The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field

Generally, quantum states are abstract states that carry probabilistic information of position and momentum of any dynamical physical quantity in quantum system. E.P.Wigner (1932) had introduced a function that can determine the combination of position and momentum simultaneously, and it was the starting point to define a phase space probability distribution for a quantum mechanical system using density matrix formalism. This function named as Wigner Function. Recently, Wootters (1987) has developed a discrete phase space analogous to Wigner’s ideas. The space is based on Galois field or finite field. The geometry of the space is represented by N ´ N point, where N denoted the number of elements in the field and it must be a prime or a power of a prime numbers. In this work, we study the simplest way to compute the binary operations in finite field in order to form such a discrete space. We developed a program using Mathematica software to solve the binary operation in the finite field for the case of 3-qubit and 2-qutrit systems. The program developed should also be extendible for the higher number of qubit and qutrit. Each state is defined by a line aq + bp = c and parallel lines give equivalent states. The results show that, there are 9 set of parallel lines for the 3-qubit system and 10 sets of parallel lines for 2-qutrit system. These complete set of parallel lines called a ‘striation’

Preparation of highly water dispersible functional graphene/silver nanocomposite for the detection of melamine

A stable aqueous suspension of a functional graphene/silver (FG/Ag) nanocomposite was prepared by an environmentally friendly hydrothermal method. The precursor, functional graphene oxide (FGO), was prepared by covalent functionalisation of graphene oxide (GO) with a hydrophilic organosilane, N-(trimethoxysilylpropyl) ethylenediaminetriacetic acid trisodium salt (TETA). The attachment of functional groups on the GO surface maintained the aqueous stability of the FG/Ag nanocomposite even after the hydrothermal reduction. Field emission scanning electron microscopy (FESEM) images illustrated a uniform distribution of Ag nanoparticles on the FG surface. The surface enhanced Raman spectroscopy (SERS) activity of the nanocomposite was investigated using p-aminothiophenol (p-ATP) and melamine which can be detected as low as 2 × 10−8 and 2 × 10−7 M, respectively. The impressive water stability and the high SERS sensitivity of the FG/Ag nanocomposite make it a suitable substrate for trace analysis of a variety of drugs, additives or organic contaminants in water. The nanocomposite also showed a positive inhibition effect against the growth of Escherichia coli bacteria, eliminating the possibility of bacterial contamination of the sensor, thus prolonging the shelf-life of the sensing device

No-Go theorems and quantization

In this review, we would like to highlight the three known no-go theorems in quantum physics in relation to the process of quantization that maps classical observables to quantum ones. The quantization approach considered is a mixture of Isham’s group-theoretic quantization and geometric quantization with special emphasis on underlying compact phase space geometry of spheres. The first is Groenewold-van Hove theorem that states the obstruction of quantizing the full algebra of observables and in the sphere case, only limited to the spin observables plus the constant functions. The other two are theorems of Bell and Kochen-Specker stating that the only hidden variable theories allowed by quantum physics are nonlocal and contextual ones. We give simple examples of these no-go theorems and indicate some interesting problems arising from them for the field of quantizatio