Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Total quantum coherence and its applications   Quantum coherence is the most fundamental feature of quantum mechanics. The
usual understanding of it depends on the choice of the basis, that is, the
coherence of the same quantum state is different within different reference
framework. To reveal all the potential coherence, we present the total quantum
coherence measures in terms of two different methods. One is optimizing maximal
basis-dependent coherence with all potential bases considered and the other is
quantifying the distance between the state and the incoherent state set.
Interestingly, the coherence measures based on relative entropy and $l_2$ norm
have the same form in the two different methods. In particular, we show that
the measures based on the non-contractive $l_2$ norm is also a good measure
different from the basis-dependent coherence. In addition, we show that all the
measures are analytically calculable and have all the good properties. The
experimental schemes for the detection of these coherence measures are also
proposed by multiple copies of quantum states instead of reconstructing the
full density matrix. By studying one type of quantum probing schemes, we find
that both the normalized trace in the scheme of deterministic quantum
computation with one qubit (DQC1) and the overlap of two states in quantum
overlap measurement schemes (QOM) can be well described by the change of total
coherence of the probing qubit. Hence the nontrivial probing always leads to
the change of the total coherence.

16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat