Quantum Entanglement-Based Data Compression via Phase Space Mapping

Abstract

This paper proposes a novel data compression technique leveraging the unique properties of quantum entanglement. The core idea involves encoding data into the correlated phase space of entangled qubits, achieving lossless compression. The algorithm utilizes controlled phase manipulation for both encoding and decoding, capitalizing on the inherent correlations between entangled particles. Unlike traditional entropy-based compression methods, this approach directly exploits quantum mechanical phenomena. We demonstrate a theoretical framework and outline a compression algorithm with the potential for significant improvements in compression ratios. The key mathematical representation of the compression process is defined as follows: Let $x = (x_1, x_2, ..., x_N)$ be the original data sequence, where each $x_i$ is a binary value (0 or 1). The compression algorithm maps this sequence to an entangled state $(|\psi_1\rangle, |\psi_2\rangle, ..., |\psi_N\rangle)$, where $|\psi_i\rangle$ represents the state of the *i*-th qubit in the entangled pair. The compression ratio *R* is defined as: $R = \frac{N}{N_{encoded}}$ where *N* is the length of the original data sequence and *Nencoded* is the number of qubits used to represent the data. The encoding process is described by: $|\psi_i\rangle = \alpha_i |0\rangle + \beta_i |1\rangle$ where $\alpha_i$ and $\beta_i$ are complex amplitudes determined by the data bit $x_i$. The decoding process reverses this operation, reconstructing the original data from the measured state of the qubits. The fidelity of the reconstruction is crucial, and the algorithm incorporates techniques to minimize errors due to measurement noise. The overall compression algorithm can be summarized as follows: