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 \(\mu \rightarrow 1\).     

Noise effects on entanglement distribution by separable state

We investigate noise effects on the performance of entanglement distribution by separable state. We consider a realistic situation in which the mediating particle between two distant nodes of the network goes through a noisy channel. For a large class of noise models, we show that the average value of distributed entanglement between two parties is equal to entanglement between particular bipartite partitions of target qubits and exchange qubit in intermediate steps of the protocol. This result is valid for distributing two-qubit/qudit and three-qubit entangled states. In explicit examples of the noise family, we show that there exists a critical value of noise parameter beyond which distribution of distillable entanglement is not possible. Furthermore, we determine how this critical value increases in terms of Hilbert space dimension, when distributing d-dimensional Bell states.     

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.     

Pairwise quantum correlations of a three-qubit XY chain with phase decoherence

Quantum correlations, including entanglement and discord with its geometric measure in a three-qubit Heisenberg XY chain, with phase decoherence, are investigated when a nonuniform magnetic field is applied. When the qubits are initially in an unentangled state, the nearest neighbor pairwise correlations are destroyed by phase decoherence, but stationary correlations appear for next-to-neighbor qubits. With an inhomogeneous magnetic field, the stationary correlations appear for nearest neighbor qubits and they disappear for next-to-nearest neighbor qubits. But when the qubits are initially in an entangled state, an inhomogeneous magnetic field can enhance the stationary correlations of next-to-neighbor qubits, but it cannot do so for nearest neighbor qubits. The decoherence effect on stationary correlations is much stronger for next-to-nearest neighbor qubits than it is for nearest neighbor qubits. Finally, a uniform magnetic field can affect the correlations when the qubits are initially in an entangled state, but it cannot affect them when the qubits are initially in an unentangled state.     

Transferring multiqubit entanglement onto memory qubits in a decoherence-free subspace

Different from the previous works on generating entangled states, this work is focused on how to transfer the prepared entangled states onto memory qubits for protecting them against decoherence. We here consider a physical system consisting of n operation qubits and 2n memory qubits placed in a cavity or coupled to a resonator. A method is presented for transferring n-qubit Greenberger–Horne–Zeilinger (GHZ) entangled states from the operation qubits (i.e., information processing cells) onto the memory qubits (i.e., information memory elements with long decoherence time). The transferred GHZ states are encoded in a decoherence-free subspace against collective dephasing and thus can be immune from decoherence induced by a dephasing environment. In addition, the state transfer procedure has nothing to do with the number of qubits, the operation time does not increase with the number of qubits, and no measurement is needed for the state transfer. This proposal can be applied to a wide range of hybrid qubits such as natural atoms and artificial atoms (e.g., various solid-state qubits).     

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.     

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.     

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.     

Abrupt decay of entanglement and quantum communication through noise channels

We investigate the dynamics of two qubits state through the Bloch channel. Starting from partially entangled states as input state, the output states are more robust compared with those obtained from initial maximally entangled states. Also the survivability of entanglement increased as the absolute equilibrium values of the channel increased or the ratio between the longitudinal and transverse relaxation times gets smaller. The ability of using the output states as quantum channels to perform quantum teleportation is investigated. The useful output states are used to send information between two users by using the original quantum teleportation protocol.     

Preparing large-scale maximally entangled <Emphasis Type="Italic">W</Emphasis> states in optical system

We propose an optical scheme to prepare large-scale maximally entangled W states by fusing arbitrary-size polarization entangled W states via polarization-dependent beam splitter. Because most of the currently existing fusion schemes are suffering from the qubit loss problem, that is the number of the output entangled qubits is smaller than the sum of numbers of the input entangled qubits, which will inevitably decrease the fusion efficiency and increase the number of fusion steps as well as the requirement of quantum memories, in our scheme, we design a effect fusion mechanism to generate \(W_{m+n}\) state from a n-qubit W state and a m-qubit W state without any qubit loss. As the nature of this fusion mechanism clearly increases the final size of the obtained W state, it is more efficient and feasible. In addition, our scheme can also generate \(W_{m+n+t-1}\) state by fusing a \(W_m\), a \(W_n\) and a \(W_t\) states. This is a great progress compared with the current scheme which has to lose at least two particles in the fusion of three W states. Moreover, it also can be generalized to the case of fusing k different W states, and all the fusion schemes proposed here can start from Bell state as well.     

Bidirectional controlled teleportation by using nine-qubit entangled state in noisy environments

A theoretical scheme is proposed to implement bidirectional quantum controlled teleportation (BQCT) by using a nine-qubit entangled state as a quantum channel, where Alice may transmit an arbitrary two-qubit state called qubits \(A_1\) and \(A_2\) to Bob; and at the same time, Bob may also transmit an arbitrary two-qubit state called qubits \(B_1\) and \(B_2\) to Alice via the control of the supervisor Charlie. Based on our channel, we explicitly show how the bidirectional quantum controlled teleportation protocol works. And we show this bidirectional quantum controlled teleportation scheme may be determinate and secure. Taking the amplitude-damping noise and the phase-damping noise as typical noisy channels, we analytically derive the fidelities of the BQCT process and show that the fidelities in these two cases only depend on the amplitude parameter of the initial state and the decoherence noisy rate.     

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.     

A revisit to non-maximally entangled mixed states: teleportation witness,noisy channel and discord

We constructed a class of non-maximally entangled mixed states (Adhikari et al. in Quantum Inf Comput 10:0398, 2010) and extensively studied their entanglement properties and also their usefulness as teleportation channels. In this article, we have revisited our constructed state and have studied it from three different perspectives. Since every entangled state is associated with a witness operator, we have found a suitable entanglement as well as teleportation witness operator for our non-maximally entangled mixed states. We considered the noisy channel’s effects on our constructed states to see how much it affects the states’ capacities as teleportation channels. For this purpose, we have mainly focussed on amplitude damping channel. A comparative study on concurrence and quantum discord of our constructed state of Adhikari et al. (2010) has also been carried out here.     

The general theory of three-party quantum secret sharing protocols over phase-damping channels

The general theory of three-party QSS protocols with the noisy quantum channels is discussed. When the particles are transmitted through the noisy quantum channels, the initial pure three-qubit tripartite entangled states would be changed into mixed states. We analyze the security of QSS protocols with the different kinds of three-qubit tripartite entangled states under phase-damping channels and figure out, for different kinds of initial states, the successful probabilities that Alice’s secret can be recovered by legal agents are different. Comparing with one recent QSS protocol based on GHZ states, our scheme is secure, and has a little smaller key rate than that of the recent protocol.     

Disentanglement and quantum states transitions dynamics in spin-qutrit systems: dephasing random telegraph noise and the relevance of the initial state

Using negativity and realignment criterion as quantifiers of free and bound entanglements respectively, we present in details the analytical study of the entanglements and quantum states transitions dynamics in a two-qutrit system driven by dephasing random telegraph noise channel(s). Both collective and independent system–environment couplings as well as the Markovian and the non-Markovian regimes of the noise channel(s) are considered. Two non-equivalent initial states and their locally equivalent through a local unitary operation (LUO) are also considered. We demonstrate a stronger entanglement under independent Markovian environments than with a collective one; meanwhile, for the non-Markovian regime, entanglement is stronger under a collective environment than with independent ones. States transitions as well as the (re)activation of bound entanglement (for initially free entangled states) can be found for a specific class of initial states, but can, however, be avoided by means of a LUO on the initial state. While unavoidable disentanglement occurs for independents coupling, we demonstrate the possibility of indefinite free entanglement survival in the qutrit system under a common environment by converting the initial entangled state using the local unitary operation.     

Quantum teleportation with partially entangled states via noisy channels

Using a partially entangled EPR-type state as quantum channel, we investigate quantum teleportation (QT) of a qubit state in noisy environments by solving the master equation in the Lindblad form. We analyze the different influence for the partially entangled EPR-type channel and the EPR channel on the fidelity and the average fidelity of the QT process in the presence of Pauli noises. It is found that the fidelity depends on the type and the strength of the noise, and the initial state to be teleported. Moreover, the EPR channel is more robust than the partially entangled EPR-type channel against the influence of the noises. It is also found that the partially entangled EPR-type channel enables the average fidelity as a function of the decoherence parameter $kt$ to decay with different velocities for different Pauli noises.     

Dynamics of tripartite quantum correlations and decoherence in flux qubit systems under local and non-local static noise

We investigate the dynamics of entanglement, decoherence and quantum discord in a system of three non-interacting superconducting flux qubits (fqubits) initially prepared in a Greenberger–Horne–Zeilinger (GHZ) state and subject to static noise in different, bipartite and common environments, since it is recognized that different noise configurations generally lead to completely different dynamical behavior of physical systems. The noise is modeled by randomizing the single fqubit transition amplitude. Decoherence and quantum correlations dynamics are strongly affected by the purity of the initial state, type of system–environment interaction and the system–environment coupling strength. Specifically, quantum correlations can persist when the fqubits are commonly coupled to a noise source, and reaches a saturation value respective to the purity of the initial state. As the number of decoherence channels increases (bipartite and different environments), decoherence becomes stronger against quantum correlations that decay faster, exhibiting sudden death and revival phenomena. The residual entanglement can be successfully detected by means of suitable entanglement witness, and we derive a necessary condition for entanglement detection related to the tunable and non-degenerated energy levels of fqubits. In accordance with the current literature, our results further suggest the efficiency of fqubits over ordinary ones, as far as the preservation of quantum correlations needed for quantum processing purposes is concerned.     

Three-player quantum Kolkata restaurant problem under decoherence

Effect of quantum decoherence in a three-player quantum Kolkata restaurant problem is investigated using tripartite entangled qutrit states. Different qutrit channels such as, amplitude damping, depolarizing, phase damping, trit-phase flip and phase flip channels are considered to analyze the behaviour of players payoffs. It is seen that Alice’s payoff is heavily influenced by the amplitude damping channel as compared to the depolarizing and flipping channels. However, for higher level of decoherence, Alice’s payoff is strongly affected by depolarizing noise. Whereas the behaviour of phase damping channel is symmetrical around 50% decoherence. It is also seen that for maximum decoherence (p = 1), the influence of amplitude damping channel dominates over depolarizing and flipping channels. Whereas, phase damping channel has no effect on the Alice’s payoff. Therefore, the problem becomes noiseless at maximum decoherence in case of phase damping channel. Furthermore, the Nash equilibrium of the problem does not change under decoherence.     

Matched witness for multipartite entanglement

Entanglement criteria for multipartite entangled states are obtained by matching witnesses to multipartite entangled states. The necessary and sufficient criterion of separability for three qubit X states is given as an example to illustrate the procedure of finding a criterion. The result is utilized to obtain the noise tolerance of W state. The necessary and sufficient criteria of three partite separability and full separability for four qubit noisy cluster states, three partite separability for four qubit noisy GHZ states are obtained.