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Quantum Distinguishing Complexity, Zero-Error Algorithms, and Statistical Zero Knowledge
2019
Theory of Quantum Computation, Communication, and Cryptography
We define a new query measure we call quantum distinguishing complexity, denoted QD(f ) for a Boolean function f . Unlike a quantum query algorithm, which must output a state close to |0 on a 0-input and a state close to |1 on a 1-input, a "quantum distinguishing algorithm" can output any state, as long as the output states for any 0-input and 1-input are distinguishable. Using this measure, we establish a new relationship in query complexity: For all total functions f , Q 0 (f ) = O(Q(f ) 5 ),
doi:10.4230/lipics.tqc.2019.2
dblp:conf/tqc/Ben-DavidK19
fatcat:7m7noj75jnhz7ao5hop6pyzgyu