Entangling a quantum system to disentangle its parts

Abstract:In quantum systems, correlations are subject to monogamy relations between the whole and its parts. In particular, entanglement between two sets of particles constrains the entanglement within each set and viceversa. This raises the following question: In a multipartite quantum system, can global correlations disentangle all subsystems of certain size? By exploiting unitary symmetries, we formulate this question as a spectral marginal problem, namely the existence of $n$-qubit pure states whose marginals below a threshold cannot be entangled by any unitary evolution. We call such states threshold entanglement sharing (TES) states. We provide constructive existence proofs and bound the marginal sizes for up to 200 qubits. Further, we show that TES states contain both entanglement and magic, the main resources for quantum computing. Our proof strategy bridges techniques that were treated separately up to date, and independently resolves two open problems in quantum information theory: maximal multipartite entanglement and maximum purity of absolutely separable states.

arXiv:2604.13169 [quant-ph]

(or arXiv:2604.13169v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.13169 Focus to learn more arXiv-issued DOI via DataCite

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