Understanding the entanglement and mixedness introduced into a quantum system by quantum Boolean functions (BFs) circuits holds a significant potential in quantum information theory. This study provides an overview and empirical findings on purity, negativity, and von Neumann entropy with the aim to reveal an insight into the internal structure of the corresponding unitary operators. Approximately 5,000 quantum circuits were examined for BFs of different types, e.g., balanced, symmetric, bent, etc. and of various properties such as algebraic degree, algebraic immunity, resiliency order, and others. While previous research typically focuses on input superposition alone through addition of Hadamard gates (Superposition scenario), we introduce additional entanglement through random statevector generation (Random Statevector scenarios). Results show a slight increase in von Neumann entropy and negativity for the Random Statevector scenario as compared to the Superposition scenario. Surprisingly, further measurement increases were observed when adding classical randomness via random qubit rotations (Random Qubit Rotations scenario) instead of random statevector generation. The observed trends include lower mean values and wider ranges of negativity and von Neumann entropy for BFs of higher algebraic degree in the Superposition scenario. Additionally, plateaued functions of lower algebraic degree exhibit purity measurements with wider spread in the Random Statevector scenario as compared to the Superposition scenario. We hope that this work may inspire new theoretical studies on quantum BF circuits. For example, a deeper understanding of quantum BF circuits with high mixedness and entanglement may lead to the development of novel quantum error correction techniques.