4 research outputs found
Coexistence of qubit effects
Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained in the ranges of a single (joint) observable. Here we give several equivalent characterizations of coexistent pairs of qubit effects. We also establish the equivalence between our results and those obtained independently by other authors. Our approach makes explicit use of the Minkowski space geometry inherent in the four-dimensional real vector space of selfadjoint operators in a two-dimensional complex Hilbert space
Joint measurements on qubits and cloning of observables
Cloning of observables, unlike standard cloning of states, aims at copying
the information encoded in the statistics of a class of observables rather then
on quantum states themselves. In such a process the emphasis is on the quantum
operation (evolution plus measurement) necessary to retrieve the original
information. We analyze, for qubit systems, the cloning of a class generated by
two noncommuting observables, elucidating the relationship between such a
process and joint measurements. This helps in establishing an optimality
criterion for cloning of observables. We see that, even if the cloning machine
is designed to act on the whole class generated by two noncommuting
observables, the same optimal performances of a joint measurement can be
attained. Finally, the connection with state dependent cloning is enlightened.Comment: 7 pages, 1 figure, to appear on Open System & Inf. Dynamic