2008, Vol.11, No.2, pp.141-148
Quantum Information Theory is the extension of Classical
Information Theory when the quantum nature of the physical devices
plays a key role. All the information storage and processing
systems, to work in the desired quantum mechanical way, must be
isolated from environmental perturbations and classical
interactions with other systems. This isolation protects
entanglement (the fundamental resource of quantum information)
from decoherence (the deterioration of quantum coherence). But in
order to prepare the initial state of a quantum system, to control
its evolution, and measure its final state, we must interact with
it with big classical systems and thus induce unavoidable
perturbations. This is the main problem for the scalability of all
proposed architectures for quantum computers. In the search for
design optimizations it has been natural to ask whether the
classical properties of quantum systems play any role either
helping in the protection of entanglement or inducing specific
undesired behavior. Thus the question of the influence of
classical chaos or integrability has been posed and studied
extensively. While there exist many results based on specific
models of quantum systems, the picture is not definite since one
can see chaos in some cases to accelerate decoherence but in many
cases to help entanglement. In this talk we present two different
results. The first is an inequality, which holds, under certain
conditions, for general systems. The proof is based on Random
Matrix Theory. The second result is an analysis of the influence
of the existence of the scars on decoherence and of the role of
bifurcation points. This study is based on the comparison of
Classical and Quantum Kicked Tops, the latter used as a model of a
system of many qubits.
Key words:
entanglement, quantum chaos, Calogero-Moser model,
quantum kicked top, scars, bifurcations, upper bounds
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