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INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT

Teleportation of Multiparticle Entangled States

Suman Kumari

Published Jun 6, 2024• 0 citations
Publisher

Abstract

This paper investigates the theoretical basis and actual methods for teleporting entangled states using multiple particles. Beginning with Bennett et al.'s pioneering work in 1993, which established the notion of quantum teleportation. In this paper, I will discuss the quantum teleportation, quantum entanglement, Entanglement schemes such as Entanglement swapping scheme and will find out the rate of successful teleportation in terms of fidelity. Additionally discussed is minimal assured fidelity, which is the lowest level of fidelity for any unknown quantum information about the states[1]. Additionally, the success rate of teleporting a superposition of odd and even coherent states is demonstrated to be able to be raised from 50% to almost 99%[2]. We discover that by just isolating the vacuum state from the even state, it can virtually transport, divert, and exchange. Key Words: Entanglement, Quantum teleportation, Entanglement swapping scheme, Bell state measurement (BSM), Quantum information.

DOI
10.55041/ijsrem35582

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This paper investigates the theoretical basis and actual methods for teleporting entangled states using multiple particles. Beginning with Bennett et al.'s pioneering work in 1993, which established the notion of quantum teleportation. In this paper, I will discuss the quantum teleportation, quantum entanglement, Entanglement schemes such as Entanglement swapping scheme and will find out the rate of successful teleportation in terms of fidelity. Additionally discussed is minimal assured fidelity, which is the lowest level of fidelity for any unknown quantum information about the states[1]. Additionally, the success rate of teleporting a superposition of odd and even coherent states is demonstrated to be able to be raised from 50% to almost 99%[2]. We discover that by just isolating the vacuum state from the even state, it can virtually transport, divert, and exchange. Key Words: Entanglement, Quantum teleportation, Entanglement swapping scheme, Bell state measurement (BSM), Quantum information.
In the present paper, we will review the methods to produce superposition of entangled coherent state using polarizing beam splitter and Kerr non linearity. These coherent states have many attractive features and can be used in various schemes. Entanglement, refers to the superposition of a multiparticle system and explains a new type of correlations between any two subsystems of the quantum system, which is not existing in the classical physics. The present paper deals with the use of these states in quantum teleportation, entanglement diversion and entanglement swapping schemes. Entanglement diversion and entanglement-swapping refers to a scheme which may entangle those particles which had never interacted before. In the swapping scheme, two pairs of entangled state are taken. One particle from each pair is subjected to a Bell-state-measurement. This would result in projection of the other two outgoing particles in an entangled pair. Quantum Teleportation of two mode and three modes states is also studied with perfect fidelity. Minimum assured fidelity which is defined as the minimum of the fidelity for any unknown quantum information of the states is also discussed. It is also shown how the success rate of teleportation of a superposition of odd and even coherent states can be increased from 50% to almost 100%. The scheme suggested by van Enk and Hirota was modified by Prakash, Chandra, Prakash and Shivani in 2007. We find that an almost teleportation, diversion and swapping is possible by simply separating vacuum state from the even state. The present paper also deals with study of effect of decoherence and noise on these states and the effect of noise on fidelity and minimum assured fidelity. It is also discussed that these schemes can also be applied to the process of entanglement diversion and entanglement swapping.
Abstract Chapter 14 discusses the quantum communication protocol called quantum teleportation, which uses the quantum correlations in an entangled particle pair shared between two observers to transmit the information stored in the (unknown) quantum state of a target system from one of the observers to the other. After reviewing the theoretical basics we showcase some of the important experimental demonstrations of teleportation. We then turn to more general protocols related to teleportation such as entanglement swapping, and the general formalism of isometries, before inspecting the option of delayed-choice entanglement swapping. In the light of these findings we compare teleportation to classical information transfer and inspect the related dense-coding protocol. Finally, we give an overview of basic quantum key distribution protocols is given, including the Bennett-Brassard-84 protocol based on conjugate coding and the entanglement-based Ekert-91 protocol
FINDING: Quantum teleportation relies on entanglement and Bell state measurement to transfer qubit states without physical particle transport. | MATH: Bell state basis: ∣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⟩). Teleportation fidelity F=⟨ψ∣ρout∣ψ⟩F = \langle \psi | \rho_{\text{out}} | \psi \rangleF=⟨ψ∣ρout​∣ψ⟩ approaches 1 for ideal entanglement. No new constants or ratios beyond standard quantum mechanics. | CONNECTION: No explicit geometric harmony ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries appear in these video descriptions. The circuit diagrams use standard qubit rotations and CNOT gates, which relate to SU(2) symmetry and Bloch sphere geometry (a 2-sphere with Hopf fibration structure), but no novel harmonic ratios. | DEPTH: 3 — These are educational overviews, not original research. No new mathematical essence extracted beyond known quantum teleportation protocol (Bennett et al., Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Quantum entanglement is a key feature of quantum mechanics. It describes connections between quantum systems that classical theories cannot explain. The idea of entanglement started with the Einstein–Podolsky–Rosen (EPR) argument. This argument questioned whether quantum theory was complete and showed the non-classical nature of quantum correlations. Schrödinger later defined the concept and introduced the term "entanglement" to describe composite quantum states that cannot be separated. Bell then created a framework that showed the predictions of quantum mechanics clash with local hidden-variable theories, leading to Bell's inequality. Experiments by Aspect and others provided strong evidence for the violation of Bell's inequalities and supported the reality of entanglement. Building on these theories and experiments, quantum teleportation became an important protocol in quantum information science. Bennett and his team proposed a scheme that showed how an unknown quantum state can be sent between distant parties using shared entanglement and classical communication, without sending the quantum system itself. Later experiments confirmed that this protocol works across different physical platforms. This paper reviews the historical development of quantum entanglement and its role in the emergence of quantum teleportation. In addition to the theoretical discussion, the teleportation protocol is implemented using IBM's Qiskit framework. The simulation results demonstrate the successful transfer of quantum states within the circuit model, illustrating how fundamental quantum communication concepts can be explored using quantum computing simulation tools.
Quantum entanglement is a key feature of quantum mechanics. It describes connections between quantum systems that classical theories cannot explain. The idea of entanglement started with the Einstein–Podolsky–Rosen (EPR) argument. This argument questioned whether quantum theory was complete and showed the non-classical nature of quantum correlations. Schrödinger later defined the concept and introduced the term "entanglement" to describe composite quantum states that cannot be separated. Bell then created a framework that showed the predictions of quantum mechanics clash with local hidden-variable theories, leading to Bell’s inequality. Experiments by Aspect and others provided strong evidence for the violation of Bell’s inequalities and supported the reality of entanglement. Building on these theories and experiments, quantum teleportation became an important protocol in quantum information science. Bennett and his team proposed a scheme that showed how an unknown quantum state can be sent between distant parties using shared entanglement and classical communication, without sending the quantum system itself. Later experiments confirmed that this protocol works across different physical platforms. This paper reviews the historical development of quantum entanglement and its role in the emergence of quantum teleportation. In addition to the theoretical discussion, the teleportation protocol is implemented using IBM’s Qiskit framework. The simulation results demonstrate the successful transfer of quantum states within the circuit model, illustrating how fundamental quantum communication concepts can be explored using quantum computing simulation tools.
FINDING: Quantum teleportation relies on entanglement swapping and Bell-state measurements, not faster-than-light transport; fidelity and success probability are key metrics. | MATH: Bell state fidelity F=⟨ψ∣ρout∣ψ⟩ F = \langle \psi | \rho_{\text{out}} | \psi \rangle F=⟨ψ∣ρout​∣ψ⟩; success probability Psuccess=1/4 P_{\text{success}} = 1/4 Psuccess​=1/4 per Bell measurement (for qubits); entanglement swapping uses CNOT + Hadamard gates. | CONNECTION: No direct geometric ratios (0.382, 0.618, etc.) or base-60 links; however, Bell states form a 4-dimensional orthonormal basis with symmetry group S4 S_4 S4​ (tetrahedral symmetry), and the CNOT gate corresponds to a 4x4 matrix with eigenvalues ±1, linking to the D4 D_4 D4​ root system (crystallographic symmetry of the 4D hypercube). | DEPTH: 6 — mathematically sound but standard quantum information; no new constants or harmonic ratios. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com