This strange fact—that the system evolves one way between measurements — Measurement in quantum mechanics

"As we apply the results obtained in this section, we should remember that common terms like "measurement" and "information" are being used here with a specific technical meaning. In particular, this is not the place for a detailed analysis of real experimental measurements and their relation to the theoretical framework. We merely note that, in the information theoretic view of quantum mechanics, the probabilities and the related density operators and entropies, which are employed to assess the properties of quantum states and the outcomes of measurement, provide a coherent and consistent basis for understanding and interpreting the theory."

"We now consider measurements of A and B when they are compatible observables. Suppose we measure A first and obtain result a. Subsequently, we may measure B and get result b. Finally we measure A again. It follows from our measurement formalism that the third measurement always gives a with certainty; that is, the second (B) measurement does not destroy the previous information obtained in the first (A) measurement. This is rather obvious when the eigenvalues of A are nondegenerate:|\alpha \rangle \xrightarrow{\text{A measurement}} |a, b \rangle \xrightarrow{\text{B measurement}} |a, b \rangle \xrightarrow{\text{A measurement}} |a, b \rangle."

"By now the reader will have realized that measurement in quantum physics is fundamentally different from that in classical physics. In classical physics, a measurement reveals a pre-existing property of the physical system that is tested. If a car is driving at 180 km h−1 on the highway, the measurement of its speed by radar determines a property that exists prior to the measurement, which gives the police the legitimacy to give a ticket to the driver. On the contrary, the measurement of the Sx component of a spin-1/2 particle in the state |+〉 does not reveal a value of Sx existing before the measurement. The spread in the results of measuring Sx in this case is sometimes attributed to “uncontrollable perturbation of the spin due to the measurement process,” but the value of Sx does not exist before the measurement, and that which does not exist cannot be perturbed."

"We see that the measuring process in quantum mechanics has a "two- faced" character: it plays different parts with respect to the past and future of the electron. With respect to the past, it "verifies" the probabilities of the various possible results predicted from the state brought about by the previous measurement. With respect to the future, it brings about a new state. Thus the very nature of the process of measurement involves a far-reaching principle of irreversibility."

"What we have learnt from this chapter is that we cannot have a direct evidence of, i.e. directly measure, a quantum state of a single system. Our experience is only connected with the experimental values of observables, and any time we measure an observable we can only have a partial experience of a system under a certain perspective but we can never have a complete experience that would be represented by an observation of the state vector, which is – in a quantum-mechanical sense – a complete description of the system. In other words, the quantum state is not an observable in the classical sense. However, since this feature of the quantum state is not due to subjective ignorance but rather to an intrinsic characteristic of the microscopic world, there are no definitive reasons to deny the reality of a quantum state."

"Hence coherence survives to the extent to which an experiment fails to distinguish between different eigenvalues of the observable being measured, and distinct final states of the object display interference if the final states of the apparatus overlap. […] When the apparatus ends up in one member of a set of orthogonal states, the experiment unambiguously determines whether or not the object is then in a particular eigenstate of the observable of interest, but the result becomes increasingly ambiguous with increasing overlap between the states of the apparatus; furthermore, states of the object with distinct eigenvalues interfere with a visibility that is a measure of the ambiguity with which the states assumed by the apparatus determine the states of the object."