Orthogonalization of Positive Operator Valued Measures
Copyright policy )Orthogonalization of Positive Operator Valued Measures
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.
Quantum Physics, General theory of von Neumann algebras, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Mathematics - Operator Algebras, 500, FOS: Physical sciences, projection valued measure, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Noncommutative function spaces, 510, von Neumann algebra, positive operator valued measure, Quantum information, communication, networks (quantum-theoretic aspects), QA1-939, FOS: Mathematics, Operator spaces and completely bounded maps, [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Operator Algebras (math.OA), Quantum Physics (quant-ph), Mathematics, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
Quantum Physics, General theory of von Neumann algebras, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Mathematics - Operator Algebras, 500, FOS: Physical sciences, projection valued measure, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Noncommutative function spaces, 510, von Neumann algebra, positive operator valued measure, Quantum information, communication, networks (quantum-theoretic aspects), QA1-939, FOS: Mathematics, Operator spaces and completely bounded maps, [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Operator Algebras (math.OA), Quantum Physics (quant-ph), Mathematics, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
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