The paper introduces epsilon-approximate k-uniform states, proves Haar-random states and shallow random circuits produce them, and connects them to approximate quantum error-correcting codes and information masking.
good” approximate QECC can probably be constructed from Haar random unitaries, or even low depth random quantum circuits, with small failure probability. Next we show that “good
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Approximate k-uniform states: definition, construction and applications
The paper introduces epsilon-approximate k-uniform states, proves Haar-random states and shallow random circuits produce them, and connects them to approximate quantum error-correcting codes and information masking.