Mixed-State Entanglement and Quantum Teleportation through Noisy Channels

The quantum teleportation with 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 $\bar{F} \leq 2/3$, where $\bar{F}$ 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 on the optimal decomposition for higher-qubit mixed states. As an example, the optimal decompositions for the three-qubit mixed states are discussed by adopting a teleportation with W-stateComment: 18 pages, 4 figure

Amplitude Damping for single-qubit System with single-qubit mixed-state Environment

We study a generalized amplitude damping channel when environment is initially in the single-qubit mixed state. Representing the affine transformation of the generalized amplitude damping by a three-dimensional volume, we plot explicitly the volume occupied by the channels simulatable by a single-qubit mixed-state environment. As expected, this volume is embedded in the total volume by the channels which is simulated by two-qubit enviroment. The volume ratio is approximately 0.08 which is much smaller than 3/8, the volume ratio for generalized depolarizing channels.Comment: 13 pages, 2 figures incluided V2: homepage address is included in reference V3: version to appear in J. Phys. A: Mathematical and Theoretica

Compromise of Localized Graviton with a Small Cosmological Constant in Randall-Sundrum Scenario

A new mechanism which leads to a linearized massless graviton localized on the brane is found in the $AdS$/CFT setting, {\it i.e.} in a single copy of $AdS_5$ spacetime with a singular brane on the boundary, within the Randall-Sundrum brane-world scenario. With an help of a recent development in path-integral techniques, a one-parameter family of propagators for linearized gravity is obtained analytically, in which a parameter $\xi$ reflects various kinds of boundary conditions that arise as a result of the half-line constraint. In the case of a Dirichlet boundary condition ($\xi = 0$) the graviton localized on the brane can be massless {\it via} coupling constant renormalization. Our result supports a conjecture that the usual Randall-Sundrum scenario is a regularized version of a certain underlying theory.Comment: 6 pages, no figure, V2 12 pages, one more author added, will appear in PL

Electrified Fuzzy Spheres and Funnels in Curved Backgrounds

We use the non-Abelian DBI action to study the dynamics of $N$ coincident $Dp$-branes in an arbitrary curved background, with the presence of a homogenous world-volume electric field. The solutions are natural extensions of those without electric fields, and imply that the spheres will collapse toward zero size. We then go on to consider the $D1-D3$ intersection in a curved background and find various dualities and automorphisms of the general equations of motion. It is possible to map the dynamical equation of motion to the static one via Wick rotation, however the additional spatial dependence of the metric prevents this mapping from being invertible. Instead we find that a double Wick rotation leaves the static equation invariant. This is very different from the behaviour in Minkowski space. We go on to construct the most general static fuzzy funnel solutions for an arbitrary metric either by solving the static equations of motion, or by finding configurations which minimise the energy. As a consistency check we construct the Abelian $D3$-brane world-volume theory in the same generic background and find solutions consistent with energy minimisation. In the $NS$5-brane background we find time dependent solutions to the equations of motion, representing a time dependent fuzzy funnel. These solutions match those obtained from the $D$-string picture to leading order suggesting that the action in the large $N$ limit does not need corrections. We conclude by generalising our solutions to higher dimensional fuzzy funnels.Comment: 38 pages, Latex; references adde

Geometric Entanglement of Symmetric States and the Majorana Representation

Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-based quantum computing is also discussed.Comment: 10 pages, 8 figures; submitted to Lecture Notes in Computer Science (LNCS

Additivity and non-additivity of multipartite entanglement measures

We study the additivity property of three multipartite entanglement measures, i.e. the geometric measure of entanglement (GM), the relative entropy of entanglement and the logarithmic global robustness. First, we show the additivity of GM of multipartite states with real and non-negative entries in the computational basis. Many states of experimental and theoretical interests have this property, e.g. Bell diagonal states, maximally correlated generalized Bell diagonal states, generalized Dicke states, the Smolin state, and the generalization of D\"{u}r's multipartite bound entangled states. We also prove the additivity of other two measures for some of these examples. Second, we show the non-additivity of GM of all antisymmetric states of three or more parties, and provide a unified explanation of the non-additivity of the three measures of the antisymmetric projector states. In particular, we derive analytical formulae of the three measures of one copy and two copies of the antisymmetric projector states respectively. Third, we show, with a statistical approach, that almost all multipartite pure states with sufficiently large number of parties are nearly maximally entangled with respect to GM and relative entropy of entanglement. However, their GM is not strong additive; what's more surprising, for generic pure states with real entries in the computational basis, GM of one copy and two copies, respectively, are almost equal. Hence, more states may be suitable for universal quantum computation, if measurements can be performed on two copies of the resource states. We also show that almost all multipartite pure states cannot be produced reversibly with the combination multipartite GHZ states under asymptotic LOCC, unless relative entropy of entanglement is non-additive for generic multipartite pure states.Comment: 45 pages, 4 figures. Proposition 23 and Theorem 24 are revised by correcting a minor error from Eq. (A.2), (A.3) and (A.4) in the published version. The abstract, introduction, and summary are also revised. All other conclusions are unchange