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.
Select the subsystem size|A| =k, so dA =dk and dB =dn−k, we can prove the concentration result (Theorem 2) on Haar random state|ψ⟩ on dAdB-dimensional Hilbert space: Proof
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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.