Introduction: Individuality, Distinguishability, and (Non-)Entanglement

Statistical inference, distinguishability of quantum states, and quantum entanglement

We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states ~or two classes of quantum states! described by density matrices. We extend this notion to describe the amount of entanglement between two quantum systems from a statistical point of view. Our measure is independent of the number of entangled...

Entanglement Entropy and Quantum Field Theory: a Non-technical Introduction

There has been considerable interest in formulating measures of entanglement and applying them to extended quantum systems with many degrees of freedom, such as quantum spin chains, especially close to a quantum phase transition (see, e.g., several other reports in these proceedings). One of these measures is entanglement entropy. Suppose the whole system is in a pure quantum state |Ψ〉, with de...

Aneuploidy Causes Non-genetic Individuality

Phenotypic variability is a hallmark of diseases involving chromosome gains and losses, such as Down syndrome and cancer. Allelic variances have been thought to be the sole cause of this heterogeneity. Here, we systematically examine the consequences of gaining and losing single or multiple chromosomes to show that the aneuploid state causes non-genetic phenotypic variability. Yeast cell popula...

The Mathematics of Non-Individuality

“The development of the foundations of physics in the twentieth century has taught us a serious lesson. Creating and understanding these foundations turned out to have very little to do with the epistemological abstractions which were of such importance to the twentieth century critics of the foundations of mathematics: finiteness, consistency, constructibility, and, in general, the Cartesian n...

An introduction to entanglement measures