[Paper Review] How much does it cost to teleport?

H. F. Chau, Hoi‐Kwong Lo|ArXiv.org|May 16, 1996

Quantum Computing Algorithms and Architecture14 references3 citations

TL;DR

This paper establishes that the entropy of entanglement of a shared quantum state determines its teleportation capability: to teleport an unknown N-level quantum system, the minimum required entanglement is log₂N bits. The authors prove that the maximum teleportation capacity of a mixed state equals the maximum distillable entanglement from it, offering a new interpretation of entanglement purification as a resource for teleportation.

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.

Motivation & Objective

• To determine the minimum entanglement resource required for faithful quantum teleportation of an unknown N-level quantum state.
• To establish a quantitative link between the teleportation capacity of a quantum state and its distillable entanglement.
• To provide a new operational interpretation of entanglement purification as a process that extracts usable entanglement for teleportation.
• To formalize the role of entanglement entropy as a resource measure in quantum teleportation protocols.

Proposed method

• The authors analyze the teleportation protocol using a shared entangled state between two parties, Alice and Bob.
• They use the von Neumann entropy of entanglement as a measure of the entanglement resource in a bipartite quantum state.
• The analysis involves deriving a lower bound on the required entanglement entropy for successful teleportation of an N-level system.
• They compare the teleportation capacity of a mixed state with the maximum amount of pure entanglement that can be distilled from it using local operations and classical communication (LOCC).
• The proof relies on information-theoretic arguments, particularly the monogamy of entanglement and the Holevo bound.
• The authors use the concept of entanglement distillation to show that only states with sufficient entanglement entropy can support high-fidelity teleportation.

Experimental results

Research questions

• RQ1 What is the minimum amount of entanglement entropy required to teleport an unknown N-level quantum state?
• RQ2 How does the teleportation capacity of a mixed quantum state relate to its distillable entanglement?
• RQ3 Can entanglement purification be interpreted as a process that enables teleportation by extracting usable entanglement?
• RQ4 Is the entropy of entanglement a sufficient and necessary condition for faithful teleportation?
• RQ5 Can the maximum teleportation fidelity be bounded by the distillable entanglement of the shared state?

Key findings

• To teleport an unknown N-level quantum state faithfully, the shared entangled state must have at least log₂N bits of entropy of entanglement.
• The maximum teleportation capacity of a mixed state M is equal to the maximum amount of entanglement entropy that can be distilled from M via LOCC.
• Entanglement purification protocols can be interpreted as processes that extract the necessary entanglement resource for teleportation.
• The result establishes a direct operational equivalence between teleportation capability and distillable entanglement.
• The paper shows that entanglement entropy is both a necessary and sufficient resource for teleportation, with no additional classical communication increasing the capacity beyond this bound.
• The findings imply that teleportation fidelity is fundamentally limited by the amount of distillable entanglement available in the shared state.