Query Complexity of Unitary Operation Discrimination

Discrimination of unitary operations is fundamental in quantum computation and information. A lot algorithms including the well-known Deutsch-Jozsa algorithm, Simon Grover algorithm can essentially be regarded as discriminating among individual, or sets (oracle operators). The problem between two $U$ $V$ described as: Given $X\in\{U, V\}$, determine which one $X$ is. If given with multiple copies, then design an adaptive procedure that takes queries to output identification result $X$. In this paper, we consider problem: How many are required for achieving a desired failure probability $\epsilon$ discrimination $V$. We prove uniform framework: (i) if discriminated bound error , number $T$ must satisfy $T\geq \left\lceil\frac{2\sqrt{1-4\epsilon(1-\epsilon)}}{\Theta (U^\dagger V)}\right\rceil$, (ii) they one-sided $\epsilon$, there \left\lceil\frac{2\sqrt{1-\epsilon}}{\Theta where $\Theta(W)$ denotes length smallest arc containing all eigenvalues $W$ on unit circle.