Typing Quantum Superpositions and Measurement

Christian DE RONDE

Yuan Xu

In this study, we use a decoherence-based measure of interference to quantify the effective degree of quantum superposition. We show that a type of measure of the effective degree of quantum superposition can be considered from a unified theoretical framework. We use three decoherence processes to define a corresponding decoherence-based measure of quantum superposition, including amplitude damping, phase damping and quantum Brownian motion. With these definitions, we compare the effective degree of quantum superposition achieved for the different experiments. We also investigate the effective degree of quantum superposition prepared from a mixed state through the reservoir engineering technique.

Alejandro Díaz-Caro, Gilles Dowek B

We study a first-order, purely functional quantum extension of lambda calculus, that is, an extension of lambda calculus to express some quantum features, where the quantum memory is abstracted out. This calculus is a typed extension of the first-order linear-algebraic lambda-calculus. The type is linear on superpositions, so to forbid from cloning them, while allows to clone basis vectors.

Belal Ehsan Baaquie

Chang-Woo Lee, Hyunseok Jeong

Based on phase-space structures of quantum states, we propose a novel measure to quantify macroscopic quantum superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a harmonious manner: the degree of quantum coherence and the effective size of the physical system that involves the superposition. It enjoys remarkably good analytical and algebraic properties. It turns out to be the most general and inclusive measure ever proposed that it can be applied to any types of multipartite states and mixed states represented in phase space.

Mark P. Silverman