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Oxford University Press eBooks

Teleportation of a Quantum State

William J. Mullin

Published Mar 16, 2017• 1 citation
Publisher

Abstract

Teleportation here is a process by which a quantum state is transferred from one place to another, a bit analogous to the teleportation taking place in Star Trek. Alice (A) has particle 1 in a state φ (1) that she wants to transfer to Bob (B). A source sends one of a singlet pair of particles, particle 2, to A and the other, particle 3, to B. A does a Bell-state measurement on the 1–2 pair. A sends the result to B via normal communication methods, which tells B what transformation should be done on the particle B received, so that the state ends in the original φ (3). Experiments have confirmed the method. The chapter discusses the nature of the two-particle Bell states and how experimenter can measure such states. Teleportation, since it involves information transfer, may have applications in quantum computing.

DOI
10.1093/acprof:oso/9780198795131.003.0014

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Teleportation here is a process by which a quantum state is transferred from one place to another, a bit analogous to the teleportation taking place in Star Trek. Alice (A) has particle 1 in a state φ (1) that she wants to transfer to Bob (B). A source sends one of a singlet pair of particles, particle 2, to A and the other, particle 3, to B. A does a Bell-state measurement on the 1–2 pair. A sends the result to B via normal communication methods, which tells B what transformation should be done on the particle B received, so that the state ends in the original φ (3). Experiments have confirmed the method. The chapter discusses the nature of the two-particle Bell states and how experimenter can measure such states. Teleportation, since it involves information transfer, may have applications in quantum computing.
Teleporting a quantum state,the sender Alice disassembles the entire informations into two parts: one purely classical information and the another purely non-classical information,then sends them to the receiver Bob via two different channels.Firstly,sending the purely non-classical part,the EPR pair which consists of two fermions with the spin of 1 2 here plays the key role in the teleportation,one EPR particle is given to Alice,while the other is given to Bob.Alice performs a complete measurement of the von Neumann type on the joint system consisting of the original particle and her EPR particle,this measurement performed in the four eigenstates of the Bell operator leads to collapse the wave packet of the joint wavefunction into the four correlated Bell bases.Through applying the appropriate unitary transformation to the state of his EPR particle Bob can reconstruct a replica of the original state destroyed in Alice's hand.Moreover,this Bell measurement produces two bits of classical information which is sent to Bob,a quantum teleportation is therefore completed.The paper studies the interior relation between EPR pairs of particles and the quantum teleportation.
FINDING: Quantum teleportation is a protocol for transferring an unknown quantum state via shared entanglement and classical communication — not a physical transport of matter. The Oxford breakthrough (video 4) and the "trick of description" video (6) confirm this is a state-transfer, not a Star Trek-style transporter. | MATH: The core protocol uses a Bell state ∣Φ+⟩=12(∣00⟩+∣11⟩)|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)∣Φ+⟩=2​1​(∣00⟩+∣11⟩). Teleportation requires: (1) a 2-qubit entangled pair, (2) a Bell-state measurement on the sender's side (projecting onto the 4 Bell basis states), (3) 2 classical bits of information transmitted, (4) one of 4 unitary corrections {I,X,Z,XZ}\{I, X, Z, XZ\}{I,X,Z,XZ} applied by the receiver. The fidelity of teleportation without entanglement is bounded by 2/32/32/3 (classical limit); with perfect entanglement, fidelity = 1. The state transfer is instantaneous in the quantum channel but the classical bit transmission enforces the speed-of-light limit ccc. | CONNECTION: The Bell basi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
In this paper, quantum teleportation of one-to-many using ( n +1)-particle entanglement is presented. If the sender (Alice) wants to transmit an unknown quantum state to a distant receiver (Bob), similar to the previous schemes, Alice performs Bell-state measurement on particles belonging to herself and informs the receiver the results through the classical channel. After that, it needs to perform the Hadamard operation on the other ( n −1) particles and measure them as well. With the aid of the measurement results, Bob can operate a corresponding unitary transformation on his particle to reconstruct the original state. Of course, the reconstruction may realize at either location of n , but it cannot realize at all locations at the same time.
FINDING: Quantum teleportation is a real, experimentally-verified protocol for transferring an unknown quantum state via entanglement, not a sci-fi "transporter" of matter; the core mathematics is the Bell basis measurement and classical communication. MATH: - State to teleport: ∣ψ⟩=α∣0⟩+β∣1⟩|\psi\rangle = \alpha|0\rangle + \beta|1\rangle∣ψ⟩=α∣0⟩+β∣1⟩, with ∣α∣2+∣β∣2=1|\alpha|^2 + |\beta|^2 = 1∣α∣2+∣β∣2=1. - Shared entangled pair: Bell state ∣Φ+⟩=12(∣00⟩+∣11⟩)|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)∣Φ+⟩=2​1​(∣00⟩+∣11⟩). - Total 3-qubit state: ∣ψ⟩⊗∣Φ+⟩|\psi\rangle \otimes |\Phi^+\rangle∣ψ⟩⊗∣Φ+⟩. - Alice performs Bell measurement (projection onto 4 Bell states: ∣Φ±⟩,∣Ψ±⟩|\Phi^\pm\rangle, |\Psi^\pm\rangle∣Φ±⟩,∣Ψ±⟩). - Bob applies one of 4 unitary corrections: I,X,Z,XZI, X, Z, XZI,X,Z,XZ (Pauli matrices). - No-cloning theorem: the original state is destroyed — teleportation is state transfer, not duplication. - Key constants: 12\frac{1}{\sqrt{2}}2​1​ (normalization of Bell state), 4 = dimension of Bell basis (2²). CONNECTION: - The 4 Bell states form an orthonor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Through the process of quantum teleportation, a transfer of quantum information takes place from one particle to another while maintaining zero physical movement between the two. Quantum teleportation requires two entangled particles along with projective measurements followed by exchanging two bits of classical information. The process requires quantum mechanics principles which combine superposition with entanglement. Quantum entanglement occurs when two or more particles create an inseparable relationship that cuts off a separate description of an individual particle. Experimental realizations of quantum teleportation continue to operate on different physical platforms which include photons as well as atoms and superconducting circuits. Applications of Quantum teleportation includes quantum computing, secure communication, and cryptography. In future Scientists believe that a breakthrough in quantum computing technology could make teleportation a reality, including the ability to teleport a whole human. This paper provides the present research in quantum teleportation, including the theoretical framework, experimental implementations, and potential applications. We also discuss the challenges and limitations of quantum teleportation and propose future directions for research.
In this article, the authors have discussed the Alice and Bob experimental set-up for the quantum teleportation, giving a detailed step-by step mathematical explanation of each unit. Quantum teleportation of a qubit requires the creation of an entangled quantum state between the sender’s (Alice) and the receiver’s (Bob) shared quantum state/s. At the end of this experiment, actual measurements of the Alice’s share of quantum information are to be taken and shared with Bob via a classical communication channel. The teleportation is expected to open up a whole new regime of quantum communication, data encryption to be one of its applications.