Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state

A scheme is presented to implement bidirectional controlled quantum teleportation (QT) by using a five-qubit entangled state as a quantum channel, where Alice may transmit an arbitrary single qubit state called qubit A to Bob and at the same time, Bob may also transmit an arbitrary single qubit state called qubit B to Alice via the control of the supervisor Charlie. Based on our channel, we explicitly show how the bidirectional controlled QT protocol works. By using this bidirectional controlled teleportation, espcially, a bidirectional controlled quantum secure direct communication (QSDC) protocol, i.e., the so-called controlled quantum dialogue, is further investigated. Under the situation of insuring the security of the quantum channel, Alice (Bob) encodes a secret message directly on a sequence of qubit states and transmits them to Bob (Alice) supervised by Charlie. Especially, the qubits carrying the secret message do not need to be transmitted in quantum channel. At last, we show this QSDC scheme may be determinate and secure.     

Effect of quantum noise on deterministic remote state preparation of an arbitrary two-particle state via various quantum entangled channels

As one of important research branches of quantum communication, deterministic remote state preparation (DRSP) plays a significant role in quantum network. Quantum noises are prevalent in quantum communication, and it can seriously affect the safety and reliability of quantum communication system. In this paper, we study the effect of quantum noise on deterministic remote state preparation of an arbitrary two-particle state via different quantum channels including the \(\chi \) state, Brown state and GHZ state. Firstly, the output states and fidelities of three DRSP algorithms via different quantum entangled channels in four noisy environments, including amplitude-damping, phase-damping, bit-flip and depolarizing noise, are presented, respectively. And then, the effects of noises on three kinds of preparation algorithms in the same noisy environment are discussed. In final, the theoretical analysis proves that the effect of noise in the process of quantum state preparation is only related to the noise type and the size of noise factor and independent of the different entangled quantum channels. Furthermore, another important conclusion is given that the effect of noise is also independent of how to distribute intermediate particles for implementing DRSP through quantum measurement during the concrete preparation process. These conclusions will be very helpful for improving the efficiency and safety of quantum communication in a noisy environment.     

Multi-party quantum state sharing of an arbitrary multi-qubit state via \chi -type entangled states

By using the \(\chi \) -type entangled states, a novel scheme for multi-party quantum state sharing (MQSTS) of an arbitrary multi-qubit state is investigated. It is shown that the MQSTS scheme can be faithfully realized by performing appropriate Bell state measurements, Z basis measurements and local unitary operations, rather than multi-qubit entanglement or multi-particle joint measurements. Thus, our MQSTS scheme is more convenient in a practical application than some previous schemes. Furthermore, its intrinsic efficiency for qubits approaches 100 %, and the total efficiency really approaches the maximal value, which is higher than those of the previous MQSTS schemes. Finally, we analyze the security from the views of participant attack and outside attack in detail.     

Joint remote control of an arbitrary single-qubit state by using a multiparticle entangled state as the quantum channel

We present a scheme for joint remote implementation of an arbitrary single-qubit operation following some ideas in one-way quantum computation. All the senders share the information of implemented quantum operation and perform corresponding single-qubit measurements according to their information of implemented operation. An arbitrary single-qubit operation can be implemented upon the remote receiver’s quantum system if the receiver cooperates with all the senders. Moreover, we study the protocol of multiparty joint remote implementation of an arbitrary single-qubit operation with many senders by using a multiparticle entangled state as the quantum channel.     

On the connection between estimability and observability

It is shown that when a linear dynamic system is stochastically autonomous (that is, when the system is not excited by a random signal), its estimability property as defined by Y. Baram and T. Kailath (ibid., vol.33, p.1116-21, Dec. 1988) reduces to the classical observability property     

A new connection between quantum circuits,graphs and the Ising partition function

We present a simple construction that maps quantum circuits to graphs and vice-versa. Inspired by the results of D. A. Lidar linking the Ising partition function with quadratically signed weight enumerators (QWGTs), we also present a problem for the additive approximation of a function over hypergraphs related to the generating function of Eulerian subgraphs for ordinary graphs. Further, if E is an oracle that returns approximations of this function, we prove that P^E = BQP. We also discuss connections with the Ising partition function.      

On the connection between many-valued contexts and general geometric structures

We study the connection between certain many-valued contexts and general geometric structures. The known one-to-one correspondence between attribute-complete many-valued contexts and complete affine ordered sets is used to extend the investigation to π-lattices, class geometries, and lattices with classification systems. π-lattices are identified as a subclass of complete affine ordered sets, which exhibit an intimate relation to concept lattices closely tied to the corresponding context. Class geometries can be related to complete affine ordered sets using residuated mappings and the notion of a weak parallelism. Lattices with specific sets of classification systems allow for some sort of “reverse conceptual scaling”.     

Teleporting an unknown quantum state with unit fidelity and unit probability via a non-maximally entangled channel and an auxiliary system

Quantum Information Processing - We present a new scheme for quantum teleportation that one can teleport an unknown state via a non-maximally entangled channel with certainly, using an auxiliary...     

On the solution of trivalent decision problems by quantum state identification

The trivalent functions of a trit can be grouped into equipartitions of three elements. We discuss the separation of the corresponding functional classes by quantum state identifications.     

On the relation between quantum walks and zeta functions

We present an explicit formula for the characteristic polynomial of the transition matrix of the discrete-time quantum walk on a graph via the second weighted zeta function. As applications, we obtain new proofs for the results on spectra of the transition matrix and its positive support.     

Geometry of quantum state space and quantum correlations

Quantum state space is endowed with a metric structure, and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical considerations on the quantum state space. In this article, considering the quantum state space being spanned by \(2\times 2\) density matrices, we determine a particular Riemannian metric for a state \(\rho \) and show that if \(\rho \) gets entangled with another quantum state, the negativity of the generated entangled state is, upto a constant factor, equal to square root of that particular Riemannian metric . Our result clearly relates a geometric quantity to a measure of entanglement. Moreover, the result establishes the possibility of understanding quantum correlations through geometric approach.     

Schemes generating entangled states and entanglement swapping between photons and three-level atoms inside optical cavities for quantum communication

We propose quantum information processing schemes based on cavity quantum electrodynamics (QED) for quantum communication. First, to generate entangled states (Bell and Greenberger–Horne–Zeilinger [GHZ] states) between flying photons and three-level atoms inside optical cavities, we utilize a controlled phase flip (CPF) gate that can be implemented via cavity QED). Subsequently, we present an entanglement swapping scheme that can be realized using single-qubit measurements and CPF gates via optical cavities. These schemes can be directly applied to construct an entanglement channel for a communication system between two users. Consequently, it is possible for the trust center, having quantum nodes, to accomplish the linked channel (entanglement channel) between the two separate long-distance users via the distribution of Bell states and entanglement swapping. Furthermore, in our schemes, the main physical component is the CPF gate between the photons and the three-level atoms in cavity QED, which is feasible in practice. Thus, our schemes can be experimentally realized with current technology.     

Asymptotic distributions of quantum walks on the line with two entangled coins

We advance the previous studies of quantum walks on the line with two coins. Such four-state quantum walks driven by a three-direction shift operator may have nonzero limiting probabilities (localization), thereby distinguishing them from the quantum walks on the line in the basic scenario (i.e., driven by a single coin). In this work, asymptotic position distributions of the quantum walks are examined. We derive a weak limit for the quantum walks and explicit formulas for the limiting probability distribution, whose dependencies on the coin parameter and the initial state of quantum walks are presented. In particular, it is shown that the weak limit for the present quantum walks can be of the form in the basic scenario of quantum walks on the line, for certain initial states of the walk and certain values of the coin parameter. In the case where localization occurs, we show that the limiting probability decays exponentially in the absolute value of a walker??s position, independent of the parity of time.     

Efficient schemes for the quantum teleportation of a sub-class of tripartite entangled states

In this paper we propose two schemes for teleportation of a sub-class of tripartite states, the first one with the four-qubit cluster state and the second one with two Bell pairs as entanglement channels. A four-qubit joint measurement in the first case and two Bell measurements in the second are performed by the sender. Appropriate unitary operations on the qubits at the receiver’s end along with an ancilla qubit result in the perfect teleportation of the tripartite state. Analysis of the quantum circuits employed in these schemes reveal that in our technique the desired quantum tasks are achieved with lesser quantum cost, gate count and classical communication bits compared with other similar schemes.     

On a connection between spectral factorization and geometric control theory

We investigate here how the geometric control theory of Basile, Marro and Wonham can be obtained in a Hilbert space context, as the byproduct of the factorization of a spectral density with no zeros on the imaginary axis. We show how controlled invariant subspaces can be obtained as images of orthogonal projections of co-invariant subspaces onto a semi-invariant (Markovian) subspace of the Hardy space of square integrable functions analytic in the right half-plane. Output nulling subspaces are then related to a particular spectral factorization problem. A similar construction is presented for controllability subspaces, and a new algorithm for the computation of these subspaces is presented.     

On a connection between small set expansions and modularity clustering

In this paper we explore a connection between two seemingly different problems from two different domains: the small-set expansion problem studied in unique games conjecture, and a popular community finding approach for social networks known as the modularity clustering approach. We show that a sub-exponential time algorithm for the small-set expansion problem leads to a sub-exponential time constant factor approximation for some hard input instances of the modularity clustering problem.     

On a possible connection between wormholes and soft gamma repeaters

We consider and discuss the observational properties of gamma-ray bursts transmitted by hypothetical wormholes. We show that the known sources of soft gamma repeaters (SGR) cannot be wormhole candidates.     

Enhancing and protecting quantum correlations of a two-qubit entangled system via non-Hermitian operation

We investigate the dynamics of geometric measure of quantum discord and negativity as a measure of quantum entanglement for the system under the local non-Hermitian operation. Numerical calculations demonstrate that quantum discord and entanglement as two kinds of typical measures of quantum correlations can exceed respective initial value, and their evolution behaviors appear to violate conventional properties which formulates quantum discord and quantum entanglement are invariants under local operations. Our results show that non-Hermitian operation achieves distinctive effects on enhancement and protection of quantum correlations, which is mostly aroused by the non-Hermiticity and the non-unitarity of the non-Hermitian operation.     

On Gnutella topology dynamics by studying leaf and ultra connection jointly in phase space

In this paper, the topology dynamics of Gnutella are studied in phase space. The dynamic progress of peer degree is studied as a time series in two dimensional phase space, which is consisted of numbers of connected leaves and ultras. The reported degrees concentrate on three special software related regions which we name as ultra stable region, leaf stable region and transition belt. A method is proposed on how to classify degree traces in phase space into different categories. Then the connection churn and the degree churn are studied. It shows that the topological structure of Gnutella is more stable in its connection degree than in the topology itself. The connection drop rate is estimated and the lifetime of connections is deduced afterwards. M/M/m/m loss queue system is introduced to model the degree keeping process in Gnutella. This model reveals that the degree stability is ensured by mass new connection efforts. In other words, the stability in topological structure of Gnutella is the results of many essential unstable factors in its topology. We think it raises a challenge to the basic design philosophy for such networks.