Projective measurement is a method used in quantum mechanics to obtain information about a quantum system. It involves measuring the system in a particular basis, which collapses the system into one of the basis states. The probability of obtaining a particular outcome is determined by the overlap between the initial state and the basis state.
One example of projective measurement is the Stern-Gerlach experiment, in which a beam of silver atoms is passed through an inhomogeneous magnetic field. The atoms are measured in the z-direction, and the outcome is either spin up or spin down, depending on the orientation of their magnetic moment relative to the field.
Unlike other types of measurement, projective measurement has the unique property of collapsing the quantum system into one of the basis states. This means that the outcome of the measurement is completely determined by the initial state of the system and the basis chosen for the measurement.
In projective measurement, correlations between quantum systems are measured by performing measurements on each individual system and comparing the outcomes. The degree of correlation can be quantified using mathematical tools such as the correlation coefficient.
One limitation of projective measurement is that it can only measure certain properties of a quantum system, such as position or momentum. It cannot simultaneously measure both of these properties with arbitrary precision, due to the uncertainty principle. Additionally, projective measurement is a destructive process, meaning it changes the state of the system and prevents further measurements from being made in the same basis.