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arXiv · 2609.31841

A Universal Budget for Entanglement and Nonlocal Non-Stabilizerness

Salvatore Marco Giampaolo
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Abstract

Entanglement and nonlocal non-stabilizerness are distinct quantum resources encoded in the Schmidt spectrum of a bipartite pure state. For qubit systems, we establish a universal quadratic constraint on their simultaneous allocation, governed by the minimum number of logical qubits required on each side to encode the occupied Schmidt support. Additional spectral constraints reveal a strong asymmetry in their allocation with the Entanglement that can exhaust the logical capacity, whereas the maximal nonlocal non-stabilizerness grows only logarithmically with it. For a tensor-network cut crossed by a single separating virtual edge, the logical capacity is determined by the occupied bond dimension. We further derive a one-sided certificate for the resources of the untruncated state from a retained Schmidt spectrum and its discarded weight. For small discarded weight, the resulting corrections are linear in that weight. These results connect a universal resource budget to resource-aware control of tensor-network truncations.

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Salvatore Marco Giampaolo. 2026-09-25. A Universal Budget for Entanglement and Nonlocal Non-Stabilizerness. https://arxiv.org/abs/2609.31841

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