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Lecture notes in computer science

Exact and Approximate Quantum Independent Component Analysis for Qubit Uncoupling

Yannick Deville, Alain Deville

Published Jan 1, 2012• 4 citations
Publisher
DOI
10.1007/978-3-642-28551-6_8

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In the framework of Blind Quantum Source Separation, we investigate the adaptation of a separating system which receives coupled quantum bit (qubit) states and processes them with quantum means in its feedforward path, to uncouple them. We propose the first separation principle which ensures that the output qubit states of this system are disentangled and that they restore the non-entangled source qubit states up to limited indeterminacies. This separation principle exploits measurements of output spin components along two directions and has some links with the non-quantum Independent Component Analysis (ICA) principle. It opens the way to various practical separation criteria and algorithms, some of which are described here.
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A set of harmonic oscillators is coupled for a certain time, after which the coupling is removed. The initial and final states of the set are expressed as superpositions of the coherent states of the uncoupled oscillators, as in Glauber's formalism. It is shown that the expansion kernel for the final state can be obtained approximately by substituting into the kernel for the initial state the classical equations of motion of the amplitudes of the oscillators. The evolution of a density operator for the system can be similarly calculated. The approximation is the more exact, the longer the time of interaction compared with the periods of the uncoupled oscillators.