Abstract:
A generalized version of standard map is quantized as a model of quantum chaos. It is shown that, in hyperbolic chaotic regime, second moment of quantum level velocity is $\sim 1/\hbar$ as predicted by the random matrix theory.

Abstract:
Nonlocal two-qubit gates are geometrically represented by tetrahedron known as Weyl chamber within which perfect entanglers form a polyhedron. We identify that all edges of the Weyl chamber and polyhedron are formed by single parametric gates. Nonlocal attributes of these edges are characterized using entangling power and local invariants. In particular, SWAP (power)alpha family of gates constitutes one edge of the Weyl chamber with SWAP-1/2 being the only perfect entangler. Finally, optimal constructions of controlled-NOT using SWAP-1/2 gate and gates belong to three edges of the polyhedron are presented.

Abstract:
We show a simple relation connecting entangling power and local invariants of two-qubit gates. From the relation, a general condition under which gates have same entangling power is arrived. The relation also helps in finding the lower bound of entangling power for perfect entanglers, from which the classification of gates as perfect and nonperfect entanglers is obtained in terms of local invariants.

Abstract:
We study the entangling power and perfect entangler nature of (SWAP)1/m, for m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only perfect entangler in the family. On the other hand, a subset of CU which is locally equivalent to CNOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.

Abstract:
Within the framework of simple perturbation theory, recurrence time of quantum fidelity is related to the period of the classical motion. This indicates the possibility of recurrence in near integrable systems. We have studied such possibility in detail with the kicked rotor as an example. In accordance with the correspondence principle, recurrence is observed when the underlying classical dynamics is well approximated by the harmonic oscillator. Quantum revivals of fidelity is noted in the interior of resonances, while classical-quantum correspondence of fidelity is seen to be very short for states initially in the rotational KAM region.

Abstract:
Nonlocal two-qubit quantum gates are represented by canonical decomposition or equivalently by operator-Schmidt decomposition. The former decomposition results in geometrical representation such that all the two-qubit gates form tetrahedron within which perfect entanglers form a polyhedron. On the other hand, it is known from the later decomposition that Schmidt number of nonlocal gates can be either 2 or 4. In this work, some aspects of later decomposition are investigated. It is shown that two gates differing by local operations possess same set of Schmidt coefficients. Employing geometrical method, it is established that Schmidt number 2 corresponds to controlled unitary gates. Further, all the edges of tetrahedron and polyhedron are characterized using Schmidt strength, a measure of operator entanglement. It is found that one edge of the tetrahedron possesses the maximum Schmidt strength, implying that all the gates in the edge are maximally entangled.

Abstract:
We consider the sequence of nodal counts for eigenfunctions of the Laplace-Beltrami operator in two dimensional domains. It was conjectured recently that this sequence stores some information pertaining to the geometry of the domain, and we show explicitly that this is the case for the family of rectangular domains with Dirichlet boundary conditions.

Abstract:
We study accelerator modes of a particle, confined in an one-dimensional infinite square well potential, subjected to a time-periodic pulsed field. Dynamics of such a particle can be described by one generalization of the kicked rotor. In comparison with the kicked rotor, this generalization is shown to have a much larger parametric space for existence of the modes. Using this freedom we provide evidence that accelerator mode assisted anomalous transport is greatly enhanced when low order resonances are exposed at the border of chaos. We also present signature of the enhanced transport in the quantum domain.

Abstract:
It is known from Schmidt decomposition that Schmidt number of nonlocal two-qubit quantum gates is 2 or 4. We identify conditions on geometrical points of a gate to have Schmidt number 2. A simple analysis reveals that Schmidt number 2 corresponds to controlled unitary gates with CNOT being the only perfect entangler. Further, it is shown that Schmidt strength and entangling power are maximum only for CNOT in the controlled unitary family.

Abstract:
A discontinuous generalization of the standard map, which arises naturally as the dynamics of a periodically kicked particle in a one dimensional infinite square well potential, is examined. Existence of competing length scales, namely the width of the well and the wavelength of the external field, introduce novel dynamical behaviour. Deterministic chaos induced diffusion is observed for weak field strengths as the length scales do not match. This is related to an abrupt breakdown of rotationally invariant curves and in particular KAM tori. An approximate stability theory is derived wherein the usual standard map is a point of ``bifurcation''.