An analysis of the Spekkens toy theory with connection to Wootters discrete phase space

The toy model of Spekkens is a formalism which can partially describe quantum mechanics. The theory deals with the (epistemic) states of a spin-1/2 particle, or qubits and it is closely related to the discrete phase space formalism of Wootters and collaborators. One can apply the stabilizer formalism for finding similarities of these two models. Noting that MUB basis vectors are obtained by eigenstates of generalized Pauli operators, the MUB basis vectors are thus the set of stabilizer states. Galvao has characterized the set of states with non-negative Wigner function class; they form the convex hull of the stabilizer states used as the MUB basis vectors. By combining both approaches, one can show epistemic states that are analogous to the convex hull of the stabilizer states (used as basis vectors in the MUB set) always make valid nonmaximal knowledge epistemic states

Preparation and Measurement in Quantum Memory Models

Quantum Cognition has delivered a number of models for semantic memory, but to date these have tended to assume pure states and projective measurement. Here we relax these assumptions. A quantum inspired model of human word association experiments will be extended using a density matrix representation of human memory and a POVM based upon non-ideal measurements. Our formulation allows for a consideration of key terms like measurement and contextuality within a rigorous modern approach. This approach both provides new conceptual advances and suggests new experimental protocols.Comment: published in Journal of Mathematical Psycholog

A method of GC-MS analysis of serum metabolites

Metabolites are the intermediate and natural low molecular weight products of metabolic reactions that naturally occur within cells. Metabolomics is a post-genomics study that analyzes metabolic profile in all biological samples. Gas chromatography-mass spectrometry (GC-MS) is a powerful technique that detects volatile components. In this study we evaluate the metabolite profile of serum with a simple method for derivatization. The metabolic profile of serum taken from 16 rats was analyzed using GC-MS after protein precipitation with acetonitrile. Then, it was derivatized with a method requiring the less number and volume of materials. Acquisition chromatograms were pre-processed and analyzed using National Institute of Standards and Technology (NIST) library. We detected 35 metabolites with probability of >60% perfect match according to spectrum fragments analysis by NIST library.This study represents the metabolome profile of serum instead the change of metabolites that can be evaluated by a simple derivatization method

Generating mutually unbiased bases and discrete Wigner functions for three-qubit system

It is known that there exists 2N+ 1 mutually unbiased bases for N qubits system. Between the different MUB construction algorithms of the three-qubit case, we focus on Wootters method with discrete phase space that leads naturally to a complete set of 2N+ 1 mutually unbiased bases for the state space. We construct discrete Wigner function using mutually unbiased bases from the discrete phase space for three-qubit system by explicitly calculating the Wigner functions for exemplary three-qubit pure states such as the GHZ state, the W state and the embedded Bell state. We also highlight some quasi-probability characteristics of these entangled states

Generating mutually unbiased bases and discrete wigner function for three-qubit system

In this research, we construct Wigner functions on discrete phase spaces to represent quantum states for the special case of 3-qubit system. For determining this discrete phase space, we label the axes of phase space with finite field (Galois field) having eight elements. Based on this labeling, we developed a program in Matlab software for 3-qubit system which is also extendible for higher dimensions and more number of cubits. Results of this program lead to nine sets of parallel lines which is named as striations. Equivalently we label the horizontal and vertical axes of our phase space by quantum states of 3 cubits. This labeling and the use of suitable translation vectors on our striations produce the nine mutually unbiased bases for the Hilbert space. For calculating discrete Wigner function, we have determined appropriate quantum net Q(¸). There are 89 different choices for defining quantum nets but by using some unitary operators we reduce our choices to just eight different choices of quantum nets (eight similarity classes). We developed another program in Maple, which gives us eight different similarity classes of quantum nets. This program also gives us the phase-space point operators A® related to each class of quantum nets (these A® operators are used in calculating Wigner function). Based on one of these similarity classes, we calculated the Wigner functions for GHZ and W states and also an embedded Bell state which is not completely entangled. We discussed some of the properties of these Wigner function

Modelling the human mental lexicon using the formalism of quantum theory

Quantum cognition (QC) is a new interdisciplinary research field which applies the mathematical structure of quantum mechanics to explain and understand puzzling aspects of cognitive phenomena. This study focuses on improving the current QC models of language and memory. The researcher provides a better understanding of measurement and contextuality in processes involving language and memory. This will impact upon the field of QC, strengthening its position as a well-founded branch of mathematical psychology