The SWAP Imposter: Bidirectional Quantum Teleportation and its Performance

TL;DR

This paper analyzes the performance of bidirectional quantum teleportation, introduces error quantification methods, and evaluates bounds for various resource states, establishing benchmarks and analytical solutions for nonideal scenarios.

Contribution

It develops two error metrics for nonideal bidirectional teleportation, proves their equivalence, and provides semidefinite programming bounds with analytical solutions for key cases.

Findings

Error metrics are equal for bidirectional teleportation.

Semidefinite programming bounds are established for error quantification.

Analytical solutions are obtained for isotropic states and Bell states through GADC.

Abstract

Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two parties. Specifically, the two individuals make use of a shared resource state as well as local operations and classical communication (LOCC) to swap quantum states. In this work, we concisely highlight the contributions of our companion paper [Siddiqui and Wilde, arXiv:2010.07905]. We develop two different ways of quantifying the error of nonideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity. We then establish that the values given by both metrics are equal for this task. Additionally, by relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semidefinite programming lower bounds on the error of nonideal bidirectional teleportation. We evaluate these bounds for some key examples -- isotropic states and when there is no resource state at all. In both cases, we find an analytical solution. The second example establishes a benchmark for classical versus quantum bidirectional teleportation. Another example that we investigate consists of two Bell states that have been sent through a generalized amplitude damping channel (GADC). For this scenario, we find an analytical expression for the error, as well as a numerical solution that agrees with the former up to numerical precision.