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PreprintCC BY 4.0arXiv

Trading energy for coherence in mode discrimination

  • Shuyang Meng
  • Valerio Scarani
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Abstract

Energy is arguably the main resource in classical physics; coherence is the prototypical quantum resource. In this paper, we study the interplay between these two resources in the task of optimal mode discrimination. This task, motivated by cryptography and metrology, consists of finding in which mode a signal has been encoded, for a given finite set of possible modes. After recalling that the task can be cast as a semi-definite program, we solve completely the case of two-mode discrimination under a hard energy constraint n≤ N. Specifically, we identify the region of modes overlap, for which the maximal energy state (the Fock state with N excitations) is the best choice for discrimination. For other overlaps, having access to coherence leads to better discrimination.

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Cite

BibTeXRIS
BibTeX
@misc{meng2026trading,
  title = {{Trading energy for coherence in mode discrimination}},
  author = {Shuyang Meng and Valerio Scarani},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19897},
  eprint = {2610.19897},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19897},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Trading energy for coherence in mode discrimination
AU  - Shuyang Meng
AU  - Valerio Scarani
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19897
UR  - https://arxiv.org/abs/2610.19897
AB  - Energy is arguably the main resource in classical physics; coherence is the prototypical quantum resource. In this paper, we study the interplay between these two resources in the task of optimal mode discrimination. This task, motivated by cryptography and metrology, consists of finding in which mode a signal has been encoded, for a given finite set of possible modes. After recalling that the task can be cast as a semi-definite program, we solve completely the case of two-mode discrimination under a hard energy constraint n≤ N. Specifically, we identify the region of modes overlap, for which the maximal energy state (the Fock state with N excitations) is the best choice for discrimination. For other overlaps, having access to coherence leads to better discrimination.
ER  -