Phase-Driven Precision Boost in Quantum Compression for Postselected Metrology
We reveal the noncyclic Pancharatnam phase--arising from the coherent system-meter interaction--as a fundamental criterion that governs the optimal performance of quantum compression channels in postselected metrology. This phase embodies a geometric connection that enables precise control over the parallel evolution of the meter state, thereby maximizing the quantum Fisher information per trial and achieving lossless compression channels. Remarkably, fine-tuning the postselection parameter just below this optimal phase incurs substantial information loss, whereas tuning it just above fully suppresses undesired parallel evolution, enhancing information retention beyond that achievable in postselected protocols lacking Pancharatnam phase effects. We further reveal that leveraging qudit meter states can unlock a substantial additional enhancement. These findings establish the Pancharatnam phase as a geometric benchmark, guiding the design of high-precision quantum parameter estimation protocols.