Complete Greenberger–Horne–Zeilinger state analyzer using hyperentanglement

In this paper, a scheme for N-photon Greenberger–Horne–Zeilinger (GHZ) state analysis using hyperentangled states in multiple degrees of freedom with only linear optics and single photon detectors is proposed. The photons are separated and processed in different processing units. All the eight GHZ-states in either the polarization or the momentum degree of freedom can be completely distinguished. The scheme is implementable using present-day technology.     

Generation of three-qubit Greenberger–Horne–Zeilinger states of superconducting qubits by using dressed states

Combining the advantages of the dressed states and superconducting quantum interference device (SQUID) qubits, we propose an efficient scheme to generate Greenberger–Horne–Zeilinger (GHZ) states for three SQUID qubits. Firstly, we elaborate how to generate GHZ states of three SQUID qubits by choosing a set of dressed states suitably. Then, we compare the scheme by using dressed states with that via the adiabatic passage. Lastly, the influence of various decoherence factors, such as cavity decay, spontaneous emission and dephasing, is analyzed numerically. All of the results show that the GHZ state can be obtained fast and with high fidelity and that the present scheme is robust against the cavity decay and spontaneous emission. In addition, our scheme is more stable against the dephasing than the adiabatic scheme.     

Effective scheme for generation of N-dimension atomic Greenberger–Horne–Zeilinger states

In this paper, we propose an effective scheme for generation of $N$ -dimension atomic Greenberger–Horne–Zeilinger states with the controlled phase flip gates. The successful probability of our scheme is 100 % in principle. The scheme is implemented with simple linear optical elements, delay lines and polarization-independent circulators. We discuss the feasibility of the setups, concluding that the scheme is feasible with current technology.     

Comment on “High-dimensional deterministic multiparty quantum secret sharing without unitary operations”

Recently, a high-dimensional deterministic multiparty quantum secret sharing (DMQSS) scheme was proposed (Liu ZH et al in Quantum Inf Process 1–11 2011). However, we show that the scheme is vulnerable to a specific kind of collusion attack. In the worst case, ${\left\lfloor n/2\right\rfloor+1}$ agents can collude elaborately to reveal the dealer’s secret without the help of the other agents. We present the attack strategy in details and also give two possible improvements to resist the proposed collision attack.     

Nondestructive photonic polarization Greenberger–Horne–Zeilinger states analyzer assisted by quantum-dot cavity systems

Nondestructive entangled-state analyzers could save the physical entanglement resource and boost the efficiency of quantum information processing (QIP). However, up to now, there is no much progress in the nondestructive analysis of Greenberger–Horne–Zeilinger (GHZ) states. In this paper, a nondestructive photonic polarization GHZ-state analyzer, based on the interaction between circularly polarized light and quantum-dot cavity systems, is proposed. We can distinguish the GHZ states deterministically in theory, and the states are not destroyed because no single-photon detectors are required. Our scheme can be extended to \(n\) -photon GHZ states analysis directly and can be used to achieve QIP with less resource.     

Construction of quantum gates for concatenated Greenberger–Horne–Zeilinger-type logic qubit

Concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a kind of logic qubit which is robust in noisy environment. In this paper, we encode the C-GHZ state as the logic qubit and design two kinds of quantum gates for such logic qubit. The first kind is the single logic-qubit gate which contains the logic-qubit bit-flip gate and phase-flip gate. The second kind is the logic-qubit controlled-not (CNOT) gate. We exploit the single quantum gate for physical qubit, such as bit-flip gate and phase-flip gate, and two-qubit CNOT gate to realize the logic-qubit gate. We also calculated the success probability of such logic-qubit gate based on the imperfect physical quantum gate. This protocol may be useful for future quantum computation.     

Effective protocol for preparation of N-photon Greenberger–Horne–Zeilinger states with conventional photon detectors

In this work we show that the generating N-photon Greenberger–Horne–Zeilinger entangled state protocol proposed by Xia et al. (Appl Phys Lett 92(1–3):021127, 2008) which can be realized by a simpler optical setup and with a higher success probability. The present protocol setup involves simple linear optical elements, N single-photon superposition states and conventional photon detectors. This makes the protocol more realizable in experiments.     

Self-assisted complete analysis of three-photon hyperentangled Greenberger–Horne–Zeilinger states with nitrogen-vacancy centers in microcavities

We propose a self-assisted complete analysis scheme of three-photon hyperentangled Greenberger–Horne–Zeilinger (GHZ) states with nitrogen-vacancy (NV) centers in microcavities (NV center-cavity systems), which is used to distinguish 64 three-photon hyperentangled GHZ states entangled in polarization and spatial-mode degrees of freedom. In our scheme, only three NV center-cavity systems are required for distinguishing the 64 three-photon hyperentangled GHZ states, which is much simpler than the previous schemes. Moreover, the three-photon spatial-mode GHZ states are distinguished with the three NV center-cavity systems without affecting the hyperentangled state of three-photon system, so the three-photon polarization GHZ states can be distinguished with linear optical elements assisted by the spatial-mode entangled state of three-photon system. With our scheme, the difficulty in the experimental realization of complete analysis of hyperentangled GHZ states may be largely decreased, which could potentially improve the performance of high-capacity multi-party quantum communication.     

Non-ideal teleportation of tripartite entanglement: Einstein–Podolsky–Rosen versus Greenberger–Horne–Zeilinger schemes

Channels composed by Einstein–Podolsky–Rosen (EPR) pairs are capable of teleporting arbitrary multipartite states. The question arises whether EPR channels are also optimal against imperfections. In particular, the teleportation of Greenberger–Horne–Zeilinger states (GHZ) requires three EPR states as the channel and full measurements in the Bell basis. We show that, by using two GHZ states as the channel, it is possible to transport any unknown three-qubit state of the form \(c_0|000\rangle +c_1|111\rangle \). The teleportation is made through measurements in the GHZ basis, and, to obtain deterministic results, in most of the investigated scenarios, four out of the eight elements of the basis need to be unambiguously distinguished. Most importantly, we show that when both systematic errors and noise are considered, the fidelity of the teleportation protocol is higher when a GHZ channel is used in comparison with that of a channel composed by EPR pairs.     

Generation of concatenated Greenberger–Horne–Zeilinger-type entangled coherent state based on linear optics

The concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a new type of multipartite entangled state, which has potential application in future quantum information. In this paper, we propose a protocol of constructing arbitrary C-GHZ entangled state approximatively. Different from previous protocols, each logic qubit is encoded in the coherent state. This protocol is based on the linear optics, which is feasible in experimental technology. This protocol may be useful in quantum information based on the C-GHZ state.     

Comment on “Dynamic quantum secret sharing”

Hsu et al. (Quantum Inf Process 12:331–344,2013) proposed a dynamic quantum secret sharing (DQSS) protocol using the entanglement swapping of Bell states for an agent to easily join (or leave) the system. In 2013, Wang and Li (Quantum Inf Process 12(5):1991–1997, 2013) proposed a collusion attack on Hsu et al.’s DQSS protocol. Nevertheless, this study points out a new security issue on Hsu et al.’s DQSS protocol regarding to the honesty of a revoked agent. Without considering this issue, the DQSS protocol could be failed to provide secret sharing function.     

Comment on “Proactive quantum secret sharing”

In the paper, Qin and Dai (Quantum Inf Process 14:4237–4244, 2015) proposed a proactive quantum secret sharing scheme. We study the security of the proposed scheme and find that it is not secure. In the distribution phase of the proposed scheme, two dishonest participants may collaborate to eavesdrop the secret of the dealer without introducing any error.     

Fast generation of <Emphasis Type="Italic">N</Emphasis>-atom Greenberger–Horne–Zeilinger state in separate coupled cavities via transitionless quantum driving

By jointly using quantum Zeno dynamics and the approach of “transitionless quantum driving (TQD)” proposed by Berry to construct shortcuts to adiabatic passage, we propose an efficient scheme to fast generate multiatom Greenberger–Horne–Zeilinger (GHZ) state in separate cavities connected by optical fibers only by one-step manipulation. We first detail the generation of the three-atom GHZ state via TQD; then, we compare the proposed TQD scheme with the traditional ones with adiabatic passage. At last, the influence of various decoherence factors, such as spontaneous emission, cavity decay and fiber photon leakage, is discussed by numerical simulations. All of the results show that the present TQD scheme is fast and insensitive to atomic spontaneous emission and fiber photon leakage. Furthermore, the scheme can be directly generalized to realize N-atom GHZ state generation by the same principle in theory.     

Thwarting intercept-and-resend attack on Zhang’s quantum secret sharing using collective rotation noises

This work deliberately introduces collective-rotation noise into quantum states to prevent an intercept-resend attack on Zhang’s quantum secret sharing scheme over a collective-noise quantum channel (Zhang in Phys A 361:233–238, 2006). The noise recovering capability of the scheme remains intact. With this design, the quantum bit efficiency of the protocol is doubled when compared to Sun et al.’s improvement on Zhang’s scheme (Sun et al. in Opt Commun 283:181–183, 2010).     

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.     

Adiabatic passage for one-step generation of <Emphasis Type="Italic">n</Emphasis>-qubit Greenberger–Horne–Zeilinger states of superconducting qubits via quantum Zeno dynamics

An efficient scheme is proposed for generating n-qubit Greenberger–Horne–Zeilinger states of n superconducting qubits separated by (\(n-1\)) coplanar waveguide resonators capacitively via adiabatic passage with the help of quantum Zeno dynamics in one step. In the scheme, it is not necessary to precisely control the time of the whole operation and the Rabi frequencies of classical fields because of the introduction of adiabatic passage. The numerical simulations for three-qubit Greenberger–Horne–Zeilinger state show that the scheme is insensitive to the dissipation of the resonators and the energy relaxation of the superconducting qubits. The three-qubit Greenberger–Horne–Zeilinger state can be deterministically generated with comparatively high fidelity in the current experimental conditions, though the scheme is somewhat sensitive to the dephasing of superconducting qubits.     

Establishing the equivalence between Szegedy’s and coined quantum walks using the staggered model

Coined quantum walks (QWs) are being used in many contexts with the goal of understanding quantum systems and building quantum algorithms for quantum computers. Alternative models such as Szegedy’s and continuous-time QWs were proposed taking advantage of the fact that quantum theory seems to allow different quantized versions based on the same classical model, in this case the classical random walk. In this work, we show the conditions upon which coined QWs are equivalent to Szegedy’s QWs. Those QW models have in common a large class of instances, in the sense that the evolution operators are equal when we convert the graph on which the coined QW takes place into a bipartite graph on which Szegedy’s QW takes place, and vice versa. We also show that the abstract search algorithm using the coined QW model can be cast into Szegedy’s searching framework using bipartite graphs with sinks.     

Yang–Baxter equations and quantum entanglements

In this paper some results associated with a new type of Yang–Baxter equation (YBE) are reviewed. The braiding matrix of Kauffman–Lomonaco has been extended to the solution (called type-II) of Yang–Baxter equation (YBE) and the related chain Hamiltonian is given. The Lorentz additivity for spectral parameters is found, rather than the Galilean rule for the familiar solutions (called type-I) of YBE associated with the usually exact solvable models. Based on the topological basis, the N-dimensional solution of YBE is found to be the Wigner D-functions. The explicit examples for spin-\(\frac{1}{2}\) and spin-1 have been shown. The extremes of \(\ell _1\)-norm of \(D\)-functions are introduced to distinguish the type-I from type-II of braiding matrices that also correspond to those of von Neumann entropy for quantum information.     

A quantum particle swarm optimization for the 0–1 generalized knapsack sharing problem

This study proposes a new hybrid heuristic approach that combines the quantum particle swarm optimization (QPSO) technique with a local search phase to solve the binary generalized knapsack sharing problem (GKSP). The approach also incorporates a heuristic repair operator that uses problem-specific knowledge instead of the penalty function technique commonly used for constrained problems. This study is the first to report on the application of the QPSO method to the GKSP. The efficiency of our proposed approach was tested on a large set of instances, and the results were compared to those produced by the commercial mixed integer programming solver CPLEX 12.5 of IBM-ILOG. The Experimental results demonstrated the good performance of the QPSO in solving the GKSP.