---
title: "Entanglement between Two Coupled Two-Level Systems"
author: "Kwan-yuet Ho, Ph.D."
date: "April 9, 2018"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Entanglement between Two Coupled Two-Level Systems}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

```{r loading library, include=FALSE}
library(RQEntangle)
```

## Quantum Entanglement of Discrete Systems

Define the coupled two-level systems:

```{r singlet}
singlet<- matrix(c(0, sqrt(0.7), sqrt(0.3), 0), byrow = TRUE, nrow = 2)
```

## Schmidt Decompostions

Then run the Schmidt decompotions:

```{r run_decompose, echo=FALSE}
modes<- schmidt.decompose(singlet)
```

We can easily print the modes:

```{r display_modes}
modes
```

And their corresponding entanglement entropy:

```{r entropy}
entanglement.entropy(modes)
```