Quantum teleportation of quantum causal structures

TL;DR

This paper introduces methods for teleporting quantum causal structures, including indefinite causal orders, by focusing on inputs and outputs rather than physical degrees of freedom, using process matrix formalism.

Contribution

It develops quantum teleportation protocols for arbitrary quantum causal structures, including indefinite causal order, using partial and full post-selection techniques.

Findings

Protocols are compatible with all quantum causal structures.

Partial post-selected teleportation works with indefinite causal order.

Teleportation of inputs and outputs enables causal structure transfer.

Abstract

Quantum teleportation is a very helpful information-theoretic protocol that allows to transfer an unknown arbitrary quantum state from one location to another without having to transmit the quantum system through the intermediate region. Quantum states, quantum channels, and indefinite causal structures are all examples of quantum causal structures that not only enable advanced quantum information processing functions, but can also model causal structures in nonclassical spacetimes. In this letter, we develop quantum teleportation of arbitrary quantum causal structures, as formalized by the process matrix framework. Instead of teleporting all the physical degrees of freedom that implement the causal structure, the central idea is to just teleport the inputs to and outputs from the operations of agents. The communication of outcomes of Bell state measurements, which is necessary for deterministic quantum teleportation, is not possible for all causal structures that one might wish to investigate. To avoid this problem, we propose partially and fully post-selected teleportation protocols. We prove that our partially post-selected teleportation protocol is compatible with all quantum causal structures, including those that involve indefinite causal order.