Sayatnova Tamaryan

Greenberger-Horne-Zeilinger versus W states : Quantum teleportation through noisy channels

Eylee Jung, Mi-Ra Hwang, You Hwan Ju, Min-Soo Kim, Sahng-Kyoon Yoo, Hungsoo Kim, D. K. Park, Jin-Woo Son, S. Tamaryan, Seong-Keuck Cha 1 Department of Physics, Kyungnam University, Masan, 631-701, Korea 2 Department of Mathematics, Kyungnam University, Masan, 631-701, Korea 3 Green University, Hamyang, 676-872, Korea 4 The Institute of Basic Science, Kyungnam University, Masan, 631-701, Korea 5 Theory Department, Yerevan Physics Institute, Yerevan-36, 375036, Armenia 6 Department of Chemistry, Kyungnam University, Masan, 631-701, Korea Abstract Which state does lose less quantum information between GHZ and W states when they are prepared for two-party quantum teleportation through noisy channel? We address this issue by solving analytically a master equation in the Lindbald form with introducing the noisy channels which makes the quantum channels to be mixed states. It is found that the answer of the question is dependent on the type of the noisy channel. If, for example, the noisy channel is (L2,x, L3,x, L4,x)-type where L s denote the Lindbald operators, GHZ state is always more robust than W state, i.e. GHZ state preserves more quantum information. In, however, (L2,y, L3,y, L4,y)-type channel the situation becomes completely reversed. In (L2,z, L3,z, L4,z)-type channel W state is more robust than GHZ state when the noisy parameter (κ) is comparatively small while GHZ state becomes more robust when κ is large. In isotropic noisy channel we found that both states preserve equal amount of quantum information. A relation between the average fidelity and entanglement for the mixed state quantum channels are discussed.

Maximally entangled three-qubit states via geometric measure of entanglement

Bipartite maximally entangled states have the property that the largest Schmidt coefficient reaches its lower bound. However, for multipartite states, the standard Schmidt decomposition generally does not exist. We use a generalized Schmidt decomposition and the geometric measure of entanglement to characterize three-qubit pure states and derive a single-parameter family of maximally entangled three-qubit states. The paradigmatic Greenberger-Horne-Zeilinger (GHZ) and

Analytic expressions for geometric measure of three-qubit states

W

Duality and the geometric measure of entanglement of general multiqubit W states

states emerge as extreme members in this family of maximally entangled states. This family of states possesses different trends of entanglement behavior: in going from GHZ to

Geometric measure of entanglement and shared quantum states

W

Mixed-state entanglement and quantum teleportation through noisy channels

states, the geometric measure, the relative entropy of entanglement, and the bipartite entanglement all increase monotonically whereas the three-tangle and bipartition negativity both decrease monotonically.

Reduced state uniquely defines the Groverian measure of the original pure state

A method is developed to derive algebraic equations for the geometric measure of entanglement of three-qubit pure states. The equations are derived explicitly and solved in the cases of most interest. These equations allow one to derive analytic expressions of the geometric entanglement measure in a wide range of three-qubit systems, including the general class of W states and states which are symmetric under the permutation of two qubits. The nearest separable states are not necessarily unique, and highly entangled states are surrounded by a one-parametric set of equally distant separable states. A possibility for physical applications of the various three-qubit states to quantum teleportation and superdense coding is suggested from the aspect of entanglement.

Toward an understanding of entanglement for generalized n-qubit W-states

We find the nearest product states for arbitrary generalized W states of n qubits, and show that the nearest product state is essentially unique if the W state is highly entangled. It is specified by a unit vector in Euclidean n-dimensional space. We use this duality between unit vectors and highly entangled W states to find the geometric measure of entanglement of such states.

Universal behavior of the geometric entanglement measure of many-qubit W states

We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different expressions depending on the range of definition in parameter space. Each expression of the measure has its own geometrically meaningful interpretation. Such an interpretation allows oneself to take one step toward a complete understanding for the general properties of the entanglement measure. The states that lie on joint surfaces separating different ranges of definition, designated as shared states, seem to have particularly interesting features. The properties of the shared states are fully discussed.

Logarithmic correction to Newton potential in Randall-Sundrum scenario

The quantum teleportation with a noisy EPR state is discussed. Using an optimal decomposition technique, we compute the concurrence, entanglement of formation and Groverian measure for various noisy EPR resources. It is shown analytically that all entanglement measures reduce to zero when , where is an average fidelity between Alice and Bob. This fact indicates that the entanglement is a genuine physical resource for the teleportation process. This fact gives valuable clues to the optimal decomposition for higher-qubit mixed states. As an example, the optimal decompositions for the 3-qubit mixed states are discussed by adopting a teleportation with a W-state.