相关论文: Geometry of Kirkwood-Dirac classical states: A cas…

Recent work on cosmological amplitudes has established reality conditions (derived from unitarity) for general particle-creation processes in flat FLRW cosmologies, in the Bunch-Davies wavefunction. In light of these results, we propose a…

We consider the phase space for a system of $n$ identical qudits (each one of dimension $d$, with $d$ a primer number) as a grid of $d^{n} \times d^{n}$ points and use the finite field $GF(d^{n})$ to label the corresponding axes. The…

We discuss the concept of transformations among reference frames (classical or quantum). Usually transformations among classical reference frames have sharply defined parameters; geometrically they can be considered as {pure states in the…

Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…

The Kirkwood-Dirac (KD) distribution has recently emerged as a powerful quasiprobability framework with wide-ranging applications in quantum information processing tasks. In this work, we introduce an experimentally motivated criterion for…

Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…

Continuous quantum phase transitions that are beyond the conventional paradigm of fluctuations of a symmetry breaking order parameter are challenging for theory. These phase transitions often involve emergent deconfined gauge fields at the…

We study multiple tilings of 3-dimensional Euclidean space by a convex body. In a multiple tiling, a convex body $P$ is translated with a discrete multiset $\Lambda$ in such a way that each point of the space gets covered exactly $k$ times,…

The notion of a K\"ahler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantum flag manifolds. It was subsequently shown that any…

Hypergraph states, a generalization of graph states, constitute a large class of quantum states with intriguing non-local properties and have promising applications in quantum information science and technology. In this paper, we generalize…

Dual of K-frames in a right quaternionic Hilbert space has been recently introduced and studied by Ellouz[1]. In this paper, we study duals of K-frames and prove a characterization of a K-dual in terms of the canonical K-dual of a K-frame…

We investigate the driven states of a two-dimensional crystal whose ground state can be tuned through a square-triangular transition. The depinning of such a system from a quenched random background potential occurs via a complex sequence…

The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there is another class of unitary transforms,…

It is a well-studied phenomenon in AdS$_3$/CFT$_2$ that pure states often appear 'too thermal' in the classical gravity limit, leading to a version of the information puzzle. One example is the case of a heavy scalar primary state, whose…

Given a real closed polytope $P$, we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transform formulations, together with the Poisson summation formula,…

The set of quantum states consists of density matrices of order $N$, which are hermitian, positive and normalized by the trace condition. We analyze the structure of this set in the framework of the Euclidean geometry naturally arising in…

Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They…

Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…

The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…

Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics,…