Frame-dependent coherence of Gaussian quantum states
Abstract
A Hilbert space is usually described using an orthonormal basis, but a more general description can be defined using a tight frame. In the case of continuous-variable Gaussian states, the coherence is usually described using the Hermite-Gauss basis. We present an alternative description using the tight frame of all canonical coherent states. The description of Gaussian states in terms of coherent states is simpler than in terms of Hermite-Gauss basis, and this allows us to obtain an explicit formula describing the frame-dependent coherence of a mixed Gaussian state as a function of the determinant and the trace of covariance matrix. For each mixed Gaussian state, we construct a sequence of discrete-variable quantum states rapidly convergent to it (as concern the purity and coherence) when the dimension of Hilbert space becomes large enough (15 or more). In the discrete case, the coherence is measured with respect to the tight frame of all discrete coherent states.
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BibTeX
@misc{cotfas2026framedependent,
title = {{Frame-dependent coherence of Gaussian quantum states}},
author = {Nicolae Cotfas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05623},
eprint = {2610.05623},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05623},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Frame-dependent coherence of Gaussian quantum states
AU - Nicolae Cotfas
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05623
UR - https://arxiv.org/abs/2610.05623
AB - A Hilbert space is usually described using an orthonormal basis, but a more general description can be defined using a tight frame. In the case of continuous-variable Gaussian states, the coherence is usually described using the Hermite-Gauss basis. We present an alternative description using the tight frame of all canonical coherent states. The description of Gaussian states in terms of coherent states is simpler than in terms of Hermite-Gauss basis, and this allows us to obtain an explicit formula describing the frame-dependent coherence of a mixed Gaussian state as a function of the determinant and the trace of covariance matrix. For each mixed Gaussian state, we construct a sequence of discrete-variable quantum states rapidly convergent to it (as concern the purity and coherence) when the dimension of Hilbert space becomes large enough (15 or more). In the discrete case, the coherence is measured with respect to the tight frame of all discrete coherent states.
ER -