A Universal Budget for Entanglement and Nonlocal Non-Stabilizerness

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.

4 pages of letter + 14 pages of supp. Mat., No figure. Accompanynig ancillar files available at request

arXiv:2609.31841 [quant-ph]

(or arXiv:2609.31841v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.31841 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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