An Encryption Method of 8-Qubit States Using Unitary Matrix and Permutation

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Abstract

These paper explores the methods for encrypting and decrypting a quantum state of an 8-qubit system using unitary and permutation matrices. The core of our approach utilizes the unity matrix to create superpositions of 8-qubits states. By applying a permutation matrix, we shuffle the state vectors, adding an additional layer of security. The encryption process will be performed on the encrypted state X using the formula X^'=X⋅U⋅P, where X is the original state vector, X is the unity matrix, and P is the permutation matrix. To ensure the total probability remains normalized, the unity matrix is scaled appropriately. The decryption process is achieved by applying the following operations,X=X^'⋅P^T⋅U^† retrieving the original state. This paper demonstrate is showing that the original quantum state can be accurately recovered post-decryption. This highlights the robustness of our approach in maintaining the integrity of quantum information. Furthermore, we aim to create n block for n different 8-qubits state using a different key in each block. In order to implement these method, we needs to define a new unitary matrix or a new permutation matrix for each block. either by random pick or using iteration. In fact, we can create a new unitary matrix using iteration for each block. Here we showed that the matrix UP is also a unitary matrix so that we can aim to create n block for n different 8-qubits state so that we can generate unitary matrix U_n from U_(n-1) as key in block n. This result in the encryption of each block for each 8-qubits state using the formula X_n^'=X_n⋅U_n⋅P resulting in a more robust security.