Correction to: Scientific Reports https://doi.org/10.1038/s41598-018-19634-1, published online 23 January 2018

The previous version of this Article contained errors in the Introduction under the subheading ‘Twin beam and its transformation on a beam splitter’,

\({\boldsymbol{\lambda }}\,={(1,{{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{2},{{\rm{\lambda }}}_{1}{{\rm{\lambda }}}_{2})}^{{\rm{T}}}\)

now reads:

\({\boldsymbol{\lambda }}\,\equiv {(1,{{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{2},{{\rm{\lambda }}}_{1}{{\rm{\lambda }}}_{2})}^{{\rm{T}}}\)

Additionally, the Publisher Correction published on 30th April 2018 contains errors.

“This Article contains errors in Equation 18.

\({{\rm{G}}}_{{\mathscr{N}}}({{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{1})=\frac{1}{{[{{\rm{\lambda }}}^{{\rm{T}}}{\bf{K}}{\rm{\lambda }}]}^{1/2}}\)

and \({\rm{\lambda }}\,\equiv {(1,{{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{2},{{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{2},)}^{{\rm{T}}}\).

should read:

\({{\rm{G}}}_{{\mathscr{N}}}({{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{1})=\frac{1}{{{[{\rm{\lambda }}}^{{\rm{T}}}{\bf{K}}{\rm{\lambda }}]}^{1/2}}\)

and \({\rm{\lambda }}\,\equiv {(1,{{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{2},{{\rm{\lambda }}}_{1}{{\rm{\lambda }}}_{2})}^{{\rm{T}}}\).”

should read:

“The original version of this Article contained errors in Equation 18.

\({{\rm{G}}}_{{\mathscr{N}}}({{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{2})=\frac{1}{{[{{\boldsymbol{\lambda }}}^{{\rm{T}}}{\bf{K}}{\boldsymbol{\lambda }}]}^{1/2}}\)

and \({\boldsymbol{\lambda }}\,={(1,{{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{2},{{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{2},)}^{{\rm{T}}}\).

now reads:

\({{\rm{G}}}_{{\mathscr{N}}}({\lambda }_{1},{\lambda }_{2})=\frac{1}{{[{{\boldsymbol{\lambda }}}^{{\rm{T}}}{\bf{K}}{\boldsymbol{\lambda }}]}^{1/2}}\)

and \({\boldsymbol{\lambda }}\,\equiv {(1,{{\rm{\lambda }}}_{1},{{\rm{\lambda }}}_{2},{{\rm{\lambda }}}_{1}{{\rm{\lambda }}}_{2})}^{{\rm{T}}}\).”