Related papers: An analytic function approach to weak mutually unb…
We apply analytic perturbation theory to the QCD analysis of the xF_3(x,Q^2) structure function considering a combined set of deep inelastic scattering data presented by several collaborations, and extract values of the scale parameter…
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,…
It is pointed out that the "counter example" presented in the Comment is a family of probe wave functions which are increasingly broad as the shift becomes large. Furthermore, the author's variational calculation is not correct in the sense…
Many deep, mysterious connections have been observed between collections of mutually unbiased bases (MUBs) and combinatorial designs called $k$-nets (and in particular, between complete collections of MUBs and finite affine - or…
Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in…
Repeated unbiased measurements cause a continual application of the weak causality principle, leading to an apparent arrow of time for continuously-monitored quantum systems.
A wide array of graphical models can be parametrised to have atomic probabilities represented by monomial functions. Such monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…
In this paper, we establish an analytic version of critical spaces $Q_{\alpha}^{\beta}(\mathbb{R}^{n})$ on unit disc $\mathbb{D}$, denoted by $Q^{\beta}_{p}(\mathbb{D})$. Further we prove a relation between $Q^{\beta}_{p}(\mathbb{D})$ and…
One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed…
We propose the Lie-algebraic interpretation of poly-analytic functions in $L_2(\C,d\mu)$, with the Gaussian measure $d\mu$, based on a flag structure formed by the representation spaces of the $\mathfrak{sl}(2)$-algebra realized by…
Weak values are typically obtained experimentally by performing weak measurements, which involve weak interactions between the measured system and a probe. However, the determination of weak values does not necessarily require weak…
The structural characterization of high-dimensional mutually unbiased bases (MUBs) by classifying MUBs subsets remains a major open problem. The existing methods not only fail to conclude on the exact classification, but also are severely…
The effects of different forms of weak measurements on the nature of the measurement induced phase transition are theoretically studied in hybrid random quantum circuits of qubits. We use a combination of entanglement measures, ancilla…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
We discover new analytic properties of classical partial and false theta functions and their potential applications to representation theory of W-algebras and vertex algebras in general. More precisely, motivated by clues from conformal…
The modular forms are revisited from a geometric and an algebraic point of view leading to a geometric interpretation of the weak Maass forms connecting them to the Ramanujan Mock Theta functions and to the cusp forms generated from the…
This note is a short elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as an…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…
Weak values are the fundamental values for observables in a pre- and post-selected system. Weak values are typically measured by weak measurement, in which weak values appear in the change of not the pre- and post-selected system but the…