Southwest Quantum Information and Technology

Quantifying the performance of bidirectional quantum teleportation

Presenting Author: Aliza Siddiqui, Louisiana State University
Contributing Author(s): Mark M. Wilde

Bidirectional teleportation is a fundamental protocol for exchanging quantum information between two parties by means of a shared resource state and local operations and classical communication (LOCC). In this work, we develop two seemingly different ways of quantifying the simulation error of unideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity, and we prove that they are equivalent. By relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semi-definite programming lower bounds on the simulation error of unideal bidirectional teleportation. We evaluate these bounds for three key examples: when there is no resource state at all and for isotropic and Werner states, in each case finding an analytical solution. The first aforementioned example establishes a benchmark for classical versus quantum bidirectional teleportation. We then evaluate the performance of some schemes for bidirectional teleportation due to [Kiktenko et al., Phys. Rev. A 93, 062305 (2016)] and find that they are suboptimal and do not go beyond the aforementioned classical limit for bidirectional teleportation. We offer a scheme alternative to theirs that is provably optimal. Finally, we generalize the whole development to the setting of bidirectional controlled teleportation, in which there is an additional assisting party who helps with the exchange of quantum information.

Read this article online: https://arxiv.org/abs/2010.07905

(Session 5 : Thursday from 12:00pm-2:00 pm)