Relative entropy of entanglement of two-qubit ’X’ states

Two closest single-qubit states could be diagonalised by the same unitary matrix,which helps to find the relative entropy of entanglement of a two-qubit ’X’ state.We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ’X’ state.This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states,such as pure states,Werner states,and so on.     

Maps of Matrices and Portrait Maps of the Density Operators of Composite and Noncomposite Systems

We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary N × N matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite qudit systems. The structure of the maps is inspired by “portrait” map of the probability vectors corresponding to the action on the vectors by stochastic matrices containing either unity or zero matrix elements. We obtain new entropic inequalities for arbitrary qudit states including a single qudit and discuss entangled single qudit state. We consider in detail the examples of N = 3 and 4. Also we point out the possible use of entangled states of systems without subsystems (e.g., a single qudit) as a resource for quantum computations.     

Resource-Efficient Direct Entanglement Measurement of Werner State with Hybrid Spin-Photon Interaction System

We propose two resource-efficient schemes of direct entanglement measurement of two-qubit Werner states via hybrid interaction system with nitrogen-vacancy (NV) center coupled to micro-cavity. Based on the unconventional encoding mode on auxiliary qubits, our physical unit can realize the hybrid controlled phase gate and controlled-NOT gate between spin and polarization qubits. Utilizing only one copy of initial entangled state, we implement direct concurrence measurement of spin Werner states in NV centers and polarization Werner states of single photons. Both schemes can be transformed into remote ones with the initial entangled states possessed by spatially separated participants. Experimental feasibility analyses indicate that the presented schemes have reliable performance in the current available experimental conditions.

     

Inequalities for Purity Parameters of Multiqudit and Single-Qudit States

We analyze the recently found inequality for eigenvalues of the density matrix and purity parameters describing either a bipartite-system state or a single-qudit state. We rewrite the Minkowski-type trace inequality for the density matrices of the qudit states in terms of the purity parameters and discuss the properties of the inequality obtained, paying special attention to the X-states of two qubits and a single qudit. Also we study the relation of the purity inequalities obtained with the entanglement.     

Deformed Subadditivity Condition for Qudit States and Hybrid Positive Maps

We extend the subadditivity condition for q-deformed entropy of a bipartite quantum system to the case of an arbitrary quantum system including the single qudit state. We present the subadditivity condition for the density matrix of the single qutrit state in an explicit form. We obtain the inequality for the purity parameters of a bipartite quantum system and its subsystems. We propose a positive map construction using the fiducial density matrix.     

Decay of entanglement in coupled,driven systems with bipartite decoherence

We analyze a system of two qubits embedded in two different environments. The qubits are coupled to each other and driven on-resonance by two external classical sources. In the secular limit, we obtain exact analytical results for the evolution of the system for several classes of two-qubit mixed initial states. For Werner states we show that the decay of entanglement does not depend on coupling. For other initial states with “X"-type density matrices we find that the sudden death time displays a rich dependence on the coupling energy and state parameters due to the existence of processes of delayed sudden birth of entanglement.     

Concrete Representation and Separability Criteria for Symmetric Quantum State

Using the typical generators of the special unitary groups S U(2), the concrete representation of symmetric quantum state is established, then the relations satisfied by those coefficients in the representation are presented. Based on the representation of density matrix, the PPT criterion and CCNR criterion are proved to be equivalent on judging the separability of symmetric quantum states. Moreover, it is showed that the matrix Γ _ρ of symmetric quantum state only has five efficient entries, thus the calculation of ∥Γ _ρ ∥ is simplified. Finally, the quantitative expressions of real symmetric quantum state under the ∥Γ _ρ ∥ separability criterion are obtained.     

Improving Accuracy of Estimating Two-Qubit States with Hedged Maximum Likelihood

As a widely used reconstruction algorithm in quantum state tomography,maximum likelihood estimation tends to assign a rank-deficient matrix,which decreases estimation accuracy for certain quantum states.Fortunately,hedged maximum likelihood estimation(HMLE)[Phys.Rev.Lett.105(2010)200504] was proposed to avoid this problem.Here we study more details about this proposal in the two-qubit case and further improve its performance.We ameliorate the HMLE method by updating the hedging function based on the purity of the estimated state.Both performances of HMLE and ameliorated HMLE are demonstrated by numerical simulation and experimental implementation on the Werner states of polarization-entangled photons.     

Tomographic causal analysis of two-qubit states and tomographic discord

We study a behavior of two-qubit states subject to tomographic measurement. In this Letter we propose a novel approach to definition of asymmetry in quantum bipartite state based on its tomographic Shannon entropies. We consider two types of measurement bases: the first is one that diagonalizes density matrices of subsystems and is used in a definition of tomographic discord, and the second is one that maximizes Shannon mutual information and relates to symmetrical form quantum discord. We show how these approaches relate to each other and then implement them to the different classes of two-qubit states. Consequently, new subclasses of X-states are revealed.     

Role of dipole image forces in molecular adsorption

The transverse-field XY model in one dimension is a well-known spin model for which the ground state properties and excitation spectrum are known exactly. The model has an interesting phase diagram describing quantum phase transitions (QPTs) belonging to two different universality classes. These are the transverse-field Ising model and the XX model universality classes with both the models being special cases of the transverse-field XY model. In recent years, quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity have been shown to provide signatures of QPTs. Another interesting issue is that of decoherence to which a quantum system is subjected due to its interaction, represented by a quantum channel, with an environment. In this paper, we determine the dynamics of different types of correlations present in a quantum system, namely, the mutual information I(?? _AB ), the classical correlations C(?? _AB ) and the quantum correlations Q(?? _AB ), as measured by the quantum discord, in a two-qubit state. The density matrix of this state is given by the nearest-neighbour reduced density matrix obtained from the ground state of the transverse-field XY model in 1d. We assume Markovian dynamics for the time-evolution due to system-environment interactions. The quantum channels considered include the bit-flip, bit-phase-flip and phase-flip channels. Two different types of dynamics are identified for the channels in one of which the quantum correlations are greater in magnitude than the classical correlations in a finite time interval. The origins of the different types of dynamics are further explained. For the different channels, appropriate quantities associated with the dynamics of the correlations are identified which provide signatures of QPTs. We also report results for further-neighbour two-qubit states and finite temperatures.     

Tensor representation in teleportation and controlled teleportation

We propose the tensor representation of teleportation and controlled teleportation. By using this representation, it is easy to describe the process of teleporting an unknown N-qubit state via a genuine 2N-qubit channel, and to find the necessary and sufficient condition of realizing a successful teleportation (which is determined by the measurement matrix T^α and the quantum channel parameter matrix X). For controlled teleportation, if composing tensor representation with graph, one can easily design any kind of controlled teleportation. As examples, we give a scheme of symmetrically controlled teleportation of two-qubit states and a scheme of representative network controlled of three-qubit states. This method can also be generalized to the controlled teleportation of N-qubit states.     

Density matrix interpretation of solutions of Lie-Nambu equations

The spectrum of a density matrix ρ(t) is conserved by the Lie-Nambu dynamics if ρ(t) is a self-adjoint and Hilbert-Schmidt solution of a nonlinear triple-bracket equation. This generalizes the previous result, which was valid for finite-dimensional Hilbert spaces, to arbitrary separable (positive- and indefinite-metric) Hilbert spaces.     

Assisted Cloning and Orthogonal Complementing of an Arbitrary Unknown Two-Qubit State with χ-Type Entangled States

We propose a scheme for cloning an arbitrary unknown two-qubit state and its orthogonal complement state with the assistance from the state preparer. Our scheme includes two stages. The first stage requires a quantum teleportation process, in which an arbitrary unknown two-qubit state can be deterministically teleported from the sender to the receiver with χ-type entangled states as the quantum channel. In the second stage, with the assistance of the state preparer, either a perfect copy or an orthogonal complement state of an arbitrary unknown two-qubit state can be obtained with a certain probability.     

Monogamy and entanglement in tripartite quantum states

We present an interesting monogamy equation for (2⊗2⊗n)-dimensional pure states, by which a quantity is found to characterize the tripartite entanglement with the GHZ type and W type entanglements as a whole. In particular, we, for the first time, reveals that for any quantum state of a pair of qubits, the difference between the two remarkable entanglement measures, concurrence and negativity, characterizes the W type entanglement of tripartite pure states with the two-qubit state as reduced density.     

Classical and fractal analysis of vehicle demand on the ferry-boat system

Transportation problems are important complex systems because of the increased number of vehicles in cities. In this paper, we study time series of vehicle demand by using the ferry-boat system between Salvador city and Itaparica island, in Bahia, Brazil. We compare the traditional demand analysis (ARIMA method) with the self-affine ones (the scaling exponent α and the density of crossing points ρ). In addition, taking into account the inherent self-affine behavior we study the stationary states of this dynamic process by using a nonlinear Fokker-Planck equation. The present findings indicate that the scaling exponent α describes some properties of flux of vehicles using the ferry-boat system. The behavior of α gives an alternative explanation about demand analysis, and the nonlinear Fokker-Planck equation presents a solution close to the stationary behavior of this complex dynamical analysis.     

Nonlinear interference in a mean-field quantum model

Using similar nonlinear stationary mean-field models for both a 2D axisymmetricalBose-Einstein Condensate and an electron pair in a parabolic trap, we propose to describethe original many-particle ground state as a one-particle mixed state (in contrast to apure state), i.e. as a statistical ensemble of several one-particle quantum states. Thesequantum states are the eigenfunctions of the corresponding stationary nonlinearSchrödinger equation (hence called “nonlinear eigenstates”). Due to their nonlinearity,they are not orthogonal. Therefore, taking the simple example of a two-level system, weshow that each of these two nonlinear eigenstates |i? and|j? occurs with a probability (or statistical weight) that isdefined by their non-orthogonality ?i|j? 0. We givethe corresponding density matrix. We search for physical grounds in the interpretation ofour two main results, namely, a quantum-classical nonlinear transition and theinterference between two “nonlinear eigenstates”.     

Quark condensate in the nuclear matter

We calculate the quark condensate in the nuclear matter, taking into account the single-pion and two-pion exchanges between nucleons. We find the dependence of the averaged value of the quark operator¯qq on the density of the matterρ. At very low density the nonlinear terms are proportional toρ ² and increase the tendency to restoration of the chiral symmetry. At larger values of density the account of interaction inside the matter slower down the restoration of chiral symmetry compared to the gas approximation law. The leading nonlinear term in Fermi momentum power expansion becomes of the orderρ ^4/3 . The value of the condensate at the saturation value of density is obtained. The role of multinucleon effects is analyzed.     

Von Neumann entropy-preserving quantum operations

For a given quantum state ρ and two quantum operations Φ and Ψ, the information encoded in the quantum state ρ is quantified by its von Neumann entropy S(ρ). By the famous Choi-Jamio?kowski isomorphism, the quantum operation Φ can be transformed into a bipartite state, the von Neumann entropy Smap(Φ) of the bipartite state describes the decoherence induced by Φ. In this Letter, we characterize not only the pairs (Φ,ρ) which satisfy S(Φ(ρ))=S(ρ), but also the pairs (Φ,Ψ) which satisfy Smap(Φ°Ψ)=Smap(Ψ).     

God Plays Coins or Superposition Principle for Classical Probabilities in Quantum Suprematism Representation of Qubit States

We construct the quantum density matrix of a spin-1/2 state for three given probability distributions describing positions of three classical coins and associate its matrix elements with the Triada of Malevich’s squares. We present the superposition principle of spin-1/2 states in the form of a nonlinear addition rule for these classical coin probabilities. We illustrate the obtained formulas by the statement “God does not play dice – God plays coins.”