Author: Kwan-yuet Ho, Ph.D.

# Entanglement between Two Coupled Two-Level Systems

#### Kwan-yuet Ho, Ph.D.

#### April 9, 2018

## Quantum Entanglement of Discrete Systems

Define the coupled two-level systems:

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

## Schmidt Decompostions

Then run the Schmidt decompotions:

We can easily print the modes:

    modes

    ## [[1]]
    ## [[1]]$eigenvalue
    ## [1] 0.7
    ##
    ## [[1]]$sys1vector
    ## [1] -1  0
    ##
    ## [[1]]$sys2vector
    ## [1]  0 -1
    ##
    ##
    ## [[2]]
    ## [[2]]$eigenvalue
    ## [1] 0.3
    ##
    ## [[2]]$sys1vector
    ## [1]  0 -1
    ##
    ## [[2]]$sys2vector
    ## [1] -1  0

And their corresponding entanglement entropy:

    entanglement.entropy(modes)

    ## [1] 0.6108643