Teleportation of quantum coherence

TL;DR

This paper explores the conditions under which quantum coherence can be teleported using classical communication and entangled states, revealing that partial knowledge and certain shared states enable coherence teleportation even without entanglement.

Contribution

It introduces a protocol for teleporting quantum coherence with limited classical communication and analyzes the role of entanglement and partial knowledge in this process.

Findings

Perfect coherence teleportation with one cbit for partially known states

Coherence teleportation possible with non-maximally entangled states probabilistically

Coherence can be teleported without entanglement using Werner states

Abstract

We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a lesser number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a non-maximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's lab in terms of the composition of the completely positive maps corresponding to the shared resource state and joint POVM performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is possible perfectly with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with the Werner states and show that even when the Werner states become separable, the amount of teleported coherence is non-zero, implying the possibility of teleportation of coherence without entanglement.