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arXiv:1904.02066

Teleporting digital images

Mario Mastriani

Published Jan 23, 2019• 0 citations
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Abstract

During the last 25 years the scientific community has coexisted with the most fascinating protocol due to Quantum Physics: quantum teleportation (QTele), which would have been impossible if quantum entanglement, so questioned by Einstein, did not exist. In this work, a complete architecture for the teleportation of Computational Basis States (CBS) is presented. Such CBS will represent each of the possible 24 classical bits commonly used to encode every pixel of a 3-color-channel-image (red-green-blue, or cyan-yellow-magenta). For this purpose, a couple of interfaces: classical-to-quantum (Cl2Qu) and quantum-to-classical (Qu2Cl) are presented with two versions of the teleportation protocol: standard and simplified.

DOI
10.48550/arxiv.1904.02066

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During the last 25 years the scientific community has coexisted with the most fascinating protocol due to Quantum Physics: quantum teleportation (QTele), which would have been impossible if quantum entanglement, so questioned by Einstein, did not exist. In this work, a complete architecture for the teleportation of Computational Basis States (CBS) is presented. Such CBS will represent each of the possible 24 classical bits commonly used to encode every pixel of a 3-color-channel-image (red-green-blue, or cyan-yellow-magenta). For this purpose, a couple of interfaces: classical-to-quantum (Cl2Qu) and quantum-to-classical (Qu2Cl) are presented with two versions of the teleportation protocol: standard and simplified.
During the last 25 years the scientific community has coexisted with the most fascinating protocol due to Quantum Physics: quantum teleportation (QTele), which would have been impossible if quantum entanglement, so questioned by Einstein, did not exist. In this work, a complete architecture for the teleportation of Computational Basis States (CBS) is presented. Such CBS will represent each of the possible 24 classical bits commonly used to encode every pixel of a 3-color-channel-image (red-green-blue, or cyan-yellow-magenta). For this purpose, a couple of interfaces: classical-to-quantum (Cl2Qu) and quantum-to-classical (Qu2Cl) are presented with two versions of the teleportation protocol: standard and simplified.
Quantum teleportation is a transfer protocol of quantum states, which cannot be realized only with classical physics. The essence of this protocol is quantum entanglement, which was proposed by Einstein as a counter example for quantum mechanics. In terms of quantum information processing, quantum teleportation can be regarded as an “Identity” operation. So one can modify the quantum circuit to make an arbitrary operation and universal quantum computing. One of the application of the quantum computing is “quantum version of coherent communication”, which enables us to get the channel capacity beyond the classical limit (Shannon limit).
FINDING: Quantum teleportation transfers a qubit's *state* (not matter) via a shared entangled pair plus 2 classical bits — the state is destroyed at source and reconstructed at destination. | MATH: Protocol: prepare Bell pair |Φ⁺⟩ = (|00⟩+|11⟩)/√2; Alice performs CNOT + H on her two qubits, measures → 2 classical bits (00,01,10,11); Bob applies I, X, Z, or XZ (Pauli corrections). General state |ψ⟩ = α|0⟩ + β|1⟩ with |α|²+|β|² = 1. No-cloning: ⟨ψ|ψ⟩ preserved, original destroyed. Fidelity = 1 for ideal channel. | CONNECTION: Bell basis is a maximally entangled orthonormal basis of C²⊗C²; amplitudes 1/√2 mirror the 0.7071 normalization recurring in SU(2) spinors and the 45° projection in the 0.382/0.618 family (1/√2 ≈ 0.7071 sits between 0.618 and 0.786). | DEPTH: 7 FINDING: Oxford/Google-class experiments demonstrate teleportation over logical qubits and modular/optical architectures — scaling, not new physics. | MATH: Entanglement entropy S = -Tr(ρ_A log ρ_A); for Bell state S = ln 2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
This thesis presents, initially, an analysis of the teleportation protocol of two qubits quantum gates, which uses an four qubits entangled state as a resource. It will be shown that the set of four qubits pure states is divided into two classes: Class 1 and Class 2, which determine, respectively, the realization of a deterministic gate teleportation, or a probabilistic remote preparation. It is still shown that when there is additional information on search problems that are not applicable to a standard quantum search algorithm, it is possible to obtain better performance using a quantum algorithm in conjunction with a classical search algorithm. Finally, a new model of image representation in quantum states is proposed, the new model has a less complex preparation and recovery compared to the other models currently proposed and allows the processing of images in both gray and colored scales.
This paper investigates two distinct protocols and one combined protocol for image teleportation based on three quantum states. It begins by reviewing key linear algebraic concepts and formalized quantum states in Hilbert space. Building on this, it analyzes a variation of dense coding using non-maximally entangled (polluted) states. It demonstrates that while full distinguishability of four Bell-like states is lost under entanglement degradation, it is possible to design a restricted set of operations that maximizes distinguishability; it designs a new protocol of superdense coding based on three Bell states. In the next section of the article, it introduces a three-level energy system and designs a quantum teleportation protocol based on the three states. It also introduces the HSV color model, which features three parameters that are used to represent a color. With such a protocol, it can teleport a color with high confidence and security. Both of these protocols can be used for image teleportation technologies. Finally, it integrates the superdense coding protocol and the quantum teleportation protocol to create a highly theoretical image teleportation protocol that can perform filtering, encoding and decoding, and emergency destruction on colored images with enhanced security. An additional participant is added, so that the quantum state will be modified during the teleportation process by this new participant. All of these protocols can be applied in future image teleportation techniques.
FINDING: Quantum teleportation is a confirmed protocol for transferring quantum states via entanglement, not physical matter transport; Oxford's recent work extends this to distributed quantum computing. | MATH: Core protocol uses Bell basis measurement: ∣Ψ⟩AB=12(∣0⟩A∣0⟩B+∣1⟩A∣1⟩B)|\Psi\rangle_{AB} = \frac{1}{\sqrt{2}}(|0\rangle_A|0\rangle_B + |1\rangle_A|1\rangle_B)∣Ψ⟩AB​=2​1​(∣0⟩A​∣0⟩B​+∣1⟩A​∣1⟩B​); teleportation requires 2 classical bits + 1 ebit (entangled bit) per qubit; fidelity approaches 1 with error correction; Oxford's breakthrough involves deterministic teleportation between nodes with success probability scaling as P∝1−e−γtP \propto 1 - e^{-\gamma t}P∝1−e−γt (decoherence-limited). | CONNECTION: The Bell states form an orthonormal basis in C2⊗C2\mathbb{C}^2 \otimes \mathbb{C}^2C2⊗C2 — this is the root system A1×A1A_1 \times A_1A1​×A1​ (tetragonal symmetry, 4-fold). The 4 Bell states correspond to the vertices of a square (dihedral group D4D_4D4​), and the 2 classical bits map to the 4 elements of Z2×Z2\mathbb{Z}_2 \times \mathbb{Z}_2Z2​×Z2​ — a Klein four-group, wh Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com