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Assignment maps for arbitrary reduced quantum dynamics

  • James Fullwood
  • Weixiang Ye
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Abstract

Given an open quantum system S with environment E, we establish a one-to-one correspondence between completely positive trace-preserving (CPTP) maps from S to E and assignment maps initializing the composite system SE in a possibly correlated state prior to unitary evolution. We show that every possible joint state ρSE can be realized by such assignment maps, which are inherently Hermiticity-preserving and trace-preserving (HPTP). While these maps sacrifice global positivity, we derive a simple necessary and sufficient condition for any local state of S to belong to their domain of validity. Furthermore, we prove that the geometry of this domain is governed by the joint state assigned to the maximally mixed input, ensuring that a non-zero volume of admissible local states can readily coexist with initial system-environment entanglement. Finally, we provide an operational protocol for witnessing such limits of validity.

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Cite

BibTeXRIS
BibTeX
@misc{fullwood2026assignment,
  title = {{Assignment maps for arbitrary reduced quantum dynamics}},
  author = {James Fullwood and Weixiang Ye},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27338},
  eprint = {2610.27338},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27338},
}
RIS
TY  - UNPB
TI  - Assignment maps for arbitrary reduced quantum dynamics
AU  - James Fullwood
AU  - Weixiang Ye
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27338
UR  - https://arxiv.org/abs/2610.27338
AB  - Given an open quantum system S with environment E, we establish a one-to-one correspondence between completely positive trace-preserving (CPTP) maps from S to E and assignment maps initializing the composite system SE in a possibly correlated state prior to unitary evolution. We show that every possible joint state ρ_SE can be realized by such assignment maps, which are inherently Hermiticity-preserving and trace-preserving (HPTP). While these maps sacrifice global positivity, we derive a simple necessary and sufficient condition for any local state of S to belong to their domain of validity. Furthermore, we prove that the geometry of this domain is governed by the joint state assigned to the maximally mixed input, ensuring that a non-zero volume of admissible local states can readily coexist with initial system-environment entanglement. Finally, we provide an operational protocol for witnessing such limits of validity.
ER  -