Related papers: Weak value analogue in classical stochastic proces…
It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to…
This paper investigates weak convergence of U-statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying U-statistic exists is relaxed to having 4/3 moments only (modulo a…
The aim of this expos\'e is to make explicit the analogy between the classical notion of non-independent probability distribution and the quantum notion of entangled state. To bring that analogy forth, we consider a classical systems with…
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…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
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…
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the…
In this chapter we offer an introduction to weak values from a three-fold perspective: first, outlining the protocols that enable their experimental determination; next, deriving their correlates in the quantum formalism and, finally,…
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…
Evidently, some relaxation dynamics, e.g. exponential decays, are much more common in nature than others. Recently there have been attempts to explain this observation on the basis of ``typicality of perturbations'' with respect to their…
Various quantum measurement procedures are analyzed and it is shown that under certain conditions they yield consistently {\em weak values} which might be very different from the eigenvalues, the allowed outcomes according to the standard…
The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That…
This paper establishes a direct, robust and intimate connection between (i) non classicality tests for various quantum features, e.g., non-Boolean logic, quantum coherence, nonlocality, quantum entanglement, quantum discord; (ii) negative…
We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor is here the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar…
The notion of trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any…
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…
Experimentally, the imaginary parts of complex weak values are obtained from the response of the system to small unitary phase shifts generated by the target observable. The complex conditional probabilities obtained from weak measurements…
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…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focussing on their dissociation probabilities. It is found that the quantum system is more robust than the classical…