Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplified formalism of the algebra of partially transposed permutation
  operators with applications   Hereunder we continue the study of the representation theory of the algebra
of permutation operators acting on the $n$-fold tensor product space, partially
transposed on the last subsystem. We develop the concept of partially reduced
irreducible representations, which allows to simplify significantly previously
proved theorems and what is the most important derive new results for
irreducible representations of the mentioned algebra. In our analysis we are
able to reduce complexity of the central expressions by getting rid of sums
over all permutations from symmetric group obtaining equations which are much
more handy in practical applications. We also find relatively simple matrix
representations for the generators of underlying algebra. Obtained
simplifications and developments are applied to derive characteristic of the
deterministic port-based teleportation scheme written purely in terms of
irreducible representations of the studied algebra. We solve an eigenproblem
for generators of algebra which is the first step towards to hybrid port-based
teleportation scheme and gives us new proofs of asymptotic behaviour of
teleportation fidelity. We also show connection between density operator
characterising port-based teleportation and particular matrix composed of
irreducible representation of the symmetric group which encodes properties of
the investigated algebra.

0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex