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Pure states are optimal for total energy-constrained quantum channel discrimination

  • Christos N. Gagatsos
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Abstract

We consider the discrimination of two quantum channels acting on bosonic modes, with a probe state of fixed mean photon number and no ancilla. We prove that pure probes are optimal: for every mixed probe there is a pure probe with exactly the same mean photon number that performs at least as well. The result holds for arbitrary channels and for every figure of merit built from the Chernoff quantities Tr[ρ1sρ21−s], including the quantum Chernoff exponent, as well as for the single-shot error probability. The proof relies on a decomposition of any state of mean photon number nb into pure states of mean photon number exactly nb, which extends a matrix rank-one decomposition of Huang and Zhang to density operators of infinite rank.

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Cite

BibTeXRIS
BibTeX
@misc{gagatsos2026pure,
  title = {{Pure states are optimal for total energy-constrained quantum channel discrimination}},
  author = {Christos N. Gagatsos},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30295},
  eprint = {2610.30295},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30295},
}
RIS
TY  - UNPB
TI  - Pure states are optimal for total energy-constrained quantum channel discrimination
AU  - Christos N. Gagatsos
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30295
UR  - https://arxiv.org/abs/2610.30295
AB  - We consider the discrimination of two quantum channels acting on bosonic modes, with a probe state of fixed mean photon number and no ancilla. We prove that pure probes are optimal: for every mixed probe there is a pure probe with exactly the same mean photon number that performs at least as well. The result holds for arbitrary channels and for every figure of merit built from the Chernoff quantities Tr[ρ_1^sρ_2^1−s], including the quantum Chernoff exponent, as well as for the single-shot error probability. The proof relies on a decomposition of any state of mean photon number nb into pure states of mean photon number exactly nb, which extends a matrix rank-one decomposition of Huang and Zhang to density operators of infinite rank.
ER  -