Distillation of Bell states in open systems

In this work we review the entire classification of 2x2 distillable states for protocols with a finite numbers of copies. We show a distillation protocol that allows to distill Bell states with non zero probability at any time for an initial singlet in vacuum. It is shown that the same protocol used in non zero thermal baths yields a considerable recovering of entanglement.Comment: 10 pages, 3 figure

Pedestrian index theorem a la Aharonov-Casher for bulk threshold modes in corrugated multilayer graphene

Zero-modes, their topological degeneracy and relation to index theorems have attracted attention in the study of single- and bilayer graphene. For negligible scalar potentials, index theorems explain why the degeneracy of the zero-energy Landau level of a Dirac hamiltonian is not lifted by gauge field disorder, for example due to ripples, whereas other Landau levels become broadened by the inhomogenous effective magnetic field. That also the bilayer hamiltonian supports such protected bulk zero-modes was proved formally by Katsnelson and Prokhorova to hold on a compact manifold by using the Atiyah-Singer index theorem. Here we complement and generalize this result in a pedestrian way by pointing out that the simple argument by Aharonov and Casher for degenerate zero-modes of a Dirac hamiltonian in the infinite plane extends naturally to the multilayer case. The degeneracy remains, though at nonzero energy, also in the presence of a gap. These threshold modes make the spectrum asymmetric. The rest of the spectrum, however, remains symmetric even in arbitrary gauge fields, a fact related to supersymmetry. Possible benefits of this connection are discussed.Comment: 6 pages, 2 figures. The second version states now also in words that the conjugation symmetry that in the massive case gets replaced by supersymmetry is the chiral symmetry. Changes in figure

Torsion induces Gravity

In this work the Poincare-Chern Simons and Anti de Sitter Chern Simons gravities are studied. For both a solution that can be casted as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions respectively.Comment: 4 pages, RevTe

Temporal meson correlators at finite temperature on quenched anisotropic lattice

We study charmonium correlators at finite temperature in quenched anisotropic lattice QCD. The smearing technique is applied to enhance the low energy part of the correlator. We use two analysis procedures: the maximum entropy method for extraction of the spectral function without assuming specific form, as an estimate of the shape of spectral function, and the $\chi^2$ fit assuming typical forms as quantitative evaluation of the parameters associated to the forms. We find that at $T\simeq 0.9T_c$ the ground state peak has almost the same mass as at T=0 and almost vanishing width. At $T\simeq 1.1T_c$, our result suggests that the correlator still has nontrivial peak structure at almost the same position as below $T_c$ with finite width.Comment: Lattice 2002 Nonzero temperature 3page

Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation

The isoholonomic problem in a homogeneous bundle is formulated and solved exactly. The problem takes a form of a boundary value problem of a variational equation. The solution is applied to the optimal control problem in holonomic quantum computer. We provide a prescription to construct an optimal controller for an arbitrary unitary gate and apply it to a $k$-dimensional unitary gate which operates on an $N$-dimensional Hilbert space with $N \geq 2k$. Our construction is applied to several important unitary gates such as the Hadamard gate, the CNOT gate, and the two-qubit discrete Fourier transformation gate. Controllers for these gates are explicitly constructed.Comment: 19 pages, no figures, LaTeX2

Single-experiment-detectable multipartite entanglement witness for ensemble quantum computing

In this paper we provide an operational method to detect multipartite entanglement in ensemble-based quantum computing. This method is based on the concept of entanglement witness. We decompose the entanglement witness for each class of multipartite entanglement into nonlocal operations in addition to local measurements. Individual single qubit measurements are performed simultaneously, hence complete detection of entanglement is performed in a single run experiment. This approach is particularly important for experiments where it is operationally difficult to prepare several copies of an unknown quantum state and in this sense the introduced scheme in this work is superior to the generally used entanglement witnesses that require a number of experiments and preparation of copies of quantum state.Comment: 9 pages, 5 figures, minor changes have been mad

Topological Signature of First Order Phase Transitions

We show that the presence and the location of first order phase transitions in a thermodynamic system can be deduced by the study of the topology of the potential energy function, V(q), without introducing any thermodynamic measure. In particular, we present the thermodynamics of an analytically solvable mean-field model with a k-body interaction which -depending on the value of k- displays no transition (k=1), second order (k=2) or first order (k>2) phase transition. This rich behavior is quantitatively retrieved by the investigation of a topological invariant, the Euler characteristic, of some submanifolds of the configuration space. Finally, we conjecture a direct link between the Euler characteristic and the thermodynamic entropy.Comment: 6 pages, 2 figure

Quantum critical scaling of the geometric tensors

Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.Comment: Typos correcte

Reply to the comment by D. Kreimer and E. Mielke

We respond to the comment by Kreimer et. al. about the torsional contribution to the chiral anomaly in curved spacetimes. We discuss their claims and refute its main conclusion.Comment: 9 pages, revte