Related papers: Full characterization of modular values for two-di…
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One…
In recent years weak values have been used to explore interesting quantum features in novel ways. In particular, the real part of the weak value of the momentum operator has been widely studied, mainly in connection with (nonlocal) Bohmian…
Current quantum computer technology is sufficient to realize weak measurements and the corresponding concept of weak values. We demonstrate how the weak value anomaly can be tested, along with consistency and simultaneity of weak values,…
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…
A model is proposed for the statistical analysis of arbitrary-strength quantum measurements, based on a picture of "sampling weak values" from different configurations of the system. The model is comprised of two elements: a "local weak…
In this presentation, I argue that weak measurements empirically support the notion of quantum superpositions as statistical alternatives. In short, weak measurements show that Schroedinger's cat is already dead or alive before the…
In the conventional formulation, it is broadly accepted that simultaneous measurability and commutativity of observables are equivalent. However, several objections have been claimed that there are cases in which even nowhere commuting…
Recent controversy regarding the meaning and usefulness of weak values is reviewed. It is argued that in spite of recent statistical arguments by Ferrie and Combes, experiments with anomalous weak values provide a useful amplification…
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…
A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal…
Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify…
In this paper we associate with an infinite family of real extended functions defined on a locally convex space, a sum, called robust sum, which is always well-defined. We also associate with that family of functions a dual pair of problems…
We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…
We express modular and weak values of observables of three- and higher-level quantum systems in their polar form. The Majorana representation of N-level systems in terms of symmetric states of N-1 qubits provides us with a description on…
Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of…
Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as…
Weak values and measurements have been proposed as means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur…
We calculate the energy and wave functions of two particles confined to two spatial dimensions interacting via arbitrary anisotropic potentials with negative or zero net volume. The general rigorous analytic expressions are given in the…
We provide lower bounds for the sum of the negative eigenvalues of the operator $|\sigma\cdot p_A|^{2s} - C_s/|x|^{2s} + V$ in three dimensions, where $s\in (0, 1]$, covering the interesting physical cases $s = 1$ and $s = 1/2$. Here…