A modified LCU circuit turns every ancilla measurement into a useful projection, forming a low-rank matrix that enables classical low-rank completion for full quantum output reconstruction and a secret-key-based quantum trapdoor function.
Phase retrieval via matrix completion.SIAM review, 57(2):225–251, 2015
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Exploiting all ancilla outcomes in linear combinations of unitaries: low-rank recovery and quantum trapdoor functions
A modified LCU circuit turns every ancilla measurement into a useful projection, forming a low-rank matrix that enables classical low-rank completion for full quantum output reconstruction and a secret-key-based quantum trapdoor function.