Approximate pushforward designs and image bounds on approximations

• URL: http://arxiv.org/abs/2512.01858v1
• Date: Mon, 01 Dec 2025 16:44:25 GMT
• Title: Approximate pushforward designs and image bounds on approximations
• Abstract summary: We derive bounds on the approximation parameters of pushforward designs obtained from complex projective spaces.<n>In the mixed-state case, we refine the bounds by exploiting the symmetric subspace structure.<n> Numerical simulations support our theoretical results, showing near-optimality in low-dimensional scenarios.
• Score: 2.676349883103404
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We extend the framework of quantum pushforward designs to the approximate setting, where averaging is achieved only up to finite precision. Using Schatten $p$-norms and Lipschitz continuity arguments, we derive bounds on the approximation parameters of pushforward designs obtained from complex projective spaces, including simplices, mixed states, and quantum channels. In the mixed-state case, we refine the bounds by exploiting the symmetric subspace structure, leading to asymptotically tighter estimates. Numerical simulations support our theoretical results, showing near-optimality in low-dimensional scenarios.

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