Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessary and sufficient conditions for macrorealism using two and
  three-time Leggett-Garg inequalities   The Leggett-Garg (LG) inequalities were introduced, as a temporal parallel of
the Bell inequalities, to test macroscopic realism -- the view that a
macroscopic system evolving in time possesses definite properties which can be
determined without disturbing the future or past state. The original LG
inequalities are only a necessary condition for macrorealism, and are therefore
not a decisive test. We argue, for the case of measurements of a single
dichotomic variable Q, that when the original four three-time LG inequalities
are augmented with a set of twelve two-time inequalities also of the LG form,
Fine's theorem applies and these augmented conditions are then both necessary
and sufficient. A comparison is carried out with the alternative necessary and
sufficient conditions for macrorealism based on no-signaling in time conditions
which ensure that all probabilities for Q at one and two times are independent
of whether earlier or intermediate measurements are made. We argue that the two
tests differ in their implementation of the key requirement of non-invasive
measurability so are testing different notions of macrorealism, and these
notions are elucidated.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th