Beyond Measurement: Exponential Advantages in Coherent Quantum Inference

Zhaoyi Li compares inference protocols that preserve quantum coherence with those that first convert inputs to classical measurements. Tasks include purity amplification, approximate purification, mixed-state cloning and density-matrix exponentiation. Coherent processing can require exponentially fewer copies: principal-eigenstate amplification needs O(1/ε) copies rather than the Ω(d/ε) required by incoherent protocols. The talk develops the case for a theory of coherent quantum inference and relates its limitations to entanglement-breaking processes.