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Strictly Localized Mixed States

  • Sigurd Sørlie Rustad
  • Jan Gulla
  • Johannes Skaar
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Abstract

We study strictly localized mixed states in quantum field theory: states that are indistinguishable from vacuum outside some spacetime region. Such states are generated from the vacuum by so-called Licht maps. While the states associated with individual outcomes of local, projective measurements on the vacuum are not strictly localized, the corresponding non-selective states are strictly localized and even admit decompositions into strictly localized pure states. Remarkably, however, there are strictly localized mixed states that cannot be written as mixtures of pure states strictly localized to the same region. Such states can arise from unsharp local measurements. Finally, we extend Knight's theorem to mixed states, showing that strictly localized bosonic mixed states contain terms with arbitrarily high particle numbers.

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Cite

BibTeXRIS
BibTeX
@misc{rustad2026strictly,
  title = {{Strictly Localized Mixed States}},
  author = {Sigurd Sørlie Rustad and Jan Gulla and Johannes Skaar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17013},
  eprint = {2609.17013},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17013},
}
RIS
TY  - UNPB
TI  - Strictly Localized Mixed States
AU  - Sigurd Sørlie Rustad
AU  - Jan Gulla
AU  - Johannes Skaar
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17013
UR  - https://arxiv.org/abs/2609.17013
AB  - We study strictly localized mixed states in quantum field theory: states that are indistinguishable from vacuum outside some spacetime region. Such states are generated from the vacuum by so-called Licht maps. While the states associated with individual outcomes of local, projective measurements on the vacuum are not strictly localized, the corresponding non-selective states are strictly localized and even admit decompositions into strictly localized pure states. Remarkably, however, there are strictly localized mixed states that cannot be written as mixtures of pure states strictly localized to the same region. Such states can arise from unsharp local measurements. Finally, we extend Knight's theorem to mixed states, showing that strictly localized bosonic mixed states contain terms with arbitrarily high particle numbers.
ER  -