32,018 research outputs found
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
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