| Type: | Package |
| Title: | Quantum Entanglement of Bipartite System |
| Version: | 0.1.3 |
| Description: | It computes the Schmidt decomposition of bipartite quantum systems, discrete or continuous, and their respective entanglement metrics. See Artur Ekert, Peter L. Knight (1995) <doi:10.1119/1.17904> for more details. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| LazyData: | true |
| Depends: | R(≥ 2.15.1), itertools(≥ 0.1-3), iterators |
| Suggests: | knitr, rmarkdown, dplyr, ggplot2, roxygen2 |
| RoxygenNote: | 6.1.0 |
| URL: | https://github.com/stephenhky/RQEntangle |
| BugReports: | https://github.com/stephenhky/RQEntangle/issues |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2019-01-03 23:35:19 UTC; stephenhky |
| Author: | Kwan-Yuet Ho [aut, cre] |
| Maintainer: | Kwan-Yuet Ho <stephenhky@yahoo.com.hk> |
| Repository: | CRAN |
| Date/Publication: | 2019-01-04 10:40:08 UTC |
Interpolate values of functions.
Description
Interpolate values of functions.
Usage
continuous.function.interpolate(xarr, yarr, x)
Arguments
xarr |
a vector of x (sorted) |
yarr |
a vector of y |
x |
given value of x |
Value
interpolated value of y
Perform a continuous Schmidt decomposition
Description
Perform a continuous Schmidt decomposition
Usage
continuous.schmidt.decompose(bifunc, x1lo, x1hi, x2lo, x2hi, nbx1 = 100,
nbx2 = 100, keep = min(10, nbx1, nbx2))
Arguments
bifunc |
bipartitite continuous wavefunction |
x1lo |
lower limit of |
x1hi |
upper limit of |
x2lo |
lower limit of |
x2hi |
upper limit of |
nbx1 |
number of discretized x1 (default: 100) |
nbx2 |
number of discretized x2 (default: 100) |
keep |
number of Schmidt modes to keep (default: minimum of 10, |
Value
Schmidt modes, including the eigenvalues, and the lambda interpolated function of the Schmidt modes
Examples
coupled.harm.fcn<- function(x1,x2) exp(-((0.5*(x1+x2))**2))*exp(-(x1-x2)**2)*sqrt(2./pi)
continuous.schmidt.decompose(coupled.harm.fcn, -10, 10, -10, 10)
Making a discretized tensor for a continuous function
Description
Making a discretized tensor for a continuous function
Usage
discretize.continuous.bipartitefunc(bifunc, x1lo, x1hi, x2lo, x2hi,
nbx1 = 100, nbx2 = 100)
Arguments
bifunc |
bipartitite continuous wavefunction |
x1lo |
lower limit of |
x1hi |
upper limit of |
x2lo |
lower limit of |
x2hi |
upper limit of |
nbx1 |
number of discretized x1 (default: 100) |
nbx2 |
number of discretized x2 (default: 100) |
Value
discretized tensor for Schmidt decomposition
Calculate the entanglement entropy given the calculate Schmidt modes.
Description
Calculate the entanglement entropy given the calculate Schmidt modes.
Usage
entanglement.entropy(modes)
Arguments
modes |
Schmidt modes |
Value
entanglement entropy
Examples
singlet<- matrix(c(0, sqrt(0.7), sqrt(0.3), 0), byrow = TRUE, nrow = 2)
modes<- schmidt.decompose(singlet)
entanglement.entropy(modes)
Lambda function of the interpolated continous function.
Description
Lambda function of the interpolated continous function.
Usage
interpolated.continuous.function(xarr, yarr)
Arguments
xarr |
a vector of x (sorted) |
yarr |
a vector of y |
Value
interpolated lambda function
Calculate the negativity given the calculate Schmidt modes.
Description
Calculate the negativity given the calculate Schmidt modes.
Usage
negativity(modes)
Arguments
modes |
Schmidt modes |
Value
negativity
Examples
singlet<- matrix(c(0, sqrt(0.7), sqrt(0.3), 0), byrow = TRUE, nrow = 2)
modes<- schmidt.decompose(singlet)
negativity(modes)
Calculate the participation ratio given the calculate Schmidt modes.
Description
Calculate the participation ratio given the calculate Schmidt modes.
Usage
participation.ratio(modes)
Arguments
modes |
Schmidt modes |
Value
participation ratio
Examples
singlet<- matrix(c(0, sqrt(0.7), sqrt(0.3), 0), byrow = TRUE, nrow = 2)
modes<- schmidt.decompose(singlet)
participation.ratio(modes)
Get reduced density matrix
Description
Get reduced density matrix
Usage
reduced.denmat(bipartite.qubits, keep.dim = 1)
Arguments
bipartite.qubits |
tensor of bipartite systems |
keep.dim |
dimension to keep (default: 1) |
Value
reduced density matrix
Examples
singlet<- matrix(c(0, sqrt(0.7), sqrt(0.3), 0), byrow = TRUE, nrow = 2)
reduced.denmat(singlet)
Perform Schmidt decomposition
Description
Perform Schmidt decomposition
Usage
schmidt.decompose(bipartite.qubits)
Arguments
bipartite.qubits |
tensor of bipartite systems |
Value
Schmidt modes, including the eigenvalues, and eigenvectors of both subsystems of the modes
Examples
singlet<- matrix(c(0, sqrt(0.7), sqrt(0.3), 0), byrow = TRUE, nrow = 2)
schmidt.decompose(singlet)