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.     

Efficient hyperentanglement concentration for <Emphasis Type="Italic">N</Emphasis>-particle Greenberger–Horne–Zeilinger state assisted by weak cross-Kerr nonlinearity

In this scheme, based on the weak cross-Kerr nonlinearity, an hyperconcentration protocol for the arbitrary partially hyperentangled N-particle Greenberger–Horne–Zeilinger (GHZ) state is presented. Considering the N photons initially in the nonmaximally hyperentangled GHZ state in which photons are entangled simultaneously in the polarization and the spatial-mode degrees of freedom, we can obtain the maximally hyperentangled N-particle GHZ state by the projection measurements on the additional photons. Numerical simulation demonstrates that by iterating the entanglement concentration process, we can improve the success probability of the scheme. Furthermore, we discuss the feasibility of the setups of the protocol, concluding that the present protocol is feasible with existing experimental technology. All these advantages make this scheme more efficient and more convenient in quantum communication.     

Lower bounds of concurrence for <Emphasis Type="Italic">N</Emphasis>-qubit systems and the detection of <Emphasis Type="Italic">k</Emphasis>-nonseparability of multipartite quantum systems

Concurrence, as one of the entanglement measures, is a useful tool to characterize quantum entanglement in various quantum systems. However, the computation of the concurrence involves difficult optimizations and only for the case of two qubits, an exact formula was found. We investigate the concurrence of four-qubit quantum states and derive analytical lower bound of concurrence using the multiqubit monogamy inequality. It is shown that this lower bound is able to improve the existing bounds. This approach can be generalized to arbitrary qubit systems. We present an exact formula of concurrence for some mixed quantum states. For even-qubit states, we derive an improved lower bound of concurrence using a monogamy equality for qubit systems. At the same time, we show that a multipartite state is k-nonseparable if the multipartite concurrence is larger than a constant related to the value of k, the qudit number and the dimension of the subsystems. Our results can be applied to detect the multipartite k-nonseparable states.     

Bell inequality,steering, incompatibility and Leggett–Garg inequality under coarsening measurement

We investigate the effects of the coarsening measurement on the quantum-to-classical transition by Bell–Clauser–Horne–Shimony–Holt (Bell–CHSH) non-locality for the conventional two-qubit system, the Leggett–Garg inequality for a two-level system, and steering and incompatibility both in the equatorial plane for N measurement settings. We find that for any fixed N, steering is more vulnerable than incompatibility for coarsening measurement both in reference and in final resolution. For \(N=2\) measurement settings, under the coarsening measurement reference the Leggett–Garg inequality is the most robust, Bell–CHSH non-locality lies between steering and incompatibility, while in the coarsening measurement of final resolution for \(N=2\) measurement settings incompatibility is the most robust, steering and Bell–CHSH non-locality are equally vulnerable, and more than the Leggett–Garg inequality. However, as N increases, incompatibility and steering will become more robust than the Leggett–Garg inequality under the coarsening measurement in reference and in final resolution, respectively. Finally, for the Leggett–Garg inequality, we find that the robustness of the coarsening measurement reference is more than the coarsening temporal reference. In one word, the effects of coarsening measurement strongly depend on the ways of coarsening.     

Experimentally identifying the entanglement class of pure tripartite states

We use concurrence as an entanglement measure and experimentally demonstrate the entanglement classification of arbitrary three-qubit pure states on a nuclear magnetic resonance quantum information processor. Computing the concurrence experimentally under three different bipartitions, for an arbitrary three-qubit pure state, reveals the entanglement class of the state. The experiment involves measuring the expectation values of Pauli operators. This was achieved by mapping the desired expectation values onto the local z magnetization of a single qubit. We tested the entanglement classification protocol on twenty-seven different generic states and successfully detected their entanglement class. Full quantum state tomography was performed to construct experimental tomographs of each state and negativity was calculated from them, to validate the experimental results.     

Quantum correlation for two-qubit systems interacting with macroscopic objects

We consider two particles of spin- Open image in new window interacting with two one-dimensional N-spin arrays, respectively, which is an exactly solvable model. In this model, the one-dimensional N-spin arrays can be regarded as a macroscopic medium if we consider the number N of spins being large enough. In this paper, we investigate the dynamics of entanglement and quantum discord of the spins of two particles in the case of two particles passing through the macroscopic mediums synchronously and out-sync. In both case, we can obtain that the entanglement decreases monotonically with time and may suffer a sudden death in the evolution. Different from the entanglement dynamics, quantum discord first remains unchanged during a period of time and decreases later, which can be described as the sudden transition between classical and quantum decoherence. We also observe that the entanglement and quantum discord decay to zero in the case of enough large N, which can be understood that the interaction with the macroscopic medium can destroy the quantum correlation of a two-qubit system.     

One-step entanglements generation on distant superconducting resonators in the dispersive regime

We present a scalable quantum-bus-based device for generating the entanglement on photons in distant superconducting resonators (SRs). The device is composed of some one-dimensional (1D) SRs \(r_j\) coupled to the quantum bus (another common resonator R) in its different positions assisted by superconducting quantum interferometer devices which are used to tune the coupling strengths between \(r_j\) and R. By using the technique for catching and releasing a photon state in a 1D SR, it can work as an entanglement generator or a node in quantum communication. To demonstrate the performance of this device, we propose a one-step scheme to generate high-fidelity Bell state on photons in two distant SRs. It works in the dispersive regime of \(r_j\) and R, which enables us to extend it to generate high-fidelity multi-Bell states on different resonator pairs simultaneously.     

Classical versus quantum communication in XOR games

We introduce an intermediate setting between quantum nonlocality and communication complexity problems. More precisely, we study the value of XOR games when Alice and Bob are allowed to use a limited amount (c bits) of one-way classical communication compared to their value when they are allowed to use the same amount of one-way quantum communication (c qubits). The key quantity here is the ratio between the quantum and classical value. We provide a universal way to obtain Bell inequality violations of general Bell functionals from XOR games for which the previous quotient is larger than 1. This allows, in particular, to find (unbounded) Bell inequality violations from communication complexity problems in the same spirit as the recent work by Buhrman et al. (PNAS 113(12):3191–3196, 2016). We also provide an example of a XOR game for which the previous quotient is optimal (up to a logarithmic factor) in terms of the amount of information c. Interestingly, this game has only polynomially many inputs per player. For the related problem of separating the classical versus quantum communication complexity of a function, the known examples attaining exponential separation require exponentially many inputs per party.     

Exploring the renormalization of quantum discord and Bell non-locality in the one-dimensional transverse Ising model

In this paper, the effect of external magnet field g on the relationship among the quantum discord, Bell non-locality and quantum phase transition by employing quantum renormalization-group (QRG) method in the one-dimensional transverse Ising model is investigated. In our model, external magnet field g can influence the phase diagrams. The results have shown that both the two quantum correlation measures can develop two saturated values, which are associated with two distinct phases: long-ranged ordered Ising phase and the paramagnetic phase with the number of QRG iterations increasing. Additionally, quantum non-locality always existent in the long-ranged ordered Ising phase no matter whatever the value of g is and what times QRG steps are carried out and we conclude that the quantum non-locality always exists not only suitable for the two sites of block, but for nearest-neighbor blocks in the long-ranged ordered Ising phase. However, the block–block correlation in the paramagnetic phase is not strong enough to violate the Bell–CHSH inequality as the size of system becomes large. Furthermore, when the system violates the CHSH inequality, i.e., satisfies quantum non-locality, it needs to be entangled. On the other way, if the system obeys the CHSH inequality, it may be entangled or not. To gain further insight, the non-analytic and scaling behavior of QD and Bell non-locality have also been analyzed in detail and this phenomenon indicates that the behavior of the correlation can perfectly help one to observe the quantum critical properties of the model.     

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.     

Wigner–Yanase skew information and entanglement generation in quantum measurement

The first step of quantum measurement procedure is known as premeasurement, during which correlation is established between the system and the measurement apparatus. Such correlation may be classical or nonclassical in nature. One compelling nonclassical correlation is entanglement, a useful resource for various quantum information theoretic protocols. Quantifying the amount of entanglement, generated during quantum measurement, therefore, seeks importance from practical ground, and this is the central issue of the present paper. Interestingly, for a two-level quantum system, we obtain that the amount of entanglement, measured in term of negativity, generated in premeasurement process can be quantified by two factors: skew information, which quantifies the uncertainty in the measurement of an observable not commuting with some conserved quantity of the system, and mixedness parameter of the system’s initial state.     

Multi-party quantum private comparison based on the entanglement swapping of <Emphasis Type="Italic">d</Emphasis>-level cat states and <Emphasis Type="Italic">d</Emphasis>-level Bell states

In this paper, a novel multi-party quantum private comparison protocol with a semi-honest third party (TP) is proposed based on the entanglement swapping of d-level cat states and d-level Bell states. Here, TP is allowed to misbehave on his own, but will not conspire with any party. In our protocol, n parties employ unitary operations to encode their private secrets and can compare the equality of their private secrets within one time execution of the protocol. Our protocol can withstand both the outside attacks and the participant attacks on the condition that none of the QKD methods is adopted to generate keys for security. One party cannot obtain other parties’ secrets except for the case that their secrets are identical. The semi-honest TP cannot learn any information about these parties’ secrets except the end comparison result on whether all private secrets from n parties are equal.     

Herring–Flicker coupling and thermal quantum correlations in bipartite system

In this paper, we study thermal quantum correlations as quantum discord and entanglement in bipartite system imposed by external magnetic field with Herring–Flicker coupling, i.e., \(J(R)=1.642 e^{-2 R} R^{5/2}+O(R^{2}e^{-2R})\). The Herring–Flicker coupling strength is the function of R, which is the distance between spins and systems carry XXX Heisenberg interaction. By tuning the coupling distance R, temperature and magnetic field quantum correlations can be scaled in the bipartite system. We find the long sustainable behavior of quantum discord in comparison with entanglement over the coupling distance R. We also investigate the situations, where entanglement totally dies but quantum discord exists in the system.     

Cyclic quantum teleportation

We propose a scheme of cyclic quantum teleportation for three unknown qubits using six-qubit maximally entangled state as the quantum channel. Suppose there are three observers Alice, Bob and Charlie, each of them has been given a quantum system such as a photon or spin-\(\frac{1}{2}\) particle, prepared in state unknown to them. We show how to implement the cyclic quantum teleportation where Alice can transfer her single-qubit state of qubit a to Bob, Bob can transfer his single-qubit state of qubit b to Charlie and Charlie can also transfer his single-qubit state of qubit c to Alice. We can also implement the cyclic quantum teleportation with \(N\geqslant 3\) observers by constructing a 2N-qubit maximally entangled state as the quantum channel. By changing the quantum channel, we can change the direction of teleportation. Therefore, our scheme can realize teleportation in quantum information networks with N observers in different directions, and the security of our scheme is also investigated at the end of the paper.     

Violation of Bell inequalities for arbitrary-dimensional bipartite systems

In this paper, we consider the violation of Bell inequalities for quantum system \(\mathbb {C}^K\otimes \mathbb {C}^K\) (integer \(K\ge 2\)) with group theoretical method. For general M possible measurements, and each measurement with K outcomes, the Bell inequalities based on the choice of two orbits are derived. When the observables are much enough, the quantum bounds are only dependent on M and approximate to the classical bounds. Moreover, the corresponding nonlocal games with two different scenarios are analyzed.     

Biseparability of noisy pseudopure,W and GHZ states using conditional quantum relative Tsallis entropy

We employ the conditional version of sandwiched Tsallis relative entropy to determine \(1:N-1\) separability range in the noisy one-parameter families of pseudopure and Werner-like N-qubit W, GHZ states. The range of the noisy parameter, for which the conditional sandwiched Tsallis relative entropy is positive, reveals perfect agreement with the necessary and sufficient criteria for separability in the \(1:N-1\) partition of these one parameter noisy states.     

Simultaneous <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> stabilization for chemical reaction systems based on orthogonal complement space

This paper presents a simultaneous H₂/H_∞ stabilization problem for the chemical reaction systems which can be modeled as a finite collection of subsystems. A single dynamic output feedback controller which simultaneously stabilizes the multiple subsystems and captures the mixed H₂/H_∞ control performance is designed. To ensure that the stability condition, the H₂ characterization and the H_∞ characterization can be enforced within a unified matrix inequality framework, a novel technique based on orthogonal complement space is developed. Within such a framework, the controller gain is parameterized by the introduction of a common free positive definite matrix, which is independent of the multiple Lyapunov matrices. An iterative linear matrix inequality (ILMI) algorithm using Matlab Yalmip toolbox is established to deal with the proposed framework. Simulation results of a typical chemical reaction system are exploited to show the validity of the proposed methodology.     

Thermal quantum correlation and entanglement in the Bose–Hubbard Hamiltonian

We study a two-qutrit system which is described by the Bose–Hubbard Hamiltonian with two external magnetic fields. The entanglement (through the negativity) and quantum correlation (through the geometric discord) between the qutrits are calculated as functions of the magnetic field (B), the temperature (T), the linear and nonlinear coupling constants among two spins (J and K). Then, we compare the effect of these parameters on entanglement and quantum correlation of this system. For some values of system parameters, we show that the negativity is zero while, the geometric discord is nonzero. Moreover, we investigate the effect of finite external magnetic fields direction on these measures. This study leads to some new and interesting results as well.     

Generalized teleportation by quantum walks

We develop a generalized teleportation scheme based on quantum walks with two coins. For an unknown qubit state, we use two-step quantum walks on the line and quantum walks on the cycle with four vertices for teleportation. For any d-dimensional states, quantum walks on complete graphs and quantum walks on d-regular graphs can be used for implementing teleportation. Compared with existing d-dimensional states teleportation, prior entangled state is not required and the necessary maximal entanglement resource is generated by the first step of quantum walk. Moreover, two projective measurements with d elements are needed by quantum walks on the complete graph, rather than one joint measurement with \(d^2\) basis states. Quantum walks have many applications in quantum computation and quantum simulations. This is the first scheme of realizing communicating protocol with quantum walks, thus opening wider applications.     

Threshold quantum secret sharing based on single qubit

Based on unitary phase shift operation on single qubit in association with Shamir’s (t, n) secret sharing, a (t, n) threshold quantum secret sharing scheme (or (t, n)-QSS) is proposed to share both classical information and quantum states. The scheme uses decoy photons to prevent eavesdropping and employs the secret in Shamir’s scheme as the private value to guarantee the correctness of secret reconstruction. Analyses show it is resistant to typical intercept-and-resend attack, entangle-and-measure attack and participant attacks such as entanglement swapping attack. Moreover, it is easier to realize in physic and more practical in applications when compared with related ones. By the method in our scheme, new (t, n)-QSS schemes can be easily constructed using other classical (t, n) secret sharing.