The coherent measurement cost of coherence distillation

TL;DR

This paper investigates the hidden measurement cost involved in quantum coherence distillation, establishing conditions and bounds for the measurement resources required, especially in the asymptotic limit, with implications for quantum resource management.

Contribution

It introduces the target effect construction to characterize measurement costs in coherence distillation and provides bounds and conjectures on their scaling behavior in the asymptotic limit.

Findings

Lower bounds on measurement coherence cost established

Cost scales extensively with the number of copies in the asymptotic limit

Measurement cost may exceed the distilled coherence yield in some cases

Abstract

Quantum coherence -- an indispensable resource for quantum technologies -- is known to be distillable from a noisy form using operations that cannot create it. However, distillation exacts a hidden coherent measurement cost, which has not previously been examined. We devise the target effect construction to characterize this cost through detailed conditions on the coherence-measuring structure necessary in any process realizing exact (maximal or non-maximal) or approximate distillation. As a corollary, we lower-bound the requisite measurement coherence, as quantified by operationally-relevant measures. We then consider the asymptotic limit of distilling from many copies of a given noisy coherent state, where we offer rigorous arguments to support the conjecture that the (necessary and sufficient) coherent measurement cost scales extensively in the number of copies. We also show that this cost is no smaller than the coherence of measurements saturating the scaling law in the generalized quantum Stein's lemma. Our results and conjectures apply to any task whereof coherence distillation is an incidental outcome (e.g., incoherent randomness extraction). But if pure coherence is the only desired outcome, our conjectures would have the cautionary implication that the measurement cost is often higher than the distilled yield, in which case coherence should rather be prepared afresh than distilled from a noisy input.