Quantum Tsallis Entropy with Localization Characteristics

This paper introduces a new of quantum Tsallis entropy with localized characteristics. Specifically, we define and characterize a localized quantum Tsallis entropy using the local density operator constructed based on Local Quantum Bernoulli Noises (LQBNs). We also present some important properties of this entropy, including non-negativity, upper bound, unitarity invariance, and concavity. Notably, we find that local quantum Tsallis entropy does not satisfy additivity in general cases. However, under specific parameter conditions, namely when \(q>1\), it exhibits the property of subadditivity. The local quantum Tsallis entropy introduced in this paper not only enriches the theoretical framework of quantum entropy but also provides a powerful tool for describing the complexity of quantum states and understanding information transmission and distribution within quantum systems.