The quantum mechanical measurement process is analyzed by means of an explicit generic model describing the interaction between object and measuring device. The solution of the Schrödinger equation for the whole system reflects the ‘collapse’ of the object wave function. A necessary condition is a sufficiently sharply peaked initial measurement device wave function, which is guaranteed in its classical limit. With this assumption, it is in particular proven that the off-diagonal elements of the object density matrix vanish. This study therefore (...) shows the reduction of the object state to be a consequence of Hamiltonian evolution of the total system. (shrink)

We investigate in this work the meaning of weak values through the prism of property ascription in quantum systems. Indeed, the weak measurements framework contains only ingredients of the standard quantum formalism, and as such weak measurements are from a technical point of view uncontroversial. However attempting to describe properties of quantum systems through weak values—the output of weak measurements—goes beyond the usual interpretation of quantum mechanics, that relies on eigenvalues. We first recall the usual form of property ascription, based (...) on the eigenstate-eigenvalue link and the existence of “elements of reality”. We then describe against this backdrop the different meanings that have been given to weak values. We finally argue that weak values can be related to a specific form of property ascription, weaker than the eigenvalues case but still relevant to a partial description of a quantum system. (shrink)

Calculation of the mean of an observable in quantum mechanics is typically assumed to require that the state vector be in the domain of the corresponding self-adjoint operator or for a mixed state that the operator times the density matrix be in the trace class. We remind the reader that these assumptions are unnecessary. We state what is actually needed to calculate the mean of an observable as well as its variance.

How long does a quantum particle take to traverse a classically forbidden energy barrier? In other words, what is the correct expression for quantum tunnelling time? This seemingly simple question has inspired widespread debate in the physics literature. I argue that we should not expect the orthodox interpretation of quantum mechanics to provide a unique correct expression for quantum tunnelling time, because to do so it would have to provide a unique correct answer to a question whose assumptions are in (...) tension with its core interpretational commitments. I explain how this conclusion connects to time’s special status in quantum mechanics, the meaningfulness of classically inspired concepts in different interpretations of quantum mechanics, the prospect of constructing experimental tests to distinguish between different interpretations, and the status of weak measurement in resolving questions about the histories of subensembles. (shrink)

Quantum mechanical weak values of projection operators have been used to answer which-way questions, e.g. to trace which arms in a multiple Mach–Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I show that this procedure might lead to logical inconsistencies in the sense that different methods used to answer composite questions, like “Has the particle traversed the way X or the way Y?”, may result in different answers depending on which methods are (...) used to find the answer. I illustrate the problem by considering some examples: the “quantum pigeonhole” framework of Aharonov et al., the three-box problem, and Hardy’s paradox. To prepare the ground for my main conclusion on the incompatibility in certain cases of weak values and logic, I study the corresponding situation for strong/projective measurements. In this case, no logical inconsistencies occur provided one is always careful in specifying exactly to which ensemble or sample space one refers. My results cast doubts on the utility of quantum weak values in treating cases like the examples mentioned. (shrink)

Spin is a fundamental and distinctive property of the electron, having far-reaching implications. Yet its purely formal treatment often blurs the physical content and meaning of the spin operator and associated observables. In this work we propose to advance in disclosing the meaning behind the formalism, by first recalling some basic facts about the one-particle spin operator. Consistently informed by and in line with the quantum formalism, we then proceed to analyse in detail the spin projection operator correlation function \=\left\langle (...) \left \left \right\rangle \) for the bipartite singlet state, and show it to be amenable to an unequivocal probabilistic reading. In particular, the calculation of \\) entails a partitioning of the probability space, which is dependent on the directions \.\) The derivation of the CHSH- or other Bell-type inequalities, on the other hand, does not consider such partitioning. This observation puts into question the applicability of Bell-type inequalities to the bipartite singlet spin state. (shrink)