R. Sankaranarayanan

Recurrence of fidelity in nearly integrable systems

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.

Quantum chaos of a particle in a square well: competing length scales and dynamical localization.

The classical and quantum dynamics of a particle trapped in a one-dimensional infinite square well with a time-periodic pulsed field is investigated. This is a two-parameter non-KAM (Kolmogorov-Arnold-Moser) generalization of the kicked rotor, which can be seen as the standard map of particles subjected to both smooth and hard potentials. The virtue of the generalization lies in the introduction of an extra parameter R, which is the ratio of two length scales, namely, the well width and the field wavelength. If R is a noninteger the dynamics is discontinuous and non-KAM. We have explored the role of R in controlling the localization properties of the eigenstates. In particular, the connection between classical diffusion and localization is found to generalize reasonably well. In unbounded chaotic systems such as these, while the nearest neighbor spacing distribution of the eigenvalues is less sensitive to the nature of the classical dynamics, the distribution of participation ratios of the eigenstates proves to be a sensitive measure; in the chaotic regimes the latter is log-normal. We find that the tails of the well converged localized states are exponentially localized despite the discontinuous dynamics while the bulk part shows fluctuations that tend to be closer to random matrix theory predictions. Time evolving states show considerable R dependence, and tuning R to enhance classical diffusion can lead to significantly larger quantum diffusion for the same field strengths, an effect that is potentially observable in present day experiments.

Classical rules and quantum strategies in penny flip game

We study the quantum single penny flip game under various classical rules of the game. For every rule of the game, there exist unitary transformations which ensure the winning for quantum player. With the aim to understand the role of entangling gate for a sequential zero sum game, we extend the single penny problem to two penny problem. While entangling gates are found to be not useful, local gates are necessary and sufficient to win the game. Further, importance of one qubit operations is indicated. Various rules of two penny game is also indicated.

Accelerator modes of square well system

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.

Operator-Schmidt decomposition and the geometrical edges of two-qubit gates

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.

Fidelity based measurement induced nonlocality

Abstract 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 state and 2 × n dimensional mixed state. 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.

Entangling characterization of SWAP 1 ∕ m and controlled unitary gates

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.

Fidelity based measurement induced nonlocality and its dynamics in quantum noisy channels

Abstract Measurement induced nonlocality (MIN) captures global nonlocal effect of bipartite quantum state due to locally invariant projective measurements. In this paper, we propose a new version of MIN using fidelity induced metric, and the same is calculated for pure and mixed states. For mixed state, the upper bound is obtained from eigenvalues of correlation matrix. Further, dynamics of MIN and fidelity based MIN under various noisy quantum channels show that they are more robust than entanglement.

Dynamics of measurement-induced nonlocality under decoherence

Measurement-induced nonlocality (MIN)—captures nonlocal effects of a quantum state due to local von Neumann projective measurements, is a bona-fide measure of quantum correlation between constituents of a composite system. In this paper, we study the dynamical behavior of entanglement (measured by concurrence), Hilbert–Schmidt MIN and fidelity-based MIN (F-MIN) under local noisy channels such as hybrid (consists of bit flip, phase flip and bit-phase flip), generalized amplitude damping (GAD) and depolarizing channels for the initial Bell diagonal state. We observed that while sudden death of entanglement occurs in hybrid and GAD channels, MIN and F-MIN are more robust against such noises. Finally, we demonstrate the revival of MIN and F-MIN after a dark point of time against depolarizing noise.

Schmidt Strength of the Geometrical Edges of Two‐Qubit Gates

Nonlocal two‐qubit 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, all the edges of tetrahedron are characterized using Schmidt strength, a measure of operator entanglement. It is found that one edge of the tetrahedron, which includes SWAP and Double‐CNOT, possesses the maximum Schmidt strength. It implies that all the gates in the edge are maximally entangled.