We present a local hidden-variable model supplemented by classical communication that reproduces the quantum-mechanical predictions for measurements of all products of Pauli operators on an n-qubit GHZ state (or "cat state"). The simulation is efficient since the required amount of communication scales linearly with the number of qubits, even though there are Bell-type inequalities for these states for which the amount of violation grows exponentially with n. The structure of our model yields insight into the Gottesman-Knill theorem by demonstrating that, at least in this limited case, the correlations in the set of nonlocal hidden variables represented by the stabilizer generators are captured by an appropriate set of local hidden variables augmented by n-2 bits of classical communication.
In the present paper, we study spin squeezing under decoherence in the superposition of tripartite maximally entangled GHZ and W states. Here we use amplitude damping, phase damping and depolarisation channel. We have investigated the dynamics of spin squeezing with the interplay of superposition and decoherence parameters with different directions of the mean spin vector. We have found the mixture of GHZ and W states is robust against spin squeezing generation for amplitude damping and phase damping channels for certain directions of the mean spin vector. However, the depolarisation channel p…
In this note, we study Cabello's nonlocality argument (CNA) for three-qubit systems configured in the generalized GHZ state. For this class of states, we show that CNA runs for almost all entangled ones, and that the maximum probability of success of CNA is 14% (approx.), which is attained for the maximally entangled GHZ state. This maximum probability is slightly higher than that achieved for the standard Hardy's nonlocality argument (HNA) for three qubits, namely 12.5%. Also, we show that the success probability of both HNA and CNA for three-qubit systems can reach a maximum of 50% in the fr…
A Multipartite entangled state has many different kinds of entanglement specified by the number of partitions. The most essential example of multipartite entanglement is the entanglement of multi-qubit Greenberger-Horne-Zeilinger (GHZ) state in white noise. We explicitly construct the entanglement witnesses for these states with stabilizer generators of the GHZ states. For a $N$ qubit GHZ state in white noise, we demonstrate the necessary and sufficient criterion of separability when it is divided into $k$ parties with $N\leq 2k-1$ for arbitrary $N$ and $k$. The criterion covers more than a ha…
We propose a way for transferring Greenberger-Horne-Zeilinger (GHZ) entangled states from $n$ qubits in one cavity onto another $n$ qubits in the other cavity. It is shown that $n$-qubit GHZ states $α\left\vert 00...0\right\rangle +β\left\vert 11...1\right\rangle $ with arbitrary degree of entanglement can be transferred deterministically. Both of the GHZ state transfer and the operation time are not dependent on the number of qubits, and there is no need of measurement. This proposal is quite general and can be applied to accomplish the same task for a wide range of physical qubits. Furthermo…
Experimental detection of entanglement in superconducting qubits has been mostly limited, for more than two qubits, to witness-based and related approaches that can certify the presence of some entanglement, but not rigorously quantify how much. Here we measure the entanglement of three- and four-qubit GHZ and linear cluster states prepared on the 16-qubit IBM Rueschlikon (ibmqx5) chip, by estimating their entanglement monotones. GHZ and cluster states not only have wide application in quantum computing, but also have the convenient property of having similar state preparation circuits and fid…
Quantum coherence and entanglement orignate from the superposition principle. We derive a rigorous relation between the ${l_1}$-norm of coherence and concurrence, in that we show that the former is always greater than the latter. This result highlights the hierarchical relationship between coherence and concurrence, and proves coherence to be a fundamental and ubiquitous resource. We derive an analogous form of monogamy inequality which is based on the partial coherence of the reduced two-qubit and reduced single qubit of the particular class of three-qubit state. Moreover, we provide coherenc…
Three experiments, with an IBM superconducting quantum computer, are presented, where the setting combinations on a three qubit GHZ(like) state were selected by two additional assistant qubits. The average of the polynomial of Mermin for the three entangled qubits was calculated; the results showed violation of the inequality of Mermin. However, given that the assistant qubits selected, imposed and informed the type of settings, it was possible to interpret the results in terms of arranged relations among hidden variables of the assistants and the entanglement BEFORE each shot; the hidden vari…
In this paper we study the protection of N-qubit Greenberger-Horne- Zeilinger (GHZ) state and generalized N-qubit GHZ states in amplitude damping channel by means of quantum weak measurement and flip operations. We derive the explicit formulas of the performances of the protection scheme: average fidelity, average probability and the average quantum fisher information (QFI). Moreover, the analytical results for maximizing the average fidelity and probability are obtained. We show that our scheme can effectively protect the average QFI of phase for GHZ states and generalized GHZ states. The pro…
Recently, Li and Nie (Int. J. Theo. Phys. 52:1630, 2013) had introduced a bidirectional controlled quantum teleportation (BCQT) protocol by using GHZ-Bell state as a quantum channel. Also, Shukla et al. (Int. J. Theo. Phys. 52:3790, 2013) had shown the Li and Nie (LN) protocol is not a BCQT scheme. In this paper, two kinds of bidirectional teleportation schemes in order to correct and improve LN protocol are presented. In the first scheme, Alice and Bob as two legitimate users can simultaneously teleport an unknown single-qubit state to each other with the help of controller Charlie. In the se…
A scheme for the deterministic joint remote preparation of a four- qubit cluster-type state using only two Greenberger-Horne-Zeilinger (GHZ) states as quantum channels is presented. In this scheme, the first sender per- forms a two-qubit projective measurement according to the real coefficient of the desired state. Then, the other sender utilizes the measurement result and the complex coefficient to perform another projective measurement. To obtain the desired state, the receiver applies appropriate unitary operations to his/her own two qubits and two CNOT operations to the two ancillary ones.…
Environment-Assisted Error Correction of Single-Qubit Phase Damping
随机么正型的开放量子系统动力学在原则上可以完全撤销。紧接着Gregoratti和Werner [M. Gregoratti和R. F. Werner，J.Mod.Opt.50（6），915-933（2003）]，我们明确地执行反转单个量子位上的相位阻尼误差所需的所有步骤。此外，我们将该方案扩展到混合状态环境。令人惊讶的是，我们发现的情况下，未校正的状态是更接近所需的状态比任何校正的。
Many-qubit entanglement is crucial for quantum information processing although its exploitation is hindered by the detrimental effects of the environment surrounding the many-qubit system. It is thus of importance to study the dynamics of general multipartite nonclassical correlation, including but not restricted to entanglement, under noise. We did this study for four-qubit GHZ state under most common noises in an experiment and found that nonclassical correlation is more robust than entanglement except when it is imposed to dephasing channel. Quantum discord presents a sudden transition in i…
Logic-qubit entanglement has attracted much attention in both quantum communication and quantum computation. Here, we present an efficient protocol to distill the logic-qubit entanglement with the help of cross-Kerr nonlinearity. This protocol not only can purify the logic bit-flip error and logic phase-flip error, but also can correct the physical bit-flip error completely. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors. Our distillation protocol for logic-qubit entanglement may be useful for the practical applications in quantum information, especially in long-di…
We theoretically investigate a possibility to establish multi-qubit quantum correlations in one-dimensional chains of qubits. We combine a reservoir engineering strategy with coherent dynamics to generate multi-qubit entangled states. We find that an interplay between the coherent and incoherent dynamics result in the generation of stable (time-independent) many-body entangled steady states. Our results will be relevant in the context of the dissipative generation of quantum states, with applications in short-distance quantum computation and for exploring the emergence of collective phenomena …
Like a three-qubit Greenberger-Horne-Zeilinger(GHZ) symmetry we explore a corresponding symmetry in the four-qubit system, which we call GHZ$_4$ symmetry. While whole GHZ-symmetric states can be represented by two real parameters, the whole set of the GHZ$_4$-symmetric states is represented by three real parameters. In the parameter space all GHZ$_4$-symmetric states reside inside a tetrahedron. We also explore a question where the given SLOCC class of the GHZ$_4$-symmetric states resides in the tetrahedron. Among nine SLOCC classes we have examined five SLOCC classes, which results in three l…
We demonstrate ultra-sensitive measurement of fluctuations in a surface-acoustic-wave~(SAW) resonator using a hybrid quantum system consisting of the SAW resonator, a microwave (MW) resonator and a superconducting qubit. The nonlinearity of the driven qubit induces parametric coupling, which up-converts the excitation in the SAW resonator to that in the MW resonator. Thermal fluctuations of the SAW resonator near the quantum limit are observed in the noise spectroscopy in the MW domain.
Provided that cavities are initially in a Greenberger-Horne-Zeilinger (GHZ) entangled state, we show that GHZ states of N-group qubits distributed in N cavities can be created via a 3-step operation. The GHZ states of the N-group qubits are generated by using N-group qutrits placed in the N cavities. Here, "qutrit" refers to a three-level quantum system with the two lowest levels representing a qubit while the third level acting as an intermediate state necessary for the GHZ state creation. This proposal does not depend on the architecture of the cavity-based quantum network and the way for co…
We introduce a class of two-level multi-particle Greenberger-Horne-Zeilinger (GHZ) states, and study entanglement swapping between two systems for Bell states and the class of GHZ states in qubit systems, respectively. We give the formulas for the entanglement swapping of Bell states and GHZ states in any number of qubit systems. We further consider entanglement swapping between any number of Bell states and between any number of the introduced GHZ states, and propose a series of entanglement swapping schemes in a detailed way. We illustrate the applications of such schemes in quantum informat…
We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of $σ_{x}$. Both these measurement outcomes are communicated to Bob classical…
The direct measurement of nonlocal properties of entangled quantum systems has been the subject of several recent experimental investigations. Of particular interest is the implementation of nonlocal measurements via indirect measurement schemes, which allow for greater flexibility in the control of the measurement strength. Building on previous results established in the bipartite case, we present a scheme to implement genuine nonlocal measurements of N-qubit systems with variable strength, using GHZ-like entangled qubit meters. This method can be applied to the joint measurement of commuting…
The hierarchy of nonlocality and entanglement in multipartite systems is one of the fundamental problems in quantum physics. We study this topic in three-qubit systems considering the entanglement classification of stochastic local operations and classical communication (SLOCC). The equivalence under SLOCC divides threequbit states into separable, biseparable, W, and Greenberger-Horne-Zeilinger (GHZ) classes. The W and GHZ are two subclasses of genuine tripartite entanglement.We adopt the family of GHZ-symmetric states as a research subject, which share the symmetries of the GHZ state and have…
We present protocols to generate quantum entanglement on nonlocal magnons in hybrid systems composed of yttrium iron garnet (YIG) spheres, microwave cavities and a superconducting (SC) qubit. In the schemes, the YIGs are coupled to respective microwave cavities in resonant way, and the SC qubit is placed at the center of the cavities, which interacts with the cavities simultaneously. By exchanging the virtual photon, the cavities can indirectly interact in the far-detuning regime. Detailed protocols are presented to establish entanglement for two, three and arbitrary $N$ magnons with reasonabl…
Generating and detecting genuine multipartite entanglement (GME) of sizeable quantum states prepared on physical devices is an important benchmark for highlighting the progress of near-term quantum computers. A common approach to certify GME is to prepare a Greenberger-Horne-Zeilinger (GHZ) state and measure a GHZ fidelity of at least 0.5. We measure the fidelities using multiple quantum coherences of GHZ states on 11 to 27 qubits prepared on the IBM Quantum ibmq_montreal device. Combinations of quantum readout error mitigation (QREM) and parity verification error detection are applied to the …
We characterize the separability of three qubit GHZ diagonal states in terms of entries. This enables us to check separability of GHZ diagonal states without decomposition into the sum of pure product states. In the course of discussion, we show that the necessary criterion of Gühne for (full) separability of three qubit GHZ diagonal states is sufficient with a simpler formula. The main tool is to use entanglement witnesses which are tri-partite Choi matrices of positive bi-linear maps.
