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Quantum teleportation plays a significant role in the field of quantum communication. This paper investigates quantum teleportation through a noisy environment by using GHZ state and non-standard W state as quantum channels. We analyze the efficiency of quantum teleportation by solving analytically a master equation in Lindblad form. Following the quantum teleportation protocol, we obtain the fidelity of quantum teleportation as a function of evolution time. The calculation results show that the teleportation fidelity using non-standard W is higher in comparison to GHZ state at the same evolution time. Moreover, we consider the efficiency of teleportation with weak measurements and reverse quantum measurement under amplitude damping noise. Our analysis suggests that the teleportation fidelity using non-standard W is also more robust to noise than GHZ state in the same conditions. Interestingly, we found that weak measurement and its reverse operation have no positive effect on the efficiency of quantum teleportation by using GHZ and non-standard W state in the amplitude damping noise environment. In addition, we also demonstrate the efficiency of quantum teleportation can be improved by making minor modifications to the protocol. [ABSTRACT FROM AUTHOR]

Noise exists inherently in realistic quantum systems and affects the evolution of quantum systems. We investigate the dynamics of quantum networks in noisy environments by using the fidelity of the quantum evolved states and the classical percolation theory. We propose an analytical framework that allows us to characterize the stability of quantum networks in terms of quantum noises and network topologies. The calculation results of the framework determine the maximal time that quantum networks with different network topologies can maintain the ability to communicate under noise. We demonstrate the results of the framework through examples of specific graphs under amplitude damping and phase damping noises. We further consider the capacity of the quantum network in a noisy environment according to the proposed framework. The analytical framework helps us better understand the evolution time of a quantum network and provides a reference for designing large quantum networks. [ABSTRACT FROM AUTHOR]

The measurement-dependent symmetric quantum discord is defined as the measurement-induced disturbance, where the given local von Neumann measurement is performed locally on both subsystems. For general bipartite quantum systems, we investigate the average measurement-dependent symmetric quantum discord. It can be considered as an upper bound of the symmetric quantum discord and the difference between them can be considered as the evaluation error as a result of the lack of prior information. Firstly, we derive a product measure on the unitary group U (d A) ⊗ U (d B) / ∼ induced by the uniform Haar measure over the unitary group U (d) . Then applying this measure, we analyze integrals related to the measurement-dependent symmetric quantum discord over the unitary group and obtain analytic expressions for the average measurement-dependent symmetric quantum discord after parameterization. The expressions allow us to calculate the symmetric quantum discord in an average sense with relatively few parameters. [ABSTRACT FROM AUTHOR]

Random unitary dynamical evolutions play an important role in characterizing quantum Markovianity. By exploiting the maximally entangled state under the representation of a set of generalized unitary Weyl operators, we present a necessary and sufficient condition for quantum Markovianity in d-level systems from the perspective of quantum mutual information. Moreover, we analyze three quantum Markovianity criteria among divisibility, BLP and LFS 0 to establish their connections and differences. It is shown that they coincide in many special cases, but different in general, and Markovianity in the sense of LFS 0 is less restrictive than Markovianities in the sense of divisibility and BLP by detailed examples. [ABSTRACT FROM AUTHOR]

Observational entropy is a generalization of Boltzmann entropy to quantum mechanics. Observational entropy based on coarse-grained measurements has a certain relations with other quantum information measures. We study the relations between observational entropy and Rényi information measures and give some examples to explain the rationality of these relations. [ABSTRACT FROM AUTHOR]

For a quantum system, violation of a Svetlichny inequality indicates the existence of genuine nonlocality. Through the same mathematical analysis approach, we derive the analytical expressions of the maximal violation of the Svetlichny inequality for certain three-qubit pure states and mixed “X” states. These pure states represented in the five-parameter form belong to extended GHZ states. It is convenient to use the obtained expression to distinguish the genuine nonlocal states in these states. We also obtain the analytical expression of the maximal violation of Svetlichny inequality for a subclass of four-qubit “X” states. We show the application potentiality of these expressions by designing two schemes where quantum resources are converted from less qubits “X” states to more qubits “X” states. [ABSTRACT FROM AUTHOR]

In quantum key distribution, it is important to ensure the secure key rate and the distribution distance. To increasing transmission distance, we propose an entanglement-based protocol relying on two Bell states. Combining the idea of remote state preparation, the protocol can double the communication distance without introducing more security loopholes related to measurement device, and maintain the key generation rate consistent with the BBM92 protocol via untrusted third party. Based on that, we investigate key rate of the protocol when transmitted qubits are subjected to four noises. The result shows that our protocol can tolerate more amplitude damping noise than ES−BBM92 protocol. In addition, we found that if noise is unavoidable and the noise parameter exceeds a certain value, in some noisy environments, it is best to subject qubit to more noise to increase the secret key generation rate. Furthermore, we calculate secret key rate under both practical experimental condition and noisy environment. [ABSTRACT FROM AUTHOR]

We study entanglement witnesses (EWs) and construct a linear map by taking two groups of mutually unbiased bases (MUBs) of two Hilbert spaces. We provide two new relations about matrices (may not be square matrices) with properties similar to unitary matrix. Using these two new relations, we obtain a positive map between two different linear spaces of complex matrices. Finally, we calculate a special case by applying our map to get an EW on ℂ 3 ⊗ ℂ 4 . We also find three entangled states detected by this EW. [ABSTRACT FROM AUTHOR]

We study the construction of mutually unbiased bases such that all the bases are unextendible maximally entangled ones. By using some results from the theory of finite fields, we construct mutually unbiased unextendible maximally entangled bases in some bipartite systems of higher dimension: C 4 ⊗ C 5 , C 6 ⊗ C 7 , C 10 ⊗ C 11 and C 12 ⊗ C 13 , which extend the known result of C 2 ⊗ C 3 . We also generalize these results to more bipartie systems of specific dimension. [ABSTRACT FROM AUTHOR]

We study the genuine tripartite nonlocality of some qubit states in a triple JCM. In this model, each atom state (A, B or C) was initially prepared with an independent cavity (a, b or c). By using two kinds of GHZ-like states as the atomic initial states, we investigate the genuine tripartite nonlocality as the time evolutions for the non-interaction three-qubit subsystems. We also study the genuine tripartite nonlocality of the subsystems by using the Svetlichny inequality. For the subsystems of three atoms ABC and three cavity modes abc, we show that they are genuinely nonlocal at certain period intervals of time. The states of all the other inequivalent subsystems satisfy the Svetlichny inequality for two types of GHZ-like states. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study separability problem using general symmetric informationally complete measurements and propose separability criteria in $$\mathbb {C}^{d_{1}}\otimes \mathbb {C}^{d_{2}}$$ and $$\mathbb {C}^{d_{1}}\otimes \mathbb {C}^{d_{2}}\cdots \otimes \mathbb {C}^{d_{n}}$$ . Our criteria just require less local measurements and provide experimental implementation in detecting entanglement of unknown quantum states. [ABSTRACT FROM AUTHOR]

We compute explicitly the four-particle amplitude in superstring theories by using the hyperelliptic language and the newly obtained chiral measure of D''Hoker and Phong. Although the algebra of the intermediate steps is a little bit involved, we obtain a quite simple expression for the four-particle amplitude. As expected, the integrand is independent of all the insertion points. As an application of the obtained result, we show that the perturbative correction to the R4 term in type II superstring theories is vanishing point-wise in (even) moduli space at two loops. [Copyright &y& Elsevier]

The vanishing of the cosmological constant and the non-renormalization theorem are verified at two loops by explicit computation using the hyperelliptic language and the newly obtained chiral measure of D''Hoker and Phong. A set of identities is found which is used in the verification of the non-renormalization theorem and leads to a great simplification of the calculation of the four-particle amplitude at two loops. [Copyright &y& Elsevier]

Following the new gauging fixing method of D'Hoker and Phong, we study two-loop superstrings in hyperelliptic language. By using hyperelliptic representation of genus 2 Riemann surface we derive a set of identities involving the Szego¨ kernel. These identities are used to prove the vanishing of the cosmological constant and the non-renormalization theorem point-wise in moduli space by doing the summation over all the 10 even spin structures. Modular invariance is maintained at every stage of the computation explicitly. The 4-particle amplitude is also computed and an explicit expression for the chiral integrand is obtained. We use this result to show that the perturbative correction to the R4 term in type II superstring theories is vanishing at two loops. In this Letter, a summary of the main results is presented with detailed derivations to be provided in two subsequent publications. [Copyright &y& Elsevier]

We use weak measurement (WM) and quantum measurement reversal (QMR) techniques to suppress the degradation of genuine nonlocality of a special class of three-qubit "X" states when they suffer from the amplitude damping noise. We choose the maximal violation of the Svetlichny inequality to quantify the genuine nonlocality of states in this paper. We analyse mathematically the sufficient and necessary condition for weak measurement or QMR to enhance the genuine nonlocality of such "X" states. We propose a specific protection scheme combined WM with QMR for such states, and calculate the maximal genuine nonlocality reached by our scheme as well as the success probability. We apply our scheme to the GHZ-like states and the Werner-type states to show the protection effect. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method for the construction of maximally entangled states in C d ⊗ C d ′ when d ′ ≥ 2 d . A systematic way of constructing a set of maximally entangled bases (MEBs) in C d ⊗ C d ′ was established. Both cases when d ′ is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in C 2 ⊗ C 4 , which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in C 2 ⊗ C 5 . [ABSTRACT FROM AUTHOR]

Quantum discord is a measure of quantumness of correlations in bipartite states, which characterizes the difference between quantum mutual information and classical correlations. Based on the generators of Lie algebra s u (d) , we study the quantum discord for two families of two-qudit states with maximally mixed marginals, and derive some upper bounds of quantum discord for such states by evaluating classical correlations. Furthermore, we make a comparison among total correlations, classical correlations and quantum discord for a class of special states in high-dimensional two-partite systems. [ABSTRACT FROM AUTHOR]

Inspired by the success of classical neural networks, there has been tremendous effort to develop classical effective neural networks into quantum concept. In this paper, a novel hybrid quantum–classical neural network with deep residual learning (Res-HQCNN) is proposed. We firstly analyse how to connect residual block structure with a quantum neural network, and give the corresponding training algorithm. At the same time, the advantages and disadvantages of transforming deep residual learning into quantum concept are provided. As a result, the model can be trained in an end-to-end fashion, analogue to the backpropagation in classical neural networks. To explore the effectiveness of Res-HQCNN , we perform extensive experiments for quantum data with or without noisy on classical computer. The experimental results show the Res-HQCNN performs better to learn an unknown unitary transformation and has stronger robustness for noisy data, when compared to state of the arts. Moreover, the possible methods of combining residual learning with quantum neural networks are also discussed. [ABSTRACT FROM AUTHOR]

We investigate the entanglement and nonlocality dynamics of a two-qubit Bell state and the three-qubit Greenberger–Home–Zeilinger (GHZ) state in a noisy environment by solving analytically a master equation in the Lindblad form. In the case of the Bell state, we obtain the analytic expressions of the concurrence and the maximal violation of the Clauser–Horne–Shimony–Holt inequality of the evolution state. In the case of the three-qubit GHZ state, we obtain the analytic formula of the genuinely multipartite concurrence of the evolution state. Usually, it is difficult to give the analytic expression of the maximum violation of the Svetlichny inequality for a general three-qubit state, but we find the analytic expression for a class of three-qubit states whose correlation matrices are of a special form. We use this result to obtain the analytic expression of the maximum violation of the Svetlichny inequality of the evolution state when parameters in the master equation meet certain conditions. [ABSTRACT FROM AUTHOR]

We investigate monogamy relations related to the Rényi- α entanglement and polygamy relations related to the Rényi- α entanglement of assistance. We present new entanglement monogamy relations satisfied by the μ th power of Rényi- α entanglement with α ∈ [ (7 - 1) / 2 , (13 - 1) / 2 ] for μ ≥ 2 , and polygamy relations satisfied by the μ th power of Rényi- α entanglement of assistance with α ∈ [ (7 - 1) / 2 , (13 - 1) / 2 ] for 0 ≤ μ ≤ 1 . These relations are shown to be tighter than the existing ones. [ABSTRACT FROM AUTHOR]

We study the concurrence for arbitrary N-partite W-class states based on the (N - 1) -partite partitions of subsystems by taking account to the structures of W-class states. By using the method of permutation and combination, we give some analytical formulas of concurrence and elegant relations between the N-partite concurrence and the (N - 1) -partite concurrence for arbitrary N-partite W-class states. Applying these relations, we present better lower bounds of concurrence for some multipartite mixed states. An example is given to demonstrate that our lower bounds can detect more entanglements. [ABSTRACT FROM AUTHOR]

Quantum key distribution(QKD) might be the most famous application of quantum information theory. The idea of QKD is not difficult to understand but in practical implementations, many problems are needed to be solved, for example, the noise of the channels. Previous works usually discuss the estimate of the channels and employ error-correcting procedures, whose feasibility and efficiency depend on the strength of the noise, or assist with entanglement distillation procedures, which often result in a large consumption of states while not all states can be distilled. This paper aims to study QKD over noisy channels including Pauli noises, amplitude damping noises, phase damping noises, collective noises as well as mixtures of them, in any strength without distillations. We provide a method, called the testing state method, to implement QKD protocols without errors over arbitrarily strength noisy channels. The method can be viewed as an error-correcting procedure, and can also be employed for other tasks. [ABSTRACT FROM AUTHOR]

We study the norms of the Bloch vectors for arbitrary n-partite quantum states. A tight upper bound of the norms is derived for n-partite systems with different individual dimensions. These upper bounds are used to deal with the separability problems. Necessary conditions are presented for m -separable states in n-partite quantum systems. Based on the upper bounds, classification of multipartite entanglement is illustrated with detailed examples. [ABSTRACT FROM AUTHOR]

We study the genuine tripartite nonlocality of Dirac fields in the noninertial frame while one or two observers are accelerated. We apply the Svetlichny inequalities and MABK inequalities to detect the local realistic description. It is difficult to calculate the Svetlichny inequalities for general states. Thus, we investigate the nonlocality of a tripartite GHZ state system in the noninertial frame. There are some subsystems violating the Svetlichny inequalities, which implies those subsystems are genuine tripartite nonlocality. But we find that all tripartite subsystems in the noninertial frames satisfy the MABK inequalities. These results may suggest that Svetlichny inequality is a better way than MABK inequality to research the local realistic description. [ABSTRACT FROM AUTHOR]

We develop monogamy relations of multiqubit quantum entanglement in terms of the concurrence, entanglement of formation, convex-roof extended negativity and Tsallis-q entanglement. These monogamy inequalities are proved to be tighter than the existing ones. The corresponding examples are also presented. [ABSTRACT FROM AUTHOR]

Motivated by the isomorphic correspondence between quantum channels and their Choi states, we define an entropy function of a quantum channel by the entropy of its Choi state. We show that it satisfies all axioms of the entropy function. We also define the relative entropy of a quantum channel and give the relation between the entropy and the relative entropy of a quantum channel. Moreover, comparing with the entropy of a quantum channel which is defined by Gour and Wilde, we find that the two definitions of the channel entropy are equal for covariant channels. As examples, we compute the entropies of the erasure channel, the d-dimensional depolarizing channel, and a particular kind of Werner–Holevo channels, respectively. [ABSTRACT FROM AUTHOR]

We study the perfectly local indistinguishability of multipartite product states. Firstly, we follow the method of Zhang et al. (Phys Rev A 93:012314, 2016) to give another more concise set of $$2n-1$$ orthogonal product states in $${\mathbb {C}}^m\otimes {\mathbb {C}}^n$$ $$(4\le m\le n)$$ which can not be distinguished by local operations and classical communication. Then we use the three-dimensional cubes to present some product states which give us an intuitive view on how to construct locally indistinguishable product states in tripartite quantum systems. At last, we give an explicit construction of locally indistinguishable orthogonal product states for general multipartite systems. [ABSTRACT FROM AUTHOR]

In this paper, we study the concurrence of arbitrary-dimensional tripartite quantum states. An explicit operational lower bound of concurrence is obtained in terms of the concurrence of substates. A given example shows that our lower bound may improve the well-known existing lower bounds of concurrence. The significance of our result is to get a lower bound when we study the concurrence of arbitrary $$m\otimes n\otimes l$$ -dimensional tripartite quantum states. [ABSTRACT FROM AUTHOR]

In this paper, we study the one-way local operations and classical communication (LOCC) problem. In $$\mathbb {C}^d\otimes \mathbb {C}^d$$ with $$d\ge 4$$ , we construct a set of $$3\lceil \sqrt{d}\rceil -1$$ one-way LOCC indistinguishable maximally entangled states which are generalized Bell states. Moreover, we show that there are four maximally entangled states which cannot be perfectly distinguished by one-way LOCC measurements for any dimension $$d\ge 4$$ . [ABSTRACT FROM AUTHOR]

Analogous to the commutant in the theory of associative algebras, one can construct a new subalgebra of a vertex algebra, known as the vertex algebra commutant. In this paper, for the highest weight module V4 of Lie algebra sl(2,C), we describe a commutant of βγ-system S(V4) by giving a finite set of generators and operator product expansion relations among generators. [ABSTRACT FROM AUTHOR]

Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays to heterogeneous multipartite systems with different individual levels. The second is the existence of k-uniform states in heterogeneous quantum systems. We present explicit constructions of two- and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of k-uniform states for heterogeneous multipartite systems for any k ≥ 2 . The non-existence of a class of IrMOAs is also proved. [ABSTRACT FROM AUTHOR]

We study the concurrence of arbitrary dimensional multipartite quantum systems. An explicit analytical lower bound of concurrence for four-partite mixed states is obtained in terms of the concurrences of tripartite mixed states. Detailed examples are given to show that our lower bounds improve the existing lower bounds of concurrence. The approach is generalized to five-partite quantum systems. [ABSTRACT FROM AUTHOR]

In this paper, we give a method for the local unitary equivalent problem which is more efficient than that was proposed by Bin Liu et al []. [ABSTRACT FROM AUTHOR]

In this paper, we prove one case of conjecture given by Hernandez and Leclerc. We give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group . As a conclusion, for every exchange relation of cluster algebra, there exists an exact sequence of the full subcategory corresponding to it. [ABSTRACT FROM AUTHOR]