SLOCC orbit of rank-deficient two-qubit states: quantum entanglement,quantum discord and EPR steering

We study selected aspects of non-classical correlations of arbitrary states from the stochastic local operations and classical communication orbit of rank-deficient two-qubit states. In particular, we find explicitly entanglement of formation and quantum discord for these states. Moreover, we determine and analyze the Einstein–Podolsky–Rosen steering ellipsoids corresponding to these states.     

Post-Markovian dynamics of quantum correlations: entanglement versus discord

Dynamics of an open two-qubit system is investigated in the post-Markovian regime, where the environments have a short-term memory. Each qubit is coupled to separate environment which is held in its own temperature. The inter-qubit interaction is modeled by XY–Heisenberg model in the presence of spin–orbit interaction and inhomogeneous magnetic field. The dynamical behavior of entanglement and discord has been considered. The results show that quantum discord is more robust than quantum entanglement, during the evolution. Also the asymmetric feature of quantum discord can be monitored by introducing the asymmetries due to inhomogeneity of magnetic field and temperature difference between the reservoirs. By employing proper parameters of the model, it is possible to maintain nonvanishing quantum correlation at high degree of temperature. The results can provide a useful recipe for studying dynamical behavior of two-qubit systems such as trapped spin electrons in coupled quantum dots.     

Quantum discord of ensemble of quantum states

We highlight an information-theoretic meaning of quantum discord as the gap between the accessible information and the Holevo bound in the framework of ensemble of quantum states. This complementary relationship implies that a large amount of preexisting arguments about the evaluation of quantum discord can be directly applied to the accessible information and vice versa. For an ensemble of two pure qubit states, we show that one can avoid the optimization problem with the help of the Koashi–Winter relation. Further, for the general case (two mixed qubit states), we recover the main results presented by Fuchs and Caves (Phys Rev Lett 73:3047, 1994), but totally from the perspective of quantum discord. Following this line of thought, we also investigate the geometric discord as an indicator of quantumness of ensembles in detail. Finally, we give an example to elucidate the difference between quantum discord and geometric discord with respect to optimal measurement strategies.     

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.     

Predominance of entanglement of formation over quantum discord under quantum channels

We present a study of the behavior of two different figures of merit for quantum correlations, entanglement of formation and quantum discord, under quantum channels showing how the former can, counterintuitively, be more resilient to such environments spoiling effects. By exploiting strict conservation relations between the two measures and imposing necessary constraints on the initial conditions we are able to explicitly show this predominance is related to build-up of the system-environment correlations.     

Realignment entanglement criterion of phase damped Gaussian states

We derive the realignment entanglement criterion for non-Gaussian states prepared by two mode symmetric Gaussian states undergoing phase damping. The entanglement detecting ability is compared with that of second moment criterion and Fock space criterion of positive partial transpose. New non-Gaussian entangled states are detected.     

基于Bell态与其纠缠性质的量子密钥分发

为了提高量子密钥分发的可行性、安全性和效率,在通信双方间通过构建经典信道和量子信道,提出了一种基于Bell态与其纠缠性质的量子密钥分发协议.该协议可行、安全、简单有效,通过严格的数学推导证明了窃听者不可能获取密钥而不被发现.此外,得出了该协议效率与安全的数学模型,并通过MATLAB仿真分析了协议效率与安全的关系.     

基于Bell态纠缠交换的身份认证协议

提出了一种新的量子身份认证协议,该协议以Bell态为传输载体,利用Bell态纠缠交换和Bell基测量对通信用户进行身份认证。两个Bell态的传送过程中不需要做任何的幺正变换,只需要执行Bell基测量和按位异或运算就可以实现信息的传输。整个过程中,量子载体操作简单且容易实现。此外,也验证了此协议的正确性。     

Genuine three-partite entanglement in coherent states via permutation and parity symmetries

By using the works, Spiridonov (Phys Rev A 52:1909, 1995), and Wang et al. (J Phys A Math Gen 33:7451, 2000), we propose an approach to obtain genuine three-partite entangled coherent states in which the permutation symmetry and the parity one play crucial roles. We exploit the permutation and parity symmetry to construct entanglement in the standard coherent states of a system composed of three-mode bosonic field and three identical atoms. It is shown that by making use of entanglement witnesses (EW) based on GHZ-states the reduced density matrices of the three-mode bosonic field and three-atomic subsystems, after encoding as three-qubit systems, in some range of their respective parameters, are genuinely entangled.     

Quantum correlations in a family of bipartite separable qubit states

Quantum correlations (QCs) in some separable states have been proposed as a key resource for certain quantum communication tasks and quantum computational models without entanglement. In this paper, a family of nine-parameter separable states, obtained from arbitrary mixture of two sets of bi-qubit product pure states, is considered. QCs in these separable states are studied analytically or numerically using four QC quantifiers, i.e., measurement-induced disturbance (Luo in Phys Rev A77:022301, 2008), ameliorated MID (Girolami et al. in J Phys A Math Theor 44:352002, 2011),quantum dissonance (DN) (Modi et al. in Phys Rev Lett 104:080501, 2010), and new quantum dissonance (Rulli in Phys Rev A 84:042109, 2011), respectively. First, an inherent symmetry in the concerned separable states is revealed, that is, any nine-parameter separable states concerned in this paper can be transformed to a three-parameter kernel state via some certain local unitary operation. Then, four different QC expressions are concretely derived with the four QC quantifiers. Furthermore, some comparative studies of the QCs are presented, discussed and analyzed, and some distinct features about them are exposed. We find that, in the framework of all the four QC quantifiers, the more mixed the original two pure product states, the bigger QCs the separable states own. Our results reveal some intrinsic features of QCs in separable systems in quantum information.     

Pairwise thermal entanglement and quantum discord in a three-ligand spin-star structure

In this work, we perform a comparative study between the pairwise thermal entanglement (PWTE) and thermal quantum discord (TQD) to detect quantum phase transitions (QPT)s in a three-ligand spin-star structure whose magnetic interactions are described by different model Hamiltonians such as pure Dzyaloshinskii–Moriya (DM) interaction, anisotropic Heisenberg model (XXZ), and XXZ model with the different components of the DM interaction. Representing the system’s energy spectrum, we also focus on the critical points of QPTs where the ground-state level crossing happens in such models. Taking advantage of the concurrence as a measure of the PWTE, we found that while the ligand–ligand concurrence in all models is sensitive to the ground-state level crossing, the concurrence between the central qubit and a ligand cannot exhibit a QPT. In contrast, the TQD between any two arbitrary qubits can be a signature of a QPT in a large range of temperature. However, depending on the model studied, the behavior of the TQD at the critical point will be different. In addition, the TQD behaves quite differently than the concurrence. Moreover, in order to confirm the numerical results, we analytically study the entanglement behavior at the low-temperature limit as well as the high-temperature regime. We realized that, at the low-temperature limit, the maximum value of the concurrence is approximately equal to 0.33, independent of the model studied. On the other hand, at high-temperature regime, the concurrence is suppressed down to zero rapidly beyond a critical value of temperature. The dependence of the critical temperature on the DM interaction and the anisotropy parameter is obtained explicitly. Finally we show that there is a perfect agreement between the analytical results and the numerical predictions.     

Time-invariant discord: high temperature limit and initial environmental correlations

We present a thorough investigation of the phenomena of frozen and time-invariant quantum discord for two-qubit systems independently interacting with local reservoirs. Our work takes into account several significant effects present in decoherence models, which have not been yet explored in the context of time-invariant quantum discord, but which in fact must be typically considered in almost all realistic models. Firstly, we study the combined influence of dephasing, dissipation and heating reservoirs at finite temperature. Contrarily to previous claims in the literature, we show the existence of time-invariant discord at high temperature limit in the weak coupling regime and also examine the effect of thermal photons on the dynamical behavior of frozen discord. Secondly, we explore the consequences of having initial correlations between the dephasing reservoirs. We demonstrate in detail how the time-invariant discord is modified depending on the relevant system parameters such as the strength of the initial amount of entanglement between the reservoirs.     

Quantum private comparison protocol based on entanglement swapping of d-level Bell states

In this paper, we propose a quantum private comparison protocol based on entanglement swapping, where two distrustful parties can compare the values of their secrets with the help of a semi-trusted third party. The protocol can determine not only whether two secrets are equal, but also the size relationship between them. The two parties can deduce the comparison result based on the keys shared between them and the announcement of the third party. Others including the third party will learn nothing about the values of the secrets, as well as the comparison result. The security of our protocol is analyzed. Furthermore, all the particles can be reused in the same protocol model theoretically. So our protocol is efficient and feasible to expand in network service, which in turn gives a solution to the left problem in Lin et al. (Quantum Inf Process, doi:10.1007/s11128-012-0395-6, 2012).     

Quantum key distribution via tripartite coherent states

We propose a quantum key distribution protocol using Greenberger Horne Zeilinger tripartite coherent states. The sender and the receiver share similar key by exchanging the correlation coherent states, without basis reconciliation. This allows the protocol to have a transmission efficiency of 100% in a perfect quantum channel. The security of the protocol is ensured by tripartite coherent states correlation and homodyne detection, which allows to detect any eavesdropping easily.     

Quantum teleportation through noisy channels with multi-qubit GHZ states

We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger–Horne–Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equation with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for \(n\) -qubit GHZ states \(n\in \{4,5,6\}\) where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity, we show that 3GHZ state is more robust than \(n\) GHZ state under most noisy channels. However, \(n\) GHZ state preserves same quantum information with respect to Einstein–Podolsky–Rosen and 3GHZ states where the noise is in \(x\) direction in which the fidelity remains unchanged. We explicitly show that Jung et al.’s conjecture (Phys Rev A 78:012312, 2008), namely “average fidelity with same-axis noisy channels is in general larger than average fidelity with different-axes noisy channels,” is not valid for 3GHZ and 4GHZ states.     

Robustness measure of hybrid intra-particle entanglement,discord, and classical correlation with initial Werner state

Quantum information processing is largely dependent on the robustness of non-classical correlations, such as entanglement and quantum discord. However, all the realistic quantum systems are thermodynamically open and lose their coherence with time through environmental interaction. The time evolution of quantum entanglement, discord, and the respective classical correlation for a single, spin-1/2 particle under spin and energy degrees of freedom, with an initial Werner state, has been investigated in the present study. The present intra-particle system is considered to be easier to produce than its inter-particle counterpart. Experimentally, this type of system may be realized in the well-known Penning trap. The most stable correlation was identified through maximization of a system-specific global objective function. Quantum discord was found to be the most stable, followed by the classical correlation. Moreover, all the correlations were observed to attain highest robustness under initial Bell state, with minimum possible dephasing and decoherence parameters.     

Quantum network dense coding via continuous-variable graph states

We present a dense coding network based on continuous-variable graph state along with its corresponding protocol. A scheme to distill bipartite entanglement between two arbitrary modes in a graph state is provided in order to realize the dense coding network. We also analyze the capacity of network dense coding and provide a method to calculate its maximum mutual information. As an application, we analyze the performance of dense coding in a square lattice graph state network. The result showed that the mutual information of the dense coding is not largely affected by the complexity of the network. We conclude that the performance of dense coding network is very optimistic.     

Relativistic entanglement in single-particle quantum states using non-linear entanglement witnesses

In this study, the spin-momentum correlation of one massive spin- ${\frac{1}{2}}$ and spin-1 particle states, which are made based on the projection of a relativistic spin operator into timelike direction is investigated. It is shown that by using Non-Linear entanglement witnesses (NLEWs), the effect of Lorentz transformation would decrease both the amount and the region of entanglement.     

Quantum entanglement and the Bell matrix

We present a class of maximally entangled states generated by a high-dimensional generalisation of the cnot gate. The advantage of our constructive approach is the simple algebraic structure of both entangling operator and resulting entangled states. In order to show that the method can be applied to any dimension, we introduce new sufficient conditions for global and maximal entanglement with respect to Meyer and Wallach’s measure.     

Fault tolerant quantum key distributions using entanglement swapping of GHZ states over collective-noise channels

This work proposes two fault tolerant quantum key distribution (QKD) protocols. Each of which is robust under one kind of collective noises: collective-dephasing noise and collective-rotation noise, respectively. Due to the use of the entanglement swapping of Greenberger–Horne–Zeilinger (GHZ) state as well as the decoy logical qubits, the new protocols provide the best qubit efficiency among the existing fault tolerant QKD protocols over the same collective-noise channel. The receiver simply performs two Bell measurements to obtain the raw key. Moreover, the proposed protocols are free from several well-known attacks and can also be secure over a lossy channel.