Abstract
Abstract
In this paper, we use graph theory to study the distinguishability of lattice states under local operations and classical communication (LOCC) in
C
p
2
⨂
C
p
2
. Firstly, we present that for the basis of lattice unitary matrices, there are (p
2 + 1)(p + 1) distinct maximal commuting sets in p
2-dimensional system. Secondly, for any set
of lattice states, we can obtain a graph G which consists of some k-complete subgraphs. Using the graph G, we show that the set
can be distinguished by one-way LOCC if
n
(
p
+
1
)
−
∑
k
=
1
p
+
1
s
k
(
k
−
1
)
<
(
p
2
+
1
)
(
p
+
1
)
, where n is the number of vertices of a graph G and s
k
is the number of k-complete subgraphs. Moreover, we also proved that this conclusion is necessary and sufficient in
C
2
2
⨂
C
2
2
. For
C
p
2
⨂
C
p
2
system, our result can cover the results in (2015, Phys. Rev. A
92, 042 320); (2020, Sci. China-Phys. Mech. Astron.
63, 280 312).
Funder
National Natural Science Foundation of China
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics
Cited by
1 articles.
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