Related papers: Three paths toward the quantum angle operator
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\"odinger field theory, obtaining the Schr\"odinger…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
We construct a generalized controlled phased gate entangler for a multi-qubit state based on the geometrical structure of quantum systems. We also investigate relation between the generalized controlled phase construction of a quantum gate…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
As the effort to scale up existing quantum hardware proceeds, it becomes necessary to schedule quantum gates in a way that minimizes the number of operations. There are three constraints that have to be satisfied: the order or dependency of…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
The coherent states for a quantum particle on a M\"{o}bius strip are constructed and their relation with the natural phase space for fermionic fields is shown. The explicit comparison of the obtained states with previous works where the…
As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation…
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the…
The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor and driven to convergence by classical outer loop optimisation. The classical co-processor varies individual…
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…
We draw attention to some tune problems in constructions of the quantum-field operators for spins 1/2 and 1. They are related to the existence of negative-energy and acausal solutions of relativistic wave equations. Particular attention is…
We show how various mathematical formalisms, specifically the catastrophe formalism and group theory, aid in the study of relevant systems in quantum optics. We describe the phase transition of the Dicke model for a finite number N of…
The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a point-particle whose transition amplitudes correspond to the…
We propose and investigate an optical scheme for probabilistic implementation of an arbitrary single-mode quantum operation that can be expressed as a function of photon number operator. The scheme coherently combines multiple photon…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…