Efficient multi port-based teleportation schemes

TL;DR

This paper introduces a generalized port-based teleportation scheme that transmits multiple quantum states simultaneously, outperforming existing protocols by leveraging group-theoretic methods and algebraic structures like the Walled Brauer Algebra.

Contribution

It presents a novel multi-port teleportation protocol with improved efficiency, employing advanced algebraic techniques and group theory to analyze and optimize quantum teleportation.

Findings

Better performance than existing PBT variants

Group-theoretic framework for analyzing teleportation

Construction of irreducible representations of the Walled Brauer Algebra

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.