{'fraction_non_alphanumeric': 0.021611001964636542, 'fraction_numerical': 0.005893909626719057, 'mean_word_length': 5.538461538461538, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Monotone metrics on statistical manifolds of density matrices by geometry of non-commutative L2-spaces

Using an integral decomposition of non-commutative monotone metrics we show that each monotone metric described by the Petz classification theorem is related to the geometry of a suitable non-commutative L2-space. This exactly reproduces and generalizes the commutative case where the unique monotone metric (Chentsov theorem about Fisher-Rao metric) is classically related to the commutative L2-geometry.