Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hierarchy for Replica Quantum Advantage   We prove that given the ability to make entangled measurements on at most $k$
replicas of an $n$-qubit state $\rho$ simultaneously, there is a property of
$\rho$ which requires at least order $2^n$ measurements to learn. However, the
same property only requires one measurement to learn if we can make an
entangled measurement over a number of replicas polynomial in $k, n$. Because
the above holds for each positive integer $k$, we obtain a hierarchy of tasks
necessitating progressively more replicas to be performed efficiently. We
introduce a powerful proof technique to establish our results, and also use
this to provide new bounds for testing the mixedness of a quantum state.

11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin