Fixed points of commutative Lüders operations

Abstract

This paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations. Specifically, it is proved that if a quantum operation has mutually commuting operation elements that are effects forming a resolution of the identity, then the fixed points set of the quantum operation is exactly the commutant of the operation elements.

References in corpus (5)

• The structure of preserved information in quantum processes
• Lüders Theorem for Unsharp Quantum Measurements
• The multiplicative domain in quantum error correction
• On Fixed Points of Lüders Operation
• Quantum Channels, Wavelets, Dilations and Representations of $O_n$

Cited by in corpus (2)

• Measurement disturbance and conservation laws in quantum mechanics
• Self-consistency of the two-point energy measurement protocol