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International Conference on Electronic Information Engineering and Computer Science (EIECS)

Study on Dense Coding of Quantum Information Transmission Process at Different Orders

Changjiang Xie

Published Sep 26, 2025• 0 citations
Publisher

Abstract

This paper first employs the mathematical framework of quantum mechanics, including Hilbert space theory and the superposition principle of quantum states, to analyze the processing methods and transmission processes of quantum information under second-order conditions. It delves into the core role of quantum gates as orthogonal operators and their correspondence with information transmission results through matrix multiplication. Subsequently, it investigates quantum information transmission and dense encoding techniques based on controllable non-qubit gates (CNOT) at different orders. The CNOT gate is represented by a second-order tensor product matrix: when the control qubit is $\mid 1\gt$, it performs a Pauli-X operation on the target qubit (matrix: [$[0,1]$, [1, 0]]), otherwise remaining unchanged. By defining the CNOT matrix, Hadamard matrix, maximum entangled state and corresponding multi-order unitary operations (described using elements of the $\mathbf{S U}(\mathbf{n})$ group for higher-order quantum system transformations), this study combines density matrix representations of quantum states with quantum measurement theories (such as the mathematical description of projection measurements). It reveals the mechanistic principles underlying quantum information transmission and decryption processes. Through computational verification of quantum state fidelity and transmission success rates across different orders, the effectiveness of cross-order information transmission is demonstrated.

DOI
10.1109/eiecs67708.2025.11283189

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In this thesis, we have proposed some novel thought experiments involving foundations of quantum mechanics and quantum information theory, using quantum entanglement property. Concerning foundations of quantum mechanics, we have suggested some typical systems including two correlated particles which can distinguish between the two famous theories of quantum mechanics, i.e. the standard and Bohmian quantum mechanics, at the individual level of pair of particles. Meantime, the two theories present the same predictions at the ensemble level of particles. Regarding quantum information theory, two theoretical quantum communication schemes including quantum dense coding and quantum teleportation schemes have been proposed by using entangled spatial states of two EPR particles shared between two parties. It is shown that the rate of classical information gain in our dense coding scheme is greater than some previously proposed multi-qubit protocols by a logarithmic factor dependent on the dimension of Hilbert space. The proposed teleportation scheme can provide a complete wave function teleportation of an object having other degrees of freedom in our three-dimensional space, for the first time. All required unitary operators which are necessary in our state preparation and Bell state measurement processes are designed using symmetric normalized Hadamard matrix, some basic gates and one typical conditional gate, which are introduced here for the first time.