Complete characterization of internal-external entanglement trade-offs in two-mode Gaussian states
Abstract
We characterize the exact trade-off between internal and external entanglement in asymmetric two-mode Gaussian states at fixed local symplectic eigenvalues. Internal entanglement is quantified by the negativity 𝒩A:B between the two modes, while external entanglement is quantified by the negativity 𝒩AB:CD across a Gaussian purification. Numerical sampling suggests the boundary structure of the attainable region in the (𝒩AB:CD,𝒩A:B) plane, which we then determine analytically. Parametrizing the global symplectic spectrum yields a closed admissible interval for the remaining spectral parameter at fixed 𝒩AB:CD. We prove constructively that every point in this interval corresponds to a physical covariance matrix, implying that all intermediate values of 𝒩A:B between the resulting sharp bounds are achievable. The upper bound is attained for opposite-sign correlations of equal magnitude, while the positive branch of the lower bound occurs when one global symplectic eigenvalue equals unity. We also identify two external-entanglement thresholds, derive a saturated monogamy-type inequality, and recover the symmetric-state limit.
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BibTeX
@misc{nambu2026complete,
title = {{Complete characterization of internal-external entanglement trade-offs in two-mode Gaussian states}},
author = {Yasusada Nambu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35183},
eprint = {2610.35183},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35183},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complete characterization of internal-external entanglement trade-offs in two-mode Gaussian states
AU - Yasusada Nambu
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35183
UR - https://arxiv.org/abs/2610.35183
AB - We characterize the exact trade-off between internal and external entanglement in asymmetric two-mode Gaussian states at fixed local symplectic eigenvalues. Internal entanglement is quantified by the negativity 𝒩_A:B between the two modes, while external entanglement is quantified by the negativity 𝒩_AB:CD across a Gaussian purification. Numerical sampling suggests the boundary structure of the attainable region in the (𝒩_AB:CD,𝒩_A:B) plane, which we then determine analytically. Parametrizing the global symplectic spectrum yields a closed admissible interval for the remaining spectral parameter at fixed 𝒩_AB:CD. We prove constructively that every point in this interval corresponds to a physical covariance matrix, implying that all intermediate values of 𝒩_A:B between the resulting sharp bounds are achievable. The upper bound is attained for opposite-sign correlations of equal magnitude, while the positive branch of the lower bound occurs when one global symplectic eigenvalue equals unity. We also identify two external-entanglement thresholds, derive a saturated monogamy-type inequality, and recover the symmetric-state limit.
ER -