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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

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