How to determine the outcome of a projective measurement?
If we now perform a standard projective measurement on M to determine the value m of the pointer observable, defined by the projection operator then the probability of obtaining the outcome m is, by (37)5: and, more generally, if the initial state of Q is a mixed state ρ, then (45)p(m) = Tr Q(MρM †).
How are projective measurements used in quantum mechanics?
In quantum mechanics, and especially in the theory of quantum information (where any read-out of the quantum information encoded in a quantum state requires a quantum measurement), it is useful to consider a more general class of measurements than the projective measurements associated with the determination of the value of an observable.
How are quantum measurements different from General measurements?
General Measurements. Quantum measurements are described by a collection of measurement operators. These are operators acting on the state space of the system being measured. The index refers to the measurement outcomes that may occur in the experiment. If the state of the quantum system is immediately before the measurement then…
How are projective measurements restricted to orthogonal states?
Projective measurements are restricted to orthogonal states: they project on an eigenspace. A standard von Neumann ‘yes-no’ measurement is associated with a projection operator; so a standard observable is represented in the spectral representation as a sum of projection operators, with coefficients representing the eigenvalues of the observable.
How is a measurement characterized in a quantum system?
A quantum measurement can be characterized, completely generally, as a certain sort of interaction between two quantum systems, Q (the measured system) and M (the measuring system). We suppose that Q is initially in a state |ψ〉 and that M is initially in some standard state |0〉, where |m〉 is an orthonormal basis of ‘pointer’ eigenstates in H M.
How to construct a non-trivial POVM measurement example?
How to construct a non-trivial (non-projective) POVM measurement example? But this is simply a projective measurement (on state Ψ ). How to construct a non-trivial (non-projective) POVM measurement example?