PreprintarXiv licencearXiv
Forbidden Subspaces in Quantum State Smoothing
Abstract
A system between a preparation and a post-selection has had no agreed state since 1964. With positivity as the criterion, a post-selection admits an interval of orderings around the symmetric one exactly when the subspace it forbids is spanned by eigenvectors of a full-rank filtered state. Otherwise it certifies contextuality, testable on a qubit. The averaged filtered state carries the entanglement spectrum of the record, so the smallest forbidden subspaces a symmetry allows are even-dimensional in the Haldane class and odd in the trivial one. That parity is the record's topological class.
Related
- A Three-Party W-State Quantum Secret Sharing Protocol with X-Gate Encoding and Forbidden-Outcome Detection
- Quantum state smoothing for tracking optical quantum dynamics and recovering purity and squeezing
- Unifying quantum smoothing theories with extended retrodiction
- Exact exponents for smoothing the max-relative entropy and quantum information decoupling in von Neumann algebras
- Decoherence-free subspaces in the noisy dynamics of discrete-step quantum walks in a photonic lattice
BibTeX
@misc{kam2026forbidden,
title = {{Forbidden Subspaces in Quantum State Smoothing}},
author = {Chon-Fai Kam and Kai-Wen Wong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17307},
eprint = {2609.17307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17307},
}
RIS
TY - UNPB
TI - Forbidden Subspaces in Quantum State Smoothing
AU - Chon-Fai Kam
AU - Kai-Wen Wong
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17307
UR - https://arxiv.org/abs/2609.17307
AB - A system between a preparation and a post-selection has had no agreed state since 1964. With positivity as the criterion, a post-selection admits an interval of orderings around the symmetric one exactly when the subspace it forbids is spanned by eigenvectors of a full-rank filtered state. Otherwise it certifies contextuality, testable on a qubit. The averaged filtered state carries the entanglement spectrum of the record, so the smallest forbidden subspaces a symmetry allows are even-dimensional in the Haldane class and odd in the trivial one. That parity is the record's topological class.
ER -