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arXiv · quant-ph/0003117

Remark on multi-particle observables and entangled states with constant complexity

Dominik Janzing·Thomas Beth
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Abstract

We show that every density matrix of an n-particle system prepared by a quantum network of constant depth is asymptotically commuting with the mean-field observables. We introduce certain pairs of hypersurfaces in the space of density matrices and give lower bounds for the depth of a network which prepares states lying outside those pairs. The measurement of an observable which is not asymptotically commuting with the mean-field observables requires a network of depth in the order of log n, if one demands the measurement to project the state into the eigenspace of the measured observable.

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Dominik Janzing, Thomas Beth. 2000-03-24. Remark on multi-particle observables and entangled states with constant complexity. https://arxiv.org/abs/quant-ph/0003117

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