This paper explores the interplay between entanglement and magic in quantum information theory, challenging the common belief that higher entanglement corresponds to greater quantumness. The authors introduce the concept of "magic," or non-stabilizerness, to quantify the amount of non-Clifford resources required to prepare a state. They investigate the operational implications of this distinction by studying tasks such as entanglement estimation, distillation, and dilution. The study reveals a computational separation between two regimes in Hilbert space: the entanglement-dominated (ED) phase and the magic-dominated (MD) phase. In the ED phase, states have entanglement that significantly surpasses their magic, while in the MD phase, magic dominates the entanglement. This separation leads to a computational phase transition, where entanglement-related tasks are efficiently solvable in the ED phase but provably intractable in the MD phase. The paper provides theoretical insights and practical applications, including efficient entanglement estimation protocols, robustness of entanglement witnesses, and applications in quantum error correction and many-body physics. The findings highlight the fundamental role of the entanglement-magic interplay in understanding the complex behavior of quantum systems.This paper explores the interplay between entanglement and magic in quantum information theory, challenging the common belief that higher entanglement corresponds to greater quantumness. The authors introduce the concept of "magic," or non-stabilizerness, to quantify the amount of non-Clifford resources required to prepare a state. They investigate the operational implications of this distinction by studying tasks such as entanglement estimation, distillation, and dilution. The study reveals a computational separation between two regimes in Hilbert space: the entanglement-dominated (ED) phase and the magic-dominated (MD) phase. In the ED phase, states have entanglement that significantly surpasses their magic, while in the MD phase, magic dominates the entanglement. This separation leads to a computational phase transition, where entanglement-related tasks are efficiently solvable in the ED phase but provably intractable in the MD phase. The paper provides theoretical insights and practical applications, including efficient entanglement estimation protocols, robustness of entanglement witnesses, and applications in quantum error correction and many-body physics. The findings highlight the fundamental role of the entanglement-magic interplay in understanding the complex behavior of quantum systems.