Neighbours of Einstein's Equations: Connections and Curvatures

Once the action for Einstein's equations is rewritten as a functional of an SO(3,C) connection and a conformal factor of the metric, it admits a family of ``neighbours'' having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in general very complicated. The Einstein case is distinguished by the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the general case the theory is bimetric on the fibers.Comment: 16 pages, LaTe

Convex politopes and quantum separability

We advance a novel perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose an criterium based on the consideration of convex subsets of quantum states. This criterium generalizes a property of product states to convex subsets (of the set of quantum-states) that is able to uncover a new geometrical property of the separability property

Truncations of Random Orthogonal Matrices

Statistical properties of non--symmetric real random matrices of size $M$, obtained as truncations of random orthogonal $N\times N$ matrices are investigated. We derive an exact formula for the density of eigenvalues which consists of two components: finite fraction of eigenvalues are real, while the remaining part of the spectrum is located inside the unit disk symmetrically with respect to the real axis. In the case of strong non--orthogonality, $M/N=$const, the behavior typical to real Ginibre ensemble is found. In the case $M=N-L$ with fixed $L$, a universal distribution of resonance widths is recovered.Comment: 4 pages, final revised version (one reference added, minor changes in Introduction

Statistical bounds on the dynamical production of entanglement

We present a random-matrix analysis of the entangling power of a unitary operator as a function of the number of times it is iterated. We consider unitaries belonging to the circular ensembles of random matrices (CUE or COE) applied to random (real or complex) non-entangled states. We verify numerically that the average entangling power is a monotonic decreasing function of time. The same behavior is observed for the "operator entanglement" --an alternative measure of the entangling strength of a unitary. On the analytical side we calculate the CUE operator entanglement and asymptotic values for the entangling power. We also provide a theoretical explanation of the time dependence in the CUE cases.Comment: preprint format, 14 pages, 2 figure

Quantifying nonclassicality: global impact of local unitary evolutions

We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. We derive the exact relation between the global state change induced by local unitary evolutions and the amount of quantum correlations. We prove that the minimal change coincides with the geometric measure of discord (defined via the Hilbert- Schmidt norm), thus providing the latter with an operational interpretation in terms of the capability of a local unitary dynamics to modify a global state. We establish that two-qubit Werner states are maximally quantum correlated, and are thus the ones that maximize this type of global quantum effect. Finally, we show that similar results hold when replacing the Hilbert-Schmidt norm with the trace norm.Comment: 5 pages, 1 figure. To appear in Physical Review

A special simplex in the state space for entangled qudits

Focus is on two parties with Hilbert spaces of dimension d, i.e. "qudits". In the state space of these two possibly entangled qudits an analogue to the well known tetrahedron with the four qubit Bell states at the vertices is presented. The simplex analogue to this magic tetrahedron includes mixed states. Each of these states appears to each of the two parties as the maximally mixed state. Some studies on these states are performed, and special elements of this set are identified. A large number of them is included in the chosen simplex which fits exactly into conditions needed for teleportation and other applications. Its rich symmetry - related to that of a classical phase space - helps to study entanglement, to construct witnesses and perform partial transpositions. This simplex has been explored in details for d=3. In this paper the mathematical background and extensions to arbitrary dimensions are analysed.Comment: 24 pages, in connection with the Workshop 'Theory and Technology in Quantum Information, Communication, Computation and Cryptography' June 2006, Trieste; summary and outlook added, minor changes in notatio

Thermal states of the Kitaev honeycomb model: a Bures metric analysis

We analyze the Bures metric over the canonical thermal states for the Kitaev honeycomb mode. In this way the effects of finite temperature on topological phase transitions can be studied. Different regions in the parameter space of the model can be clearly identified in terms of different temperature scaling behavior of the Bures metric tensor. Furthermore, we show a simple relation between the metric elements and the crossover temperature between the quasi-critical and the quasi-classical regions. These results extend the ones of [29,30] to finite temperatures.Comment: 6 pages, 2 figure

On the Interacting Chiral Gauge Field Theory in D=6 and the Off-Shell Equivalence of Dual Born-Infeld-Like Actions

A canonical action describing the interaction of chiral gauge fields in D=6 Minkowski space-time is constructed. In a particular partial gauge fixing it reduces to the action found by Perry and Schwarz. The additional gauge symmetries are used to show the off-shell equivalence of the dimensional reduction to D=5 Minkowski space-time of the chiral gauge field canonical action and the Born-Infeld canonical action describing an interacting D=5 Abelian vector field. Its extension to improve the on-shell equivalence arguments of dual D-brane actions to off-shell ones is discussed.Comment: 18 page

Climbing fiber regulation of spontaneous Purkinje cell activity and cerebellum-dependent blink responses

It has been known for a long time that GABAergic Purkinje cells in the cerebellar cortex, as well as their target neurons in the cerebellar nuclei, are spontaneously active. The cerebellar output will, therefore, depend on how input is integrated into this spontaneous activity. It has been shown that input from climbing fibers originating in the inferior olive controls the spontaneous activity in Purkinje cells. While blocking climbing fiber input to the Purkinje cells causes a dramatic increase in the firing rate, increased climbing fiber activity results in reduced Purkinje cell activity. However, the exact calibration of this regulation has not been examined systematically. Here we examine the relation between climbing fiber stimulation frequency and Purkinje cell activity in unanesthetized decerebrated ferrets. The results revealed a gradual suppression of Purkinje cell activity, starting at climbing fiber stimulation frequencies as low as 0.5 Hz. At 4 Hz, Purkinje cells were completely silenced. This effect lasted an average of 2 min after the stimulation rate was reduced to a lower level. We also examined the effect of sustained climbing fiber stimulation on overt behavior. Specifically, we analyzed conditioned blink responses, which are known to be dependent on the cerebellum, while stimulating the climbing fibers at different frequencies. In accordance with the neurophysiological data, the conditioned blink responses were suppressed at stimulation frequencies of =4 Hz

Hierarchies of Geometric Entanglement

We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows to discriminate among the different contributions. The extended measures are applied to the study of entanglement in different classes of $N$-qubit pure states. These classes include $W$ and $GHZ$ states, and their symmetric superpositions; symmetric multi-magnon states; cluster states; and, finally, asymmetric generalized $W$-like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that the entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between $GHZ$ and $W$ states, clarifying the original result of Wei and Goldbart that $W$ states possess a larger global entanglement than $GHZ$ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.Comment: 16 pages, 7 figures. Final version, to appear in Phys. Rev.