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

27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
16
The categories of this paper are: stat