Efficient multi port-based teleportation schemes
- URL: http://arxiv.org/abs/2008.00984v4
- Date: Mon, 5 Sep 2022 13:31:38 GMT
- Title: Efficient multi port-based teleportation schemes
- Authors: Micha{\l} Studzi\'nski, Marek Mozrzymas, Piotr Kopszak and Micha{\l}
Horodecki
- Abstract summary: Scheme allows for transmitting more than one unknown quantum state in one go.
New scheme gives better performance than various variants of the optimal PBT protocol used for the same task.
I turns out that the introduced formalism, and symmetries beneath it, appears in many aspects of theoretical physics and mathematics.
- Score: 0.10427337206896375
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this manuscript we analyse generalised port-based teleportation (PBT)
schemes, allowing for transmitting more than one unknown quantum state (or a
composite quantum state) in one go, where the state ends up in several ports at
Bob's side. We investigate the efficiency of our scheme discussing both
deterministic and probabilistic case, where parties share maximally entangled
states. It turns out that the new scheme gives better performance than various
variants of the optimal PBT protocol used for the same task. All the results
are presented in group-theoretic manner depending on such quantities like
dimensions and multiplicities of irreducible representations in the Schur-Weyl
duality. The presented analysis was possible by considering the algebra of
permutation operators acting on n systems distorted by the action of partial
transposition acting on more than one subsystem. Considering its action on the
n-fold tensor product of the Hilbert space with finite dimension, we present
construction of the respective irreducible matrix representations, which are in
fact matrix irreducible representations of the Walled Brauer Algebra. I turns
out that the introduced formalism, and symmetries beneath it, appears in many
aspects of theoretical physics and mathematics - theory of anti ferromagnetism,
aspects of gravity theory or in the problem of designing quantum circuits for
special task like for example inverting an unknown unitary.
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