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Related questions were recently considered by G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999); and A. W. Harrow and M. A. Nielsen, eprint quant-ph/0301108; the starting point being, respectively, noisy states and gates, rather than Hamiltonians. More directly relevant to our work is S. Montangero et al., Phys. Rev. Lett. 91, 187901 (2003), who considered the effect of a uniform random distribution of control parameters in the XY model, with qualitatively similar results.
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16
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1942449013
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Related questions were recently considered by G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999); and A. W. Harrow and M. A. Nielsen, eprint quant-ph/0301108; the starting point being, respectively, noisy states and gates, rather than Hamiltonians. More directly relevant to our work is S. Montangero et al., Phys. Rev. Lett. 91, 187901 (2003), who considered the effect of a uniform random distribution of control parameters in the XY model, with qualitatively similar results.
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note
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One may consider starting instead from an arbitrary, but known pure product state. Then the Hadamard transform on each qubit will be replaced by a general separable two-qubit unitary, that will depend on six Euler angles. As long as all these angles are Gaussian distributed with the same SD, our analysis carries through unchanged.
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23
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note
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Comment Ref. [13] still holds, with obvious modifications. Note, however, that in general, if the Euler angles have different SD's, the classes will split.
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