A necessary and sufficient condition determines when typical projections of Borel probability measures have full packing dimension, with general lower bounds in other cases, modulated by the Assouad dimension of the support.
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Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.
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On the packing dimension of projected measures
A necessary and sufficient condition determines when typical projections of Borel probability measures have full packing dimension, with general lower bounds in other cases, modulated by the Assouad dimension of the support.
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On the Complexity of Quantum States and Circuits from the Orthogonal and Symplectic Groups
Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.