[Paper Review] Quantum Entanglement and Teleportation

Brent R. Yates|arXiv (Cornell University)|Apr 14, 2011

Quantum Mechanics and Applications2 references3 citations

TL;DR

This paper provides a pedagogical explanation of quantum entanglement and quantum teleportation, using accessible language and mathematical formalism. It demonstrates how entangled particles can instantaneously correlate regardless of distance, and explains teleportation as a protocol transferring a qubit's state via entanglement and classical communication, with the key result being that no-cloning theorems and Bell-state measurements ensure fidelity in state transfer without physical particle movement.

ABSTRACT

Even Einstein has to be wrong sometimes. However, when Einstein was wrong he created a 70 year debate about the strange behavior of quantum mechanics. His debate helped prove topics such as the indeterminacy of particle states, quantum entanglement, and a rather clever use of quantum entanglement known as quantum teleportation.

Motivation & Objective

• To clarify the counterintuitive phenomena of quantum entanglement and teleportation for an advanced undergraduate audience.
• To resolve common misconceptions about faster-than-light communication in quantum teleportation.
• To illustrate how quantum teleportation enables transfer of quantum states without physical transmission of particles.
• To reinforce understanding through mathematical formalism while maintaining conceptual accessibility.
• To contextualize Einstein’s skepticism and its role in advancing quantum foundations.

Proposed method

• Uses the EPR paradox as a starting point to introduce quantum entanglement and non-local correlations.
• Applies the formalism of Bell states and density matrices to describe entangled qubit systems.
• Describes the teleportation protocol using a Bell-state measurement on the input qubit and one half of an entangled pair.
• Incorporates classical communication channels to transmit measurement outcomes to the receiver.
• Applies unitary operations conditioned on classical bits to reconstruct the original qubit state at the receiver’s location.
• Uses the no-cloning theorem to justify why teleportation is necessary and why it cannot be achieved by copying quantum states.

Experimental results

Research questions

• RQ1 How can two particles remain correlated across large distances despite no classical signal?
• RQ2 What role does entanglement play in enabling quantum teleportation?
• RQ3 Why does quantum teleportation not violate the no-signaling principle or allow faster-than-light communication?
• RQ4 How is the original quantum state reconstructed at the receiver’s location using only classical information and entanglement?
• RQ5 What mathematical framework supports the fidelity and correctness of the teleportation process?

Key findings

• Quantum teleportation successfully transfers the quantum state of a qubit from one location to another using only classical communication and shared entanglement.
• The protocol relies on Bell-state measurements and classical bits (2 bits) to convey information needed for state reconstruction.
• The fidelity of the teleported state is guaranteed to be 100% when the protocol is implemented correctly, due to unitary correction operations.
• Entanglement ensures non-local correlations, but no information is transmitted faster than light, preserving causality.
• The no-cloning theorem prevents copying of unknown quantum states, making teleportation a necessary and unique protocol for state transfer.
• Einstein’s initial objection to entanglement led to deeper investigations, ultimately confirming the non-classical nature of quantum mechanics.