Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States
Abstract
We determine the exact entanglement structure of the conditional state obtained by measuring m corresponding rungs (m≤ N/2) in two identical copies of an arbitrary half-filled free fermion Gaussian state and post-selecting the same normalized single-fermion state (|ψ⟩ = u|10⟩+v|01⟩, where 0 and 1 denote the fermion occupancy on each sites) on each rung. For m<N/2, the conditional wavefunction generally depends on the initial state. Nevertheless, whenever the selected outcome has nonzero probability, the state on the unmeasured sites remains Gaussian and factorizes exactly into N−m different orthogonal modes including m inter-copy entangling modes and N−2m spectator modes localized in one copy. Consequently, the entanglement entropy between the unmeasured parts of the two copies is S=m h2(|v|2), independent of the initial state, where h2(x)=−xln x−(1−x)ln(1−x). The success probability is given by Pm=det CLdet(Im−CL)=det(CLRCRL), determined solely by the initial correlations and independent of (u,v). Equal-weight Bell post-selection serves as a special case that achieves the maximal entanglement swapping.
Related
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BibTeX
@misc{fang2026exact,
title = {{Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States}},
author = {Jiyuan Fang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29933},
eprint = {2608.29933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29933},
}
RIS
TY - UNPB
TI - Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States
AU - Jiyuan Fang
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29933
UR - https://arxiv.org/abs/2608.29933
AB - We determine the exact entanglement structure of the conditional state obtained by measuring m corresponding rungs (m≤ N/2) in two identical copies of an arbitrary half-filled free fermion Gaussian state and post-selecting the same normalized single-fermion state (|ψ⟩ = u|10⟩+v|01⟩, where 0 and 1 denote the fermion occupancy on each sites) on each rung. For m<N/2, the conditional wavefunction generally depends on the initial state. Nevertheless, whenever the selected outcome has nonzero probability, the state on the unmeasured sites remains Gaussian and factorizes exactly into N−m different orthogonal modes including m inter-copy entangling modes and N−2m spectator modes localized in one copy. Consequently, the entanglement entropy between the unmeasured parts of the two copies is S=m h_2(|v|^2), independent of the initial state, where h_2(x)=−xln x−(1−x)ln(1−x). The success probability is given by P_m=det C_Ldet(I_m−C_L)=det(C_LRC_RL), determined solely by the initial correlations and independent of (u,v). Equal-weight Bell post-selection serves as a special case that achieves the maximal entanglement swapping.
ER -