Quantum data compression under localized features

Abstract In this paper, we first introduce the local quantum information processing task by compressing the density operator based on local quantum Bernoulli noises. Then, the local quantum compression theorem is given, that is, the local quantum entropy is the minimum achievable rate of local compression. Finally, we prove the theorem with the proof of the direct coding theorem and the inverse theorem. The direct coding theorem shows that a scheme with such a local compression rate exists, and that this local compression rate converges to the local quantum entropy. The inverse theorem shows that the compression scheme with the rate below the local entropy is unachievable. With the continuous development of quantum technology, local quantum data compression technology will have broad application prospects and development space.