Related papers: An interpretation and understanding of complex mod…
The equation of motion for a time-independent weak value of a quantum mechanical observable contains a complex valued energy factor - the weak energy of evolution. This quantity is defined by the dynamics of the pre-selected and…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
Observations in quantum weak measurements are determined by complex numbers called weak values. We present a geometrical interpretation of the argument of weak values of general Hermitian observables in $N$-dimensional quantum systems in…
Shapley values have become one of the go-to methods to explain complex models to end-users. They provide a model agnostic post-hoc explanation with foundations in game theory: what is the worth of a player (in machine learning, a feature…
Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also…
We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…
This is a comment on J. A. Barrett's article ``The Preferred-Basis Problem and the Quantum Mechanics of Everything'' in Brit. J. Phil. Sci. 56 (2005), which concerns theories postulating that certain quantum observables have determinate…
We generalize the concept of a weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory…
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…
Weak measurement has been shown to play important roles in the investigation of both fundamental and practical problems. Anomalous weak values are generally believed to be observed only when post-selection is performed, i.e, only a…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
We review the methods based on expectation value coupled cluster formalism - a common framework for the derivation of properties: the ground-state average value of an observable, cumulants of the second-order reduced density matrices,…
This paper presents a method for expressing the determinant of an N {\times} N complex block matrix in terms of its constituent blocks. The result allows one to reduce the determinant of a matrix with N^2 blocks to the product of the…
When quantitative models are used to support decision-making on complex and important topics, understanding a model's ``reasoning'' can increase trust in its predictions, expose hidden biases, or reduce vulnerability to adversarial attacks.…
By double ideal quotient, we mean $(I:(I:J))$ where ideals $I$ and $J$. In our previous work [11], double ideal quotient and its variants are shown to be very useful for checking prime divisor and generating primary component. Combining…
Periodically-modulated potentials in the form of light fields have previously been applied to induce reversible phase transitions in dilute colloidal systems with long-range interactions. Here we investigate whether similar transitions can…
Polarization of types in call-by-push-value naturally leads to the separation of inductively defined observable values (classified by positive types), and coinductively defined computations (classified by negative types), with adjoint…
The asymptotic performance of a polar code under successive cancellation decoding is determined by the exponent of its polarizing matrix. We first prove that the partial distances of a polarizing matrix constructed from the Kronecker…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…