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

Abstract

The paper explores the methods for encrypting and decrypting an 8-qubit states of quantum system using unitary and permutation matrix. Our approach utilizes a unitary matrix to create a new superpositions of an encrypted 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  using the formula , where  is the original state vector,  is the unitary matrix, and  is the permutation matrix. To ensure the total probability remains normalized, we showed that the resulting new 8-qubits state  remains normalized. The decryption process is achieved by applying the following operations  retrieving the original state. This paper also 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 block for  different 8-qubits state using a different key in each block from the initial unitary matrix  and permutation . In order to implement these methods, we need to generate a new unitary matrix for each block. Either by random pick or using iteration. In fact, we showed how to create the new unitary matrix using iteration for each block. Here we showed that the new generated matrix  is also a unitary matrix so that we can use iteration proses to create a new unitary matrix in each block for  different 8-qubits state. Here we generate the unitary matrix  from  as key in block . This result in the encryption of each block for each 8-qubits state using the formula  resulting in a more robust security. The encryption/decryption scheme we referenced can theoretically be implemented on modern quantum hardware but verifying operations involving hundreds of qubits would demand rigorous calibration and error correction