ON COEXISTENCE AND JOINT MEASURABILITY OF RANK-1 QUANTUM OBSERVABLES

Teiko Heinosaari, Daniel Reitzner, Peter Stano

For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly measurable, then their joint observable is unique and it gives the greatest lower bound for the effects corresponding to the observables; (iii) if we have two sharp observables and their every possible two outcome partitionings are jointly measurable, then the observables themselves are jointly measurable. We show that, in general, these properties do not hold. Also some possible candidates which would accompany joint measurability and generalize these apparently useful properties are discussed.

Teiko Heinosaari, Daniel Reitzner, Peter Stano

TEIKO HEINOSAARI, PETER STANO, DANIEL REITZNER

We study the existence of jointly measurable POVM approximations to two non-commuting sharp spin observables. We compare two different ways to specify optimal approximations.

PEKKA J. LAHTI