Entanglement of Periodic States, the Quantum Fourier Transform and Shor's Factoring Algorithm. (arXiv:1001.3145v1 [quant-ph])

The preprocessing stage of Shor's algorithm generates a class of quantum
states referred to as periodic states, on which the quantum Fourier transform
is applied. Such states also play an important role in other quantum algorithms
that rely on the quantum Fourier transform. Since entanglement is believed to
be a necessary resource for quantum computational speedup, we analyze the
entanglement of periodic states, and the way it is affected by the quantum
Fourier transform. To this end, we derive a formula that evaluates the
Groverian entanglement measure for periodic states. Using this formula, we
explain the surprising result that the Groverian entanglement of the periodic
states built up during the preprocessing stage is only slightly affected by the
quantum Fourier transform.

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Original source : http://arxiv.org/abs/1001.3145...