Related papers: Complex Probability Measure and Aharonov's Weak Va…
The Born rule, which is one of foundational axioms of quantum theory, states that the probability of obtain outcome $a$ for the quantum state $|\psi\rangle$ is determined by $P(a)=|\langle a|\psi\rangle|^{2}$. Despite its great success in…
The notion of weak measurement in quantum mechanics has gained a significant and wide interest in realizing apparently counterintuitive quantum effects. In recent times, several theoretical and experimental works have been reported for…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
Quantum measurements can be generalized to include complex quantities. It is possible to relate the quantum weak values of projection operators to the third order Bargmann invariants. The argument of the weak value becomes, up to a sign,…
Quantum resonance, i.e., amplification in transition probability available under certain conditions, offers a powerful means for determining fundamental quantities in physics, including the time duration of the second adopted in the SI…
We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…
Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov-Bergmann-Lebowitz rule. In this short note we present a seemingly disturbing paradox that appears…
A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are…
One of the most intriguing aspects of Quantum Mechanics is the impossibility of measuring at the same time observables corresponding to non-commuting operators. This impossibility can be partially relaxed when considering joint or…
Many quantum paradoxes based on a realistic view of weak values were discussed in the last decades. They lead to astonishing conclusions such as the measurement of a spin component of a spin-1/2 particle resulting in $100\hbar$, the…
A so called 'weak value' of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM…
The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding…
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain…
In an earlier publication we had given an exhaustive analysis of the criteria for weak value measurements of pure states to be optimal in the sense considered by Wootters and Fields. We had proved, for arbitrary spin cases, that the…
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…
How to achieve an arbitrary real-valued probability amplitude in the general single-partite or multipartite quantum system without measuring any other quantum state's probability amplitude? How to achieve an arbitrary real-valued…
A precise definition of "weak [quantum] measurements" and "weak value" (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond…
Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the pre-selection and the post-selection should…
Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on…
We formalize the hidden measurement approach within the very general notion of an interactive probability model. We narrow down the model by assuming the state space of a physical entity is a complex Hilbert space and introduce the…