No 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 derived. The relation also helps in finding the lower bound of entangling power for perfect entanglers, from which the classification of gates as perfect and non perfect entanglers is obtained in terms of local invariants.Entanglement, a nonlocal property of a quantum state, is regarded as a resource for realizing various fascinating features such as teleportation, quantum cryptography and quantum computation [1,2]. On one side, much work has been carried out to understand and exploit the entanglement for various information processing. On the other side, attention has been given to quantum operations (gates) as they are responsible for creating entanglement when acting on a state.Since two-qubit gates are capable of producing entanglement, it is of vital importance to understand their entangling characterization. One such useful tool is the entangling power of an operator which quantifies the average entanglement produced [3]. Another tool to characterize the nonlocal attributes of a two-qubit gate is local invariants, namely and (first introduced in Ref.[4]) such that gates differing only by local operations possess same invariants. Furthermore, nonlocal two-qubit gates form an irreducible geometry of tetrahedron known as Weyl chamber. Of all the gates, exactly half of them are perfect entanglers (operators capable of producing maximally entangled state from some input product state) and they form a polyhedron within the Weyl chamber [5].It is known that gates differing only by local operations possess the same entangling power.Similarly, gates which are inverse to each other possess the same entangling power. For instance, SWAP α and SWAP -α assume the same entangling power as they are inverse to each other. From our earlier study on the geometrical edges of two-qubit gates [6], it was found that gates which do not belong to the preceding category also possess same entangling power. For

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 nearly 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 revival 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 Kolmogorov-Arnold-Moser region.

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 -α family of gates with 1 0 ≤ ≤ α 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.

In this paper we propose measurement induced nonlocality (MIN) using a metric based on fidelity to capture global nonlocal effect of a quantum state due to locally invariant projective measurements. This quantity is a remedy for local ancilla problem in the original definition of MIN. We present an analytical expression of the proposed version of MIN for pure bipartite states and 2 × n dimensional mixed states. We also provide an upper bound of the MIN for general mixed state. Finally, we compare this quantity with MINs based on Hilbert-Schmidt norm and skew information for higher dimensional Werner and isotropic states.