Practical Homodyne Shadow Estimation
- URL: http://arxiv.org/abs/2512.13146v1
- Date: Mon, 15 Dec 2025 09:56:03 GMT
- Title: Practical Homodyne Shadow Estimation
- Authors: Ruyu Yang, Xiaoming Sun, Hongyi Zhou,
- Abstract summary: We develop a practical shadow estimation protocol for continuous-variable quantum systems.<n>We construct an unbiased estimator for the quantum state.<n>We show that the shadow norm scales as $mathcalO(n_mathrmmax4)$, improving upon previous $mathcalO(n_mathrmmax13/3)$ bounds.
- Score: 4.578469978594751
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Shadow estimation provides an efficient framework for estimating observable expectation values using randomized measurements. While originally developed for discrete-variable systems, its recent extensions to continuous-variable (CV) quantum systems face practical limitations due to idealized assumptions of continuous phase modulation and infinite measurement resolution. In this work, we develop a practical shadow estimation protocol for CV systems using discretized homodyne detection with a finite number of phase settings and quadrature bins. We construct an unbiased estimator for the quantum state and establish both sufficient conditions and necessary conditions for informational completeness within a truncated Fock space up to $n_{\mathrm{max}}$ photons. We further provide a comprehensive variance analysis, showing that the shadow norm scales as $\mathcal{O}(n_{\mathrm{max}}^4)$, improving upon previous $\mathcal{O}(n_{\mathrm{max}}^{13/3})$ bounds. Our work bridges the gap between theoretical shadow estimation and experimental implementations, enabling robust and scalable quantum state characterization in realistic CV systems.
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