Local Invariants and Pairwise Entanglement in Symmetric Multi-qubit System

Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classifcation scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett. 95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.Comment: 9 pages, 2 figures, REVTEX, Replaced with a published versio

The effect of spin-orbit interaction on entanglement of two-qubit Heisenberg XYZ systems in an inhomogeneous magnetic field

The role of spin-orbit interaction on the ground state and thermal entanglement of a Heisenberg XYZ two-qubit system in the presence of an inhomogeneous magnetic field is investigated. For a certain value of spin-orbit parameter $D$, the ground state entanglement tends to vanish suddenly and when $D$ crosses its critical value $D_c$, the entanglement undergoes a revival. The maximum value of the entanglement occurs in the revival region. In finite temperatures there are revival regions in $D-T$ plane. In these regions, entanglement first increases with increasing temperature and then decreases and ultimately vanishes for temperatures above a critical value. This critical temperature is an increasing function of $D$, thus the nonzero entanglement can exist for larger temperatures. In addition, the amount of entanglement in the revival region depends on the spin-orbit parameter. Also, the entanglement teleportation via the quantum channel constructed by the above system is investigated and finally the influence of the spin-orbit interaction on the fidelity of teleportation and entanglement of replica state is studied.Comment: Two columns, 9 pages, 8 Fig

Study of localization in the quantum sawtooth map emulated on a quantum information processor

Quantum computers will be unique tools for understanding complex quantum systems. We report an experimental implementation of a sensitive, quantum coherence-dependent localization phenomenon on a quantum information processor (QIP). The localization effect was studied by emulating the dynamics of the quantum sawtooth map in the perturbative regime on a three-qubit QIP. Our results show that the width of the probability distribution in momentum space remained essentially unchanged with successive iterations of the sawtooth map, a result that is consistent with localization. The height of the peak relative to the baseline of the probability distribution did change, a result that is consistent with our QIP being an ensemble of quantum systems with a distribution of errors over the ensemble. We further show that the previously measured distributions of control errors correctly account for the observed changes in the probability distribution.Comment: 20 pages, 9 figure

Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace

When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subsystem and decoherence free subspace play essential r\^oles in our implementation. The recursive relations also show that the number of gates required to encode $m$ logical qubits increases linearly in $m$.Comment: 9 pages, 3 figure

Relativistic MHD with Adaptive Mesh Refinement

This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO method (CENO) in 3+1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the $\nabla\cdot {\bf B}=0$ constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.Comment: 24 pages, 14 figures, 3 table

Quantum logic with weakly coupled qubits

There are well-known protocols for performing CNOT quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or qubits and resonators coupled by more complicated and less symmetric interactions. Here we consider a widely applicable model of weakly but otherwise arbitrarily coupled two-level systems, and use quantum gate design techniques to derive a simple and intuitive CNOT construction. Useful variations and extensions of the solution are given for common special cases.Comment: 4 pages, Revte

The Surface Brightness Fluctuations and Globular Cluster Populations of M87 and its Companions

Using the surface brightness fluctuations in HST WFPC-2 images, we determine that M87, NGC 4486B, and NGC 4478 are all at a distance of ~16 Mpc, while NGC 4476 lies in the background at ~21 Mpc. We also examine the globular clusters of M87 using archived HST fields. We detect the bimodal color distribution, and find that the amplitude of the red peak relative to the blue peak is greatest near the center. This feature is in good agreement with the merger model of elliptical galaxy formation, where some of the clusters originated in progenitor galaxies while other formed during mergers.Comment: 5 pages, 2 figure

Continuous Variable Quantum State Sharing via Quantum Disentanglement

Quantum state sharing is a protocol where perfect reconstruction of quantum states is achieved with incomplete or partial information in a multi-partite quantum networks. Quantum state sharing allows for secure communication in a quantum network where partial information is lost or acquired by malicious parties. This protocol utilizes entanglement for the secret state distribution, and a class of "quantum disentangling" protocols for the state reconstruction. We demonstrate a quantum state sharing protocol in which a tripartite entangled state is used to encode and distribute a secret state to three players. Any two of these players can collaborate to reconstruct the secret state, whilst individual players obtain no information. We investigate a number of quantum disentangling processes and experimentally demonstrate quantum state reconstruction using two of these protocols. We experimentally measure a fidelity, averaged over all reconstruction permutations, of F = 0.73. A result achievable only by using quantum resources.Comment: Published, Phys. Rev. A 71, 033814 (2005) (7 figures, 11 pages

Quantum entanglement between electronic and vibrational degrees of freedom in molecules

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with a tendency towards double welled potentials using model coupled harmonic diabatic potential-energy surfaces. The von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions in such a bipartite system. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local minima). However, in this region two distinct types of entanglement are found: (1) entanglement that arises purely from the degeneracy of energy levels in the two potential wells and which is destroyed by slight asymmetry, and (2) entanglement that involves strongly interacting states in each well that is relatively insensitive to asymmetry. These two distinct regions are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, semibullvalene, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated

Evolutions of Magnetized and Rotating Neutron Stars

We study the evolution of magnetized and rigidly rotating neutron stars within a fully general relativistic implementation of ideal magnetohydrodynamics with no assumed symmetries in three spatial dimensions. The stars are modeled as rotating, magnetized polytropic stars and we examine diverse scenarios to study their dynamics and stability properties. In particular we concentrate on the stability of the stars and possible critical behavior. In addition to their intrinsic physical significance, we use these evolutions as further tests of our implementation which incorporates new developments to handle magnetized systems.Comment: 12 pages, 8 figure