\relax \providecommand\hyper@newdestlabel[2]{} \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined \global\let\oldcontentsline\contentsline \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} \global\let\oldnewlabel\newlabel \gdef\newlabel#1#2{\newlabelxx{#1}#2} \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} \AtEndDocument{\ifx\hyper@anchor\@undefined \let\contentsline\oldcontentsline \let\newlabel\oldnewlabel \fi} \fi} \global\let\hyper@last\relax \gdef\HyperFirstAtBeginDocument#1{#1} \providecommand*\HyPL@Entry[1]{} \bibstyle{unsrt} \bibdata{references/reference} \bibcite{Metropolis:1987}{1} \bibcite{GALTON1890}{2} \bibcite{INTEL}{3} \bibcite{gude1985}{4} \bibcite{figotin2004random}{5} \bibcite{Stipcevic:07}{6} \bibcite{kwiat:09}{7} \bibcite{Fuerst2010}{8} \bibcite{Wayne:10}{9} \bibcite{Wahl2011}{10} \bibcite{Nie2014}{11} \bibcite{Ren2011}{12} \bibcite{Frauchiger2013}{13} \bibcite{Williams2010}{14} \bibcite{Kanter2009}{15} \bibcite{Sanguinetti2014}{16} \bibcite{Nie2015}{17} \bibcite{Qi2010}{18} \bibcite{Xu2012}{19} \bibcite{Abellan2014}{20} \bibcite{PhysRevLett.115.250403}{21} \bibcite{Yuan2014}{22} \bibcite{Zhou2015}{23} \bibcite{Jofre2011}{24} \HyPL@Entry{0<>} \bibcite{Gabriel2010}{25} \bibcite{Syed2011}{26} \bibcite{Shen2010}{27} \bibcite{Shi2016}{28} \bibcite{Krawczyk1994}{29} \bibcite{NISTtestsuite}{30} \bibcite{dieharder}{31} \citation{Metropolis:1987} \citation{GALTON1890,INTEL} \citation{gude1985,figotin2004random} \citation{Stipcevic:07,kwiat:09,Fuerst2010,Wayne:10,Wahl2011,Nie2014,Ren2011} \citation{Frauchiger2013} \citation{Williams2010} \citation{Kanter2009,Sanguinetti2014} \citation{Nie2015,Qi2010,Xu2012,Abellan2014,PhysRevLett.115.250403,Yuan2014,Zhou2015,Jofre2011} \citation{Gabriel2010,Syed2011,Shen2010,Shi2016} \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}} \@writefile{toc}{\contentsline {section}{\numberline {2}Optical homodyne measurement by wavefront splitting}{3}{section.2}} \newlabel{eq:beam_splitter_matrix}{{1}{3}{Optical homodyne measurement by wavefront splitting}{equation.2.1}{}} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Splitting mechanisms of the two different implementations. A conventional balanced homodyne detection scheme (a) relies on the beam splitter matrix relation between the input modes $a$, $b$ and the output modes $c$, $d$. In the wavefront-splitting implementation (b), this is replaced by spatially splitting the elliptical transverse mode of a laser beam.}}{3}{figure.1}} \newlabel{fig:splitting}{{1}{3}{Splitting mechanisms of the two different implementations. A conventional balanced homodyne detection scheme (a) relies on the beam splitter matrix relation between the input modes $a$, $b$ and the output modes $c$, $d$. In the wavefront-splitting implementation (b), this is replaced by spatially splitting the elliptical transverse mode of a laser beam}{figure.1}{}} \newlabel{eq:elliptical}{{2}{3}{Optical homodyne measurement by wavefront splitting}{equation.2.2}{}} \citation{Gabriel2010,Syed2011,Shen2010,Shi2016} \newlabel{eq:half_elliptical}{{3}{4}{Optical homodyne measurement by wavefront splitting}{equation.2.3}{}} \newlabel{eq:mixing}{{4}{4}{Optical homodyne measurement by wavefront splitting}{equation.2.4}{}} \@writefile{toc}{\contentsline {section}{\numberline {3}Implementation}{4}{section.3}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Amplified noise levels measured into a resolution bandwidth $B = 60$ kHz. The red trace is the amplified photocurrent difference $i_1 - i_2$, with equal optical power impinging on both photodiodes. The blue trace corresponds to the electronic noise which is measured without any optical input.}}{4}{figure.2}} \newlabel{fig:schematic}{{2}{4}{Amplified noise levels measured into a resolution bandwidth $B = 60$ kHz. The red trace is the amplified photocurrent difference $i_1 - i_2$, with equal optical power impinging on both photodiodes. The blue trace corresponds to the electronic noise which is measured without any optical input}{figure.2}{}} \citation{Shi2016} \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Amplified noise levels measured into a resolution bandwidth $B = 100$ kHz. The red trace is the amplified photocurrent difference $i_1 - i_2$, with equal optical power impinging on both photodiodes. The blue trace corresponds to the electronic noise which is measured without any optical input.}}{5}{figure.3}} \newlabel{fig:spectrum}{{3}{5}{Amplified noise levels measured into a resolution bandwidth $B = 100$ kHz. The red trace is the amplified photocurrent difference $i_1 - i_2$, with equal optical power impinging on both photodiodes. The blue trace corresponds to the electronic noise which is measured without any optical input}{figure.3}{}} \@writefile{toc}{\contentsline {section}{\numberline {4}Entropy estimation and randomness extraction}{5}{section.4}} \citation{Shi2016} \citation{Krawczyk1994} \citation{NISTtestsuite} \citation{dieharder} \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Autocorrelation of the total noise signal sampled at 200\tmspace +\thinmuskip {.1667em}MHz, computed over $10^7$ samples (solid line), compared with the $2\sigma $ confidence level (dashed line).}}{6}{figure.4}} \newlabel{fig:autocorrelation}{{4}{6}{Autocorrelation of the total noise signal sampled at 200\,MHz, computed over $10^7$ samples (solid line), compared with the $2\sigma $ confidence level (dashed line)}{figure.4}{}} \newlabel{eq:conditional}{{5}{6}{Entropy estimation and randomness extraction}{equation.4.5}{}} \newlabel{eq:shannon}{{6}{6}{Entropy estimation and randomness extraction}{equation.4.6}{}} \newlabel{eq:min_entropy}{{7}{6}{Entropy estimation and randomness extraction}{equation.4.7}{}} \citation{Nie2015,Williams2010,Xu2012} \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Probability distribution of the measured total noise with variance ${{\sigma }_t}^2$ (a), electronic noise with variance ${{\sigma }_e}^2$ (b), and the estimated quantum noise with variance ${{\sigma }_q}^2$ (c). The filled areas in (a), (b) show the actual measurements over $10^7$ samples, the solid lines fit to Gaussian distributions.}}{7}{figure.5}} \newlabel{fig:distribution}{{5}{7}{Probability distribution of the measured total noise with variance ${{\sigma }_t}^2$ (a), electronic noise with variance ${{\sigma }_e}^2$ (b), and the estimated quantum noise with variance ${{\sigma }_q}^2$ (c). The filled areas in (a), (b) show the actual measurements over $10^7$ samples, the solid lines fit to Gaussian distributions}{figure.5}{}} \@writefile{toc}{\contentsline {section}{\numberline {5}Performance}{7}{section.5}} \@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion}{7}{section.6}}