Orthogonalization of Positive Operator Valued Measures

• URL: http://arxiv.org/abs/2103.14126v2
• Date: Tue, 11 Jan 2022 14:44:16 GMT
• Title: Orthogonalization of Positive Operator Valued Measures
• Authors: Mikael de la Salle
• Abstract summary: We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by Kempe-Vidick and Ji-Natarajan-Vidick-Wright-Yuen. We also generalize to infinite dimension a duality result between POVMs and minimal majorants of finite subsets in the predual of a von Neumann algebra.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by Kempe-Vidick and Ji-Natarajan-Vidick-Wright-Yuen. Quantitatively, our result are also finer, as we obtain a linear dependance, which is optimal. We also generalize to infinite dimension a duality result between POVMs and minimal majorants of finite subsets in the predual of a von Neumann algebra.

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