Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.     

Connections of Coherent Information,Quantum Discord,and Entanglement

For a pure non-markovian dephasing model we derive analytic expressions of coherent information,quantum discord,and entanglement.We find that for the cases of the initial Werner states,the dynamical behavior of coherent information is similar to that of quantum discord but different from that of entanglement.Coherent information,as well as quantum discord,can reveal the quantum correlations in some mixed-states,in which the entanglement is zero.     

Switching and Swapping of Quantum Information: Entropy and Entanglement Level

Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local quantum information and its existence proof, together with some elementary properties analysed through the prism of the concept of the entropy, are presented. As an example of the local information swapping usage, we demonstrate a certain realisation of the quantum switch. Entanglement levels, during the work of the switch, are calculated with the Negativity measure and a separability criterion based on the von Neumann entropy, spectral decomposition and Schmidt decomposition. Results of numerical experiments, during which the entanglement levels are estimated for systems under consideration with and without distortions, are presented. The noise is generated by the Dzyaloshinskii-Moriya interaction and the intrinsic decoherence is modelled by the Milburn equation. This work contains a switch realisation in a circuit form—built out of elementary quantum gates, and a scheme of the circuit which estimates levels of entanglement during the switch’s operating.     

On the Entanglement Structure in Quantum Cloning

We study the entanglement properties of the output state of a universal cloning machine. We analyse in particular bipartite and tripartite entanglement of the clones, and discuss the classical limit of infinitely many output copies.     

Many-Agent Controlled Teleportation of Multi-qubit Quantum Information via Quantum Entanglement Swapping

We present a method to teleport multi-qubit quantum information in an easy way from a sender to a receiver via the control of many agents in a network. Only when all the agents collaborate with the quantum information receiver can the unknown states in the sender＇s qubits be fully reconstructed in the receiver＇s qubits. In our method, agents＇s control parameters are obtained via quantum entanglement swapping. As the realization of the many-agent controlled teleportation is concerned, compared to the recent method [G.P. Yang, et al., Phys. Rev. A 70 （2004） 022329], our present method considerably reduces the preparation difficulty of initial states and the identification difficulty of entangled states, moreover, it does not need local Hadamard operations and it is more feasible in technology.     

Many-Agent Controlled Teleportation of Multi-qubit Quantum Information via Quantum Entanglement Swapping

We present a method to teleport multi-qubit quantum information in an easy way from a sender to a receiver via the control of many agents in a network. Only when all the agents collaborate with the quantum information receiver can the unknown states in the sender‘s qubits be fully reconstructed in the receiver‘s qubits. In our method,agents‘s control parameters are obtained via quantum entanglement swapping. As the realization of the many-agent controlled teleportation is concerned, compared to the recent method [C.P. Yang, et al., Phys. Rev. A 70 (2004) 022329],our present method considerably reduces the preparation difficulty of initial states and the identification difficulty of entangled states, moreover, it does not need local Hadamard operations and it is more feasible in technology.     

Single-particle Entanglement and Its Application to Quantum Information Processing

Single-particle entanglement refers to entanglement produced with a single particle. It can be generated by illuminating a beam splitter with a single photon. We describe experimental schemes to realize quantum teleportation and quantum key distribution utilizing single-particle entanglement, and discuss the strengths and drawbacks of the schemes compared with the standard scheme utilizing two-photon polarization states. We show, in particular, that the quantum key distribution scheme based on single-particle entanglement is associated with a relatively high value of the bits of information transferred per particle sent and can thus be cost effective.     

The Role of Entanglement in Quantum Measurement and Information Processing

The significance of the quantum feature of entanglement between physical systems is investigated in the context of quantum measurements. It is shown that, while there are measurement couplings that leave the object and probe systems nonentangled, no information transfer from object to probe can take place unless there is at least some intermittent period where the two systems are entangled.     

Controlled Teleportation of Multi-qudit Quantum Information by Entanglement Swapping

In this paper, we present a scheme for teleporting multi-qudit quantum state, from the sender Alice to the receiver Charlie via many controllers Bobs, whose control parameters are obtained using entanglement swapping of maximally d-dimensional EPR pair. In our scheme, Yang＇s qutrit controlled teleportation protocol [Commun. Theor. Phys. 49 （2008） 338] based on Bell-state entanglement swapping is generalized to the qudit case. The scheme of multi-qudit owns the advantage of having higher code capacity and better security than that of multi-qutrit.     

Controlled Teleportation of Multi-qutrit Quantum Information by Swapping Entanglement

We present a scheme for teleporting multi-qutrit quantum information from a sender to a receiver via the control of many agents in a network. Agents＇s control parameters are obtained via quantum entanglement swapping. In our scheme, Zhang and Man＇s QSS protocol [Phys. Rev. A 72 （2005） 022303] based on Bell-state entanglement swapping is generalized to a qutrit case. Our scheme owns the advantage of having higher code capacity and better security than the work [Commun. Theor. Phys. 44 （2005） 847] on controlled teleportation for multi-qubit.     

Local Information as an Essential Factor for Quantum Entanglement

Quantum entanglement is not only a fundamental concept in quantum mechanics but also a special resource for many important quantum information processing tasks. An intuitive way to understand quantum entanglement is to analyze its geometric parameters which include local parameters and correlation parameters. The correlation parameters have been extensively studied while the role of local parameters have not been drawn attention. In this paper, we investigate the question how local parameters of a two-qubit system affect quantum entanglement in both quantitative and qualitative perspective. Firstly, we find that the concurrence, a measure of quantum entanglement, of a general two-qubit state is bounded by the norms of local vectors and correlations matrix. Then, we derive a sufficient condition for a two-qubit being separable in perspective of local parameters. Finally, we find that different local parameters could make a state with fixed correlation matrix separable, entangled or even more qualitatively entangled than the one with vanished local parameters.     

Exploring Tripartite Quantum Correlations: Entanglement Witness and Quantum Discord

In this study, we explore the tripartite quantum correlations by employing the quantum relative entropy as a distance measure. First, we evaluate the explicit expression for nonlinear entanglement witness (EW) of tripartite systems in the four dimensional space that lends itself to a straightforward algorithm for finding closest separable state (CSS) to the generic state. Then using nonlinear EW with specific feasible regions (FRs), quantum discord is derived analytically for the three-qubit and tripartite systems in the four dimensional space. Furthermore, we explicitly figure out the additivity relation of quantum correlations in tripartite systems.     

On Entanglement Breaking Channels for Infinite Dimensional Quantum Systems

The topic of entanglement breaking channels plays an important role in quantum information. Horodecki et al. (Rev. Math. Phys. 15:629–641, 2003) gave a complete characterization of entanglement breaking channels for finite dimensional quantum systems. In the note, we will generalize the results in Horodecki et al. (Rev. Math. Phys. 15:629–641, 2003) to the infinite dimensional case. We first generalized the positive map criterion of the entanglement breaking channel from the finite dimensional case to the infinite dimensional case. As a generalization of entanglement breaking channels for finite dimensional quantum systems, the topic of the strong entanglement breaking channel for arbitrary (finite or infinite) dimensional systems is putted forward. We obtain the operator sum representation of the strong entanglement breaking quantum channel. Applying this operator sum representation, we characterize a category of extreme points of the convex set of all strong entanglement breaking channels, which generalizes corresponding results in the finite dimensional case from Horodecki et al. (Rev. Math. Phys. 15:629–641, 2003).     

Entanglement Swapping for Cluster-Class States and Its Applications in Quantum Information Processing

Entanglement swapping for four-qubit cluster-class states is studied. It is shown that a four-qubit cluster state (maximally entangled) can be obtained with a certain probability from two four-qubit cluster-class states by entanglement swapping. The probability is related to the smallest superposition coefficient of the cluster-class states (when all the moduli of amplitudes are equivalent, they are the usual cluster states and the probability hits to one). Two examples for the applications of the entanglement swapping are also presented. One is quantum teleportation of an arbitrary two-qubit state via a quantum repeater, in which the success probability can be improved by the entanglement swapping when the quantum channels are general cluster-class states (partially entangled). The other is quantum key distribution, in which a secret random sequence of bits (a “key”) can be efficiently established between two distant parties by the entanglement swapping of two groups of cluster states.     

Entanglement, Quantum Discord, and Non-locality in Bell-Diagonal States

Experimental approach to characterize the non-locality, entanglement, and quantum correlation of a multiparity quantum system is one of the important subjects in quantum information theory. Here, by investigating the violations of Bell inequality (BI), we analyze the relations among the non-locality, concurrence C, and quantum discord Q typically for a family of Bell-diagonal states. It is shown that, for the optimal measurement basis the BI is always violated, if the quantum discord is larger than 0.5031 and the concurrence is larger than 0.5605. Certainly, the BI is maximally violated for the maximal entanglement and quantum discord, i.e., C=Q=1. Our generic results are demonstrated with a thermal XY model of the two-qubit system with controllable interbit couplings.     

Fermi-Bose Systems, Macroscopic Quantum Superposition States and Entanglement

We study the entanglement of states of a simple Fermi-Bose system. The Hilbert space is C ² l₂ (N). An explicit expression is given for the entanglement. We consider number states, coherent states and macroscopic quantum superposition states in the product system. Explicit formulas for the entanglement are also given in each of these cases.     

Entanglement in the Quantum Ising Model

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field. When the field is sufficiently strong, the entanglement grows at most logarithmically in the number of spins. The proof utilises a transformation to a model of classical probability called the continuum random-cluster model, and is based on a property of the latter model termed ratio weak-mixing. In an intermediate result, we establish an exponentially decaying bound on the operator norm of differences of the reduced density operator. Of special interest is the mathematical rigour of this work, and the fact that the proof applies equally to a large class of disordered interactions.     

Generation of Two-Atom Maximal Entanglement and Quantum Information Transfer via Microtoroidal Cavity-Atom System

We propose a scheme for generation of two-atom maximally entangled states and the quantum information transfer between two atoms via two identical atoms in resonation with ultrahigh-Q, toroidal microcavities.     

Combinatory-Algebraic Perspective on Multipartiteness,Entanglement and Quantum Localization

We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states. In a more general setting, to capture the relativity and variability of our structures with respect to the observation means, sheaves of algebras may need be introduced. We provide the general formalism based on algebras which exhibits the relativity of multipartiteness and localization.