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Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or…
We formulate a Born rule for families of quantum systems parametrized by a noncommutative space of control parameters. The resulting formalism may be viewed as a generalization of quantum mechanics where overlaps take values in a…
A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the…
The $k$-rank numerical range $\Lambda_{k}(A)$ is expressed via an intersection of a countable family of numerical ranges $\{F(M^{*}_{\nu}AM_{\nu})\}_{\nu\in\mathbb{N}}$ with respect to $n\times (n-k+1)$ isometries $M_{\nu}$. This…
The characterization of mixtures of non-interacting, spectroscopically similar quantum components has important applications in chemistry, biology, and materials science. We introduce an approach based on quantum tracking control that…
The first aim of the present paper, is to establish strong approximations of the uniform non-overlapping k-spacings process extending the results of Aly et al. (1984). Our methods rely on the invariance principle in Mason and van Zwet…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
Quantum particles, such as spins, can be used for communicating spatial directions to observers who share no common coordinate frame. We show that if the emitter's signals are the orbit of a group, then the optimal detection method may not…
The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical…
Conventional vision algorithms adopt a single type of feature or a simple concatenation of multiple features, which is always represented in a high-dimensional space. In this paper, we propose a novel unsupervised spectral embedding…
Multiphoton resonances demonstrate the physical significance of counter-rotating wave terms in light-matter interactions. These resonances, however, are sensitive to detuning errors, making the phenomena challenging to experimentally…
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…
Correlations between quantum theory and music theory - specifically between principles of quantum computing and musical harmony - can lead to new understandings and new methodologies for music theorists and composers. The quantum principle…
In this article we investigate no-resonance conditions for quantum many body chaotic systems and random matrix models. No-resonance conditions are properties of the spectrum of a model, usually employed as a theoretical tool in the analysis…
We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.
A mapping is obtained relating radial screened Coulomb systems with low screening parameters to radial anharmonic oscillators in N-dimensional space. Using the formalism of supersymmetric quantum mechanics, it is shown that exact solutions…
The knowledge of hadron spectrum is based on experimental observations of hadronic resonances. The resonances are normally observed as peaks in certain invariant mass distributions. However, neither is a peak necessarily due to the presence…
Polyharmonic maps of order k (briefly, k-harmonic maps) are a natural generalization of harmonic and biharmonic maps. These maps are defined as the critical points of suitable higher order functionals which extend the classical energy…
We examine structural and dynamical properties of quantum resonances associated with an avoided crossing and identify the parameter shifts where these properties attain maximal or extreme values, first at a general level, and then for a…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…