Relationship Between Quantum Walk and Relativistic Quantum Mechanics

Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This paper revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled form of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schrodinger form. By showing the coin to be a means to make the walk reversible, and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modelled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of quantum walk, maximum speed of the walk propagation and the earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two state system to which the study can be extended.Comment: 12 pages and 1 figure, Published versio

Entanglement generation in spatially separated systems using quantum walk

We present a novel scheme to generate entanglement between two spatially separated systems. The scheme makes use of spatial entanglement generated by a single-particle quantum walk which is used to entangle two spatially separated, not necessarily correlated, systems. This scheme can be used to entangle any two systems which can interact with the spatial modes entangled during the quantum walk evolution. A notable feature is that we can control the quantum walk dynamics and its ability to localize leads to a substantial control and improvement in the entanglement output.Comment: 9 pages, 5 figure

Self dual models and mass generation in planar field theory

We analyse in three space-time dimensions, the connection between abelian self dual vector doublets and their counterparts containing both an explicit mass and a topological mass. Their correspondence is established in the lagrangian formalism using an operator approach as well as a path integral approach. A canonical hamiltonian analysis is presented, which also shows the equivalence with the lagrangian formalism. The implications of our results for bosonisation in three dimensions are discussed.Comment: 15 pages,Revtex, No figures; several changes; revised version to appear in Physical Review

Dual composition of odd-dimensional models

A general way of interpreting odd dimensional models as a doublet of chiral models is discussed. Based on the equations of motion this dual composition is illustrated. Examples from quantum mechanics, field theory and gravity are considered. Specially the recently advocated topologically massive gravity is analysed in some details.Comment: minor modification

Effect of control procedures on the evolution of entanglement in open quantum systems

The effect of a number of mechanisms designed to suppress decoherence in open quantum systems are studied with respect to their effectiveness at slowing down the loss of entanglement. The effect of photonic band-gap materials and frequency modulation of the system-bath coupling are along expected lines in this regard. However, other control schemes, like resonance fluorescence, achieve quite the contrary: increasing the strength of the control kills entanglement off faster. The effect of dynamic decoupling schemes on two qualitatively different system-bath interactions are studied in depth. Dynamic decoupling control has the expected effect of slowing down the decay of entanglement in a two-qubit system coupled to a harmonic oscillator bath under non-demolition interaction. However, non-trivial phenomena are observed when a Josephson charge qubit, strongly coupled to a random telegraph noise bath, is subject to decoupling pulses. The most striking of these reflects the resonance fluorescence scenario in that an increase in the pulse strength decreases decoherence but also speeds up the sudden death of entanglement. This demonstrates that the behaviour of decoherence and entanglement in time can be qualitatively different in the strong-coupling non-Markovian regime