Decoherence dynamics of geometric measure of quantum discord and measurement induced nonlocality for noninertial observers at finite temperature

Quantum discord quantifies the total non-classical correlations in mixed states. It is the difference between total correlation, measured by quantum mutual information, and the classical correlation. Another step forward towards the quantification of quantum discord was by Daki? et al. (Phys Rev Lett 105:190502, 2010) who introduced the geometric measure of quantum discord (GMQD) and derived an explicit formula for a two-qubit state. Recently, Luo and Fu (Phys Rev Lett 106:120401, 2011) introduced measurement-induced nonlocality (MIN) as a measure of nonlocality for a bipartite quantum system. The dynamics of GMQD is recently considered by Song et al. (arXiv: quant/ph.1203.3356) and Zhang et al. (Eur Phys J D 66:34, 2012) for inertial observers. However, the topic requires due attention in noninertial frames, particularly, from the perspective of MIN. Here I consider $X$ -structured bipartite quantum system in noninertial frames and analyze the decoherence dynamics of GMQD and MIN at finite temperature. The dynamics under the influence of amplitude damping, depolarizing and phase flip channels is discussed. It is worth-noting that initial state entanglement plays an important role in bipartite states. It is possible to distinguish the Bell, Werner and general type initial quantum states using GMQD. Sudden transition in the behaviour of GMQD and MIN occurs depending upon the mean photon number of the local environment. The transition behaviour disappears for larger values of $\bar{n},$ i.e. $\bar{n}>0.3.$ It becomes more prominent, when environmental noise is introduced in the system. In the presence of environmental noise, as we increase the value of acceleration $r$ , GMQD and MIN decay due to Unruh effect. The effect is prominent for the phase flip and amplitude damping channels. However, in case of depolarizing channel, no sudden change in the behaviour of GMQD and MIN is observed. The environmental noise has stronger affect on the dynamics of GMQD and MIN as compared to the Unruh effect. Furthermore, Werner like states are more robust than General type initial states at finite temperature.     

Quantum coherence of two-qubit over quantum channels with memory

Using the axiomatic definition of the quantum coherence measure, such as the \(l_{1}\) norm and the relative entropy, we study the phenomena of two-qubit system quantum coherence through quantum channels where successive uses of the channels are memory. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels effect on quantum coherence have been discussed in detail. The results show that quantum channels with memory can efficiently protect coherence from noisy channels. Particularly, as channels with perfect memory, quantum coherence is unaffected by the phase damping as well as depolarizing channels. Besides, we also investigate the cohering and decohering power of quantum channels with memory.     

Entanglement sudden death in the presence of quantum decoherence in non-inertial frames: beyond the single-mode approximation

The entanglement behavior of Dirac field under quantum decoherence in the non-inertial frames is studied beyond the single-mode approximation. Two kinds of damping processes, amplitude damping channel and dephasing channel, are investigated as the sources of decoherence. The decoherence and Unruh effect will lead to entanglement degradation. This study demonstrates that as two observers experience the decoherence, the entanglement sudden death will occur in amplitude damping channel. Our study shows that the entanglement sudden death will occur in the presence of Unruh effect accompanying the decoherence. In addition, our results show that the amplitude damping channel has more remarkable impacts than the dephasing channel.     

Teleportation of a qubit using entangled non-orthogonal states: a comparative study

The effect of non-orthogonality of an entangled non-orthogonal state-based quantum channel is investigated in detail in the context of the teleportation of a qubit. Specifically, average fidelity, minimum fidelity and minimum assured fidelity (MASFI) are obtained for teleportation of a single-qubit state using all the Bell-type entangled non-orthogonal states known as quasi-Bell states. Using Horodecki criterion, it is shown that the teleportation scheme obtained by replacing the quantum channel (Bell state) of the usual teleportation scheme by a quasi-Bell state is optimal. Further, the performance of various quasi-Bell states as teleportation channel is compared in an ideal situation (i.e., in the absence of noise) and under different noise models (e.g., amplitude and phase damping channels). It is observed that the best choice of the quasi-Bell state depends on the amount non-orthogonality, both in noisy and noiseless case. A specific quasi-Bell state, which was found to be maximally entangled in the ideal conditions, is shown to be less efficient as a teleportation channel compared to other quasi-Bell states in particular cases when subjected to noisy channels. It has also been observed that usually the value of average fidelity falls with an increase in the number of qubits exposed to noisy channels (viz., Alice’s, Bob’s and to be teleported qubits), but the converse may be observed in some particular cases.     

Generation and protection of steady-state quantum correlations due to quantum channels with memory

We have proposed a scheme of the generation and preservation of two-qubit steady-state quantum correlations through quantum channels where successive uses of the channels are correlated. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels, have been taken into account. Some analytical or numerical results are presented. The effect of channels with memory on dynamics of quantum correlations has been discussed in detail. The results show that steady-state entanglement between two initial qubits whose initial states are prepared in a specific family states without entanglement subject to amplitude damping channel with memory can be generated. The entanglement creation is related to the memory coefficient of channel \(\mu \). The stronger the memory coefficient of channel \( \mu \) is, the more the entanglement creation is, and the earlier the separable state becomes the entangled state. Besides, we compare the dynamics of entanglement with that of quantum discord when a two-qubit system is initially prepared in an entangled state. We show that entanglement dynamics suddenly disappears, while quantum discord dynamics displays only in the asymptotic limit. Furthermore, two-qubit quantum correlations can be preserved at a long time in the limit of \(\mu \rightarrow 1\).     

Restoration of three-qubit entanglements and protection of tripartite quantum state sharing over noisy channels via environment-assisted measurement and reversal weak measurement

The restoration of three-qubit entanglement is investigated under the amplitude damping (AD) decoherence with environment-assisted measurement (EAM) and reversal weak measurement (RWM). The results show that there exists a critical strength of RWM dependent of the initial three-qubit entangled state under a given damping rate of the AD channel, i.e., if the selected RWM strength is higher than the critical strength, the entanglement will be reduced compared to one without RWM. Some three-qubit entangled states cannot be restored. We calculated the restorable condition of the initial entanglement and illustrated the valid area for three-qubit GHZ state and W state. Fortunately, an optimal strength of RWM corresponding to a certain damping rate of AD channels can be found within the valid area for a restorable initial state, by which a noise-infected entanglement can be restored to its maximum value. Particularly, when three qubits of W state are subjected to their respective AD channels, due to the symmetry of three qubits, the W state cannot be decohered provided the EAM is successful, and no RWM is required. This is beneficial to quantum communication over the noisy channel. Applying this protection regime to tripartite QSS and taking appropriate initial entangled state as the quantum channel, the fidelity of the shared state can be improved to the maximum 1 probabilistically. Thus, the decoherence effect of the noisy channels can be significantly suppressed or even avoided.     

Remark on the additivity conjecture for a quantum depolarizing channel

We consider bistochastic quantum channels generated by unitary representations of a discrete group. We give a proof of the additivity conjecture for a quantum depolarizing channel Φ based on the decreasing property of the relative entropy. We show that the additivity conjecture holds for a channel Ξ = Ψ o Φ, where Ψ is a phase damping channel.     

The effect of quantum noise on two different deterministic remote state preparation of an arbitrary three-particle state protocols

Multi-particle quantum state deterministic remote preparation is a fundamental and important technical branch in quantum communication. Since quantum noise is unavoidable in realistic quantum communication, it is important to analyze the effect of noise on multi-particle quantum communication protocols. In this paper, we study the effects of noise, such as amplitude damping, phase damping, bit-flip and depolarizing noises, on two deterministic remote preparation of an arbitrary three-particle state protocols, which are based on two different entangled channels, namely \(\chi \) state and Brown state. The detailed mathematical analysis shows that the output states of two deterministic remote state preparation (DRSP) protocols are the same in the same noisy environment. That is to say, in the same noisy environment, the effects of noise on two DRSP protocols are the same. This conclusion proves that these two DRSP protocols will produce the same arbitrary three-particle states in the same noise channel environment, and so that these protocols are inherently convergent and can be substituted for each other in certain circumstances. In addition, this paper also takes three-particle states \(a\left| {000} \right\rangle + b{\mathrm{e}^{ic}}\left| {111} \right\rangle \) as an example and studies the relationship between the fidelity, the target state and the size of the noise factor. The results show that if the target state can be selected, an appropriate target state can effectively resist on the bit-flip noise. If the target state cannot be selected, as the increase in the size of noise factor, the fidelities of the two DRSP schemes in the amplitude damping noise and phase damping noise are always larger than those in the bit-flip noise and depolarizing noise. This conclusion indicates that two protocols have better resistance on amplitude damping and phase damping noise than the bit-flip and depolarizing noises. These findings and analyses will provide valid help in deterministic remote preparation of an arbitrary three-particle state in a noisy environment.     

Quantum decoherence of Dirac fields in non-inertial frames beyond the single-mode approximation

The effects of Quantum decoherence on Dirac fields in an accelerated frame are studied beyond the single-mode approximation. The decoherence phenomena are investigated through the quantum channel approach using the amplitude damping channel and the dephasing one. The entanglement and purity are two distinct quantum features which are investigated. We have assumed that only the non-inertial observer experiences decoherence phenomena. The associated effects of the acceleration, damping rate, and dephasing rate are considered. It is found that acceleration and decoherence rates will decrease the degree of entanglement and purity. It turns out that beyond the single-mode approximation, the maximal entangled state cannot be achieved. Moreover, a comparison between the damping and dephasing processes is done which reveals the fact that damping effects on the entanglement are stronger than dephasing effects, whereas dephasing has stronger effects on the purity.