purities' are very small), the normalized Hilbert-Schmidt distance tends to a finite limit, which depends on the nature of the state (15% of the maximal possible distance if the deviation from pure states is characterized by the

standard purity' Tr 2 and 37% if the `superpurity' lim r →0 [Tr ( 1+1/ r )] r is chosen as a measure of deviation).

DOI: 10.1088/1464-4266/4/3/362

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