Beyond Measurement: Exponential Advantages in Coherent Quantum Inference

Abstract

Quantum inference usually begins by measuring quantum data and converting it into classical information. In this talk, I will consider a different setting in which the desired output remains quantum, allowing coherence to be preserved throughout the inference process. Examples include quantum purity amplification, approximate purification and cloning of mixed states, and density matrix exponentiation. I will show that coherent protocols can use exponentially fewer input copies than any measurement mediated strategy. For quantum purity amplification of a principal eigenstate with an input of dimension d, coherent processing achieves error ε using O(1/ε) copies, while incoherent protocols require Ω(d/ε) copies. More broadly, these results motivate a theory of coherent quantum inference and establish entanglement breaking limits as a natural connection between coherent and incoherent information processing.