Approximating incompatible von Neumann measurements simultaneously

Abstract

We study the problem of performing orthogonal qubit measurements simultaneously. Since these measurements are incompatible, one has to accept additional imprecision. An optimal joint measurement is the one with the least possible imprecision. All earlier considerations of this problem have concerned only joint measurability of observables, while in this work we also take into account conditional state transformations (i.e., instruments). We characterize the optimal joint instrument for two orthogonal von Neumann instruments as being the Luders instrument of the optimal joint observable.

9 pages, 4 figures; v2 has a more extensive introduction + other minor corrections

References in corpus (7)

• Complementarity and Uncertainty in Mach-Zehnder Interferometry and beyond
• Coexistence of qubit effects
• Estimating the expectation values of spin 1/2 observables with finite resources
• Upper bound on our knowledge about noncommuting observables for a qubit system
• Accuracy matrix in generalized simultaneous measurement of a qubit system
• Coexistence of quantum operations
• Joint measurement of two unsharp observables of a qubit