The coherent measurement cost of coherence distillation

Varun Narasimhachar

doi:10.22331/q-2025-04-15-1707

The coherent measurement cost of coherence distillation

Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, Republic of Singapore 138632

Published:	2025-04-15, volume 9, page 1707
Editor:	Paul Skrzypczyk
Eprint:	arXiv:2308.07719v2
Doi:	https://doi.org/10.22331/q-2025-04-15-1707
Citation:	Quantum 9, 1707 (2025).

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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 $\textit{target effect}$ 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.

Featured image: (Left) Resource distillation viewed as a "black box" converting noisy static resources (top pipe) to standard static resources (bottom pipe). (Right) Under the hood, the distillation mechanism is consuming dynamical resource (left pipe). We quantify this hidden resource use.

Talk given at the Quantum Resources Workshop, Singapore, December 2023

Slides of the talk can be found here

Popular summary

Quantum resource theories formalize the study of the resources that power quantum technologies. One such resource is coherence (also known as superposition). Past work has found ways of distilling this resource into a pure, high-grade form (standard coherent state) from a noisy form (mixed coherent state). But the distillation process uses coherent measurements—a dynamical form of the same resource—which has not been accounted-for in past work. Here we devise a way to estimate this coherent measurement cost. We provide lower bounds on this cost for generic instances of the distillation task. We also conjecture how the cost grows when distilling from many copies of the same state. If this conjecture is true, there would be cases where the dynamical coherence required by the measurements involved is higher than the distilled yield! In these cases, distillation should arguably be avoided and, instead, the available dynamical resource should be used to simply prepare standard static resources. Our work holds a cautionary mirror to the resource theory paradigm, suggesting scope for improvement in the operational considerations therein.

► BibTeX data

@article{Narasimhachar2025coherentmeasurement,
  doi = {10.22331/q-2025-04-15-1707},
  url = {https://doi.org/10.22331/q-2025-04-15-1707},
  title = {The coherent measurement cost of coherence distillation},
  author = {Narasimhachar, Varun},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1707},
  month = apr,
  year = {2025}
}

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