How much does it cost to teleport?

TL;DR

This paper establishes that the entanglement entropy of a shared quantum state determines its capacity to teleport unknown quantum states, linking teleportation fidelity to entanglement measures.

Contribution

It demonstrates that the entropy of entanglement sets a fundamental limit on teleportation capacity and offers an alternative interpretation of entanglement purification.

Findings

Entanglement entropy must be at least log2 N for faithful teleportation of an N-state.

Maximum teleportation capacity of a mixed state equals its distillable entanglement entropy.

Provides a new perspective on entanglement purification as a measure of teleportation ability.

Abstract

We show that the entropy of entanglement of a state characterizes its ability to teleport. In particular, in order to teleport faithfully an unknown quantum $N$-state, the two users must share an entangled state with at least $\log_2 N$ bits entropy of entanglement. We also note that the maximum capacity for a mixed state ${\cal M}$ to teleport equals the maximum amount of entanglement entropy that can be distilled out from ${\cal M}$. Our result, therefore, provides an alternative interpretation for entanglement purification.