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Springer eBooks

Quantum Teleportation

Ciarán Hughes, Joshua Isaacson, Anastasia Perry, Ranbel F. Sun, Jessica A. Turner

Published Jan 1, 2021• 0 citations
Publisher

Abstract

Abstract One interesting application of entanglement is quantum teleportation, which is a technique for transferring an unknown quantum state from one place to another. In science fiction, teleportation generally involves a machine scanning a person and another machine reassembling the person on the other end. The original body disintegrates and no longer exists. Similarly, quantum teleportation works by “scanning” the original qubit, sending a recipe, and reconstructing the qubit elsewhere. The original qubit is not physically destroyed in the science fiction sense, but it is no longer in the same state. Otherwise, the previously mentioned no-cloning theorem—which states that a qubit cannot be exactly copied onto another qubit—would be violated.1 As we will see, the “scanning” part poses a problem which can only be solved by leveraging quantum entanglement.

DOI
10.1007/978-3-030-61601-4_8

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FINDING: Quantum teleportation is a protocol for transferring an unknown quantum state via shared entanglement and classical communication, not physical matter transport; recent breakthroughs (Oxford, Japanese groups) push distance/fidelity but confirm the same mathematical framework. MATH: - State transfer: \( |\psi\rangle_C \otimes |\Phi^+\rangle_{AB} \rightarrow |\Phi^+\rangle_{CA} \otimes |\psi\rangle_B \) (Bell basis projection on C+A, classical 2-bit correction on B). - Bell states: \( |\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle) \), \( |\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle) \). - Fidelity \( F = |\langle \psi_{\text{target}} | \psi_{\text{received}} \rangle|^2 \); perfect teleportation requires \( F=1 \), achieved only with maximal entanglement. - No-cloning theorem: \( U|\psi\rangle|0\rangle \neq |\psi\rangle|\psi\rangle \) for unknown \( |\psi\rangle \) — teleportation destroys original, preserving unitarity. - Entangle Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Quantum Teleportation: Entanglement, Bell Projection, and Pauli Correction — E8 Intelligence Research

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FINDING: Quantum teleportation is a protocol for transferring an unknown quantum state via shared entanglement and classical communication — not physical matter transport. The core math is the Bell basis projection and the Pauli correction operators. MATH: - State to teleport: \(|\psi\rangle = \alpha|0\rangle + \beta|1\rangle\), with \(|\alpha|^2 + |\beta|^2 = 1\). - Shared entangled pair: Bell state \(|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)\). - Total 3-qubit state: \(|\psi\rangle \otimes |\Phi^+\rangle\). - Alice performs Bell measurement — projecting onto one of 4 Bell states: \(|\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle)\), \(|\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)\). - Outcome determines Pauli correction on Bob's qubit: \(I, X, Z, XZ\) (identity, bit-flip, phase-flip, both). - No-cloning theorem: the original state is destroyed — information is transferred, not copied. - Classical communicati Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Entanglement teleportation

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Summary form only given. Quantum teleportation is a transportation process of a quantum state where the quantum state is copied at a remote place while the original state id eliminated. We generalize the scheme of the quantum teleportation for "N-body" quantum states. Many-body quantum states are classified into uncorrelated and entangled states. An uncorrelated state can be factorized to the direct product of one-body states. The quantum teleportation of the uncorrelated state can be performed by teleporting its "one-body" states sequentially. Thus, teleporting uncorrelated states is trivial since it is practically equivalent to teleporting one body states. An entangled state, to the contrary, can not be factorized to the product of one-body states due to its entanglement.

Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)•Jan 20, 2003•1 citation
Abstract One interesting application of entanglement is quantum teleportation, which is a technique for transferring an unknown quantum state from one place to another. In science fiction, teleportation generally involves a machine scanning a person and another machine reassembling the person on the other end. The original body disintegrates and no longer exists. Similarly, quantum teleportation works by “scanning” the original qubit, sending a recipe, and reconstructing the qubit elsewhere. The original qubit is not physically destroyed in the science fiction sense, but it is no longer in the same state. Otherwise, the previously mentioned no-cloning theorem—which states that a qubit cannot be exactly copied onto another qubit—would be violated.1 As we will see, the “scanning” part poses a problem which can only be solved by leveraging quantum entanglement.
Quantum teleportation is the disembodied transport of an unknown quantum state |ψ〉 from one place to another. All protocols for accomplishing such transport require nonlocal correlations, or entanglement, between systems shared by sender and receiver. The sender is normally called Alice and the receiver is called Bob . Most attention has focused on teleporting the states of finite-dimensional systems, such as the two-dimensional polarization of a photon or the discrete level structure of an atom. First proposed in 1993 by Charles Bennett and his colleagues [17, 24, 138] quantum teleporation thus allows physicists to take a photon or any other quantum scale particle such as an atom and transfer its properties (such as the polarization) to another photon even if the two photons are on opposite sides of the galaxy. This scheme transports the particle’s properties to the remote location and not the particle itself. The state of the original particle must be destroyed to create an exact reconstruction at the other end. This is a consequence of the no cloning theorem. A role in the teleportation scheme is played by an entangled ancillary pair of particles which will be initially shared by Alice and Bob.
The objective of this article is to present a simulation of quantum information. We take advantage of quantum entanglement to ensure the spontaneous transfer of a state from one qubit to another similar qubit. Similarly, the principle of quantum teleportation is conceived in the application; it is not about transfer of matter, but of information. Indeed, two systems already exist, and at the end of the teleportation, the process is destructive—the first system will no longer be in the same state as the initial state and the second system takes the state of the first, which does not contradict the no-cloning theorem.
By quantum teleportation an unknown quantum state is destroyed at a sending place while its perfect replica state appears at a remote place via dual quantum and classical channels. Quantum teleportation allows for the transmission of quantum information to a distant location despite the impossibility of measuring or broadcasting the information to be transmitted. e classical teleportation is like a fax in which one could scan an object and send the information so that the object can be reconstructed at the destination. In this conventional facsimile transmission, the original object is scanned to extract partial information about it. e scanned information is then sent to the receiving station, where it is used to produce an approximate copy of the original object. e original object remains intact a er the scanning process. By contrast, in quantum teleportation, the uncertainty principle forbids any scanning process from extracting all the information in a quantum state. e nonlocal property of quantum mechanics enables the striking phenomenon of quantum teleportation. Bennett and coworkers28 showed that a quantum state can be teleported, provided one does not know that state, using a celebrated and paradoxical feature of quantum mechanics known as the Einstein-Podolsky-Rosen (EPR) e ect.11 ey found a way to scan out part of the information from an object A, which one wishes to teleport, while causing the remaining part of the information to pass to an object B, via the EPR e ect. In this process, two objects B and C form an entangled pair; object C is taken to the sending station, while object B is taken to the receiving station. At the sending station, object C is scanned together with the original object A, yielding some information and totally disrupting the state of A and C. e scanned information is sent to the receiving station, where it is used to select one of several treatments to be applied to object B, thereby putting B into an exact replica of the former state of A.
FINDING: Quantum teleportation is a protocol for transferring an unknown quantum state via shared entanglement and classical communication, not physical matter transport; recent breakthroughs (Oxford, Japanese groups) push distance/fidelity but confirm the same mathematical framework. MATH: - State transfer: ∣ψ⟩C⊗∣Φ+⟩AB→∣Φ+⟩CA⊗∣ψ⟩B |\psi\rangle_C \otimes |\Phi^+\rangle_{AB} \rightarrow |\Phi^+\rangle_{CA} \otimes |\psi\rangle_B ∣ψ⟩C​⊗∣Φ+⟩AB​→∣Φ+⟩CA​⊗∣ψ⟩B​ (Bell basis projection on C+A, classical 2-bit correction on B). - Bell states: ∣Φ±⟩=12(∣00⟩±∣11⟩) |\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle) ∣Φ±⟩=2​1​(∣00⟩±∣11⟩), ∣Ψ±⟩=12(∣01⟩±∣10⟩) |\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle) ∣Ψ±⟩=2​1​(∣01⟩±∣10⟩). - Fidelity F=∣⟨ψtarget∣ψreceived⟩∣2 F = |\langle \psi_{\text{target}} | \psi_{\text{received}} \rangle|^2 F=∣⟨ψtarget​∣ψreceived​⟩∣2; perfect teleportation requires F=1 F=1 F=1, achieved only with maximal entanglement. - No-cloning theorem: U∣ψ⟩∣0⟩≠∣ψ⟩∣ψ⟩ U|\psi\rangle|0\rangle \neq |\psi\rangle|\psi\rangle U∣ψ⟩∣0⟩=∣ψ⟩∣ψ⟩ for unknown ∣ψ⟩ |\psi\rangle ∣ψ⟩ — teleportation destroys original, preserving unitarity. - Entangle Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum teleportation is a protocol for transferring an unknown quantum state via shared entanglement and classical communication — not physical matter transport. The core math is the Bell basis projection and the Pauli correction operators. 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 — projecting onto one of 4 Bell states: ∣Φ±⟩=12(∣00⟩±∣11⟩)|\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle)∣Φ±⟩=2​1​(∣00⟩±∣11⟩), ∣Ψ±⟩=12(∣01⟩±∣10⟩)|\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)∣Ψ±⟩=2​1​(∣01⟩±∣10⟩). - Outcome determines Pauli correction on Bob's qubit: I,X,Z,XZI, X, Z, XZI,X,Z,XZ (identity, bit-flip, phase-flip, both). - No-cloning theorem: the original state is destroyed — information is transferred, not copied. - Classical communicati Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Summary form only given. Quantum teleportation is a transportation process of a quantum state where the quantum state is copied at a remote place while the original state id eliminated. We generalize the scheme of the quantum teleportation for "N-body" quantum states. Many-body quantum states are classified into uncorrelated and entangled states. An uncorrelated state can be factorized to the direct product of one-body states. The quantum teleportation of the uncorrelated state can be performed by teleporting its "one-body" states sequentially. Thus, teleporting uncorrelated states is trivial since it is practically equivalent to teleporting one body states. An entangled state, to the contrary, can not be factorized to the product of one-body states due to its entanglement.