Teleportation of Quantum Coherence

Sohail, Arun K Pati, Vijeth Aradhya, Indranil Chakrabarty, Subhasree Patro

Published 2023-02-22Version 1

We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating lesser number of classical bits in comparison to what is required in teleporting an unknown quantum state. We find that we cannot do perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is chosen from equatorial and polar circles, then teleportation of coherence will be possible with transfer of one cbit of information if we have maximally entangled states as a shared resource. In the case of resource being a non maximally entangled state, we can teleport quantum 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 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. With the help of this formula, we investigate the amount of coherence teleported when the resource shared state is the maximally entangled mixed state and Werner state for the unknown pure as well as mixed states state at Alice's lab. In particular, we show that when the Werner state becomes separable then also the amount of teleported coherence is non-zero, implying the possibility of teleportation of coherence without entanglement. We have also shown that teleportation of coherence of an arbitrary state with real matrix elements is exactly possible with the help of maximally entangled state as a resource.