Skeda:Entanglement vs classical correlation abstract picture.gif
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Entanglement_vs_classical_correlation_abstract_picture.gif ((përmasa 562 × 341 px, madhësia skedës: 1,49 MB, lloji MIME: image/gif), kthyer, 150 korniza, 30 s)
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Përmbledhje
| Përshkrimi |
English: The comparison of the quantum and classical correlations. The ring on the left corresponds to the singlet state of polarization of two photons, which exhibits perfect correlations in any linearly polarized measurement basis. Either the magenta detectors simultaneously fire, or both orange detectors fire. The ring on the right corresponds to the dephased singlet state , which displays only classical correlations that are perfect in the H/V basis but vanishing in the D/A basis. The latter is manifested by events when one photon activates the magenta detector whereas the other photon activates the orange detector. Čeština: Porovnání kvantového provázání a klasické korelace. Kotouč nalevo odpovídá singletovému stavu polarizace dvou fotonů, jenž vykazuje dokonalé korelace ve všech lineárně polarizovaných měřicích bázích. Buď se aktivují oba fialové detektory, nebo oba oranžové detektory. Kotouč napravo odpovídá defázovanému singletovému stavu , který vykazuje pouze klasické korelace, jež jsou dokonalé v bázi H/V, ale vytrácejí se v bázi D/A. Absence korelací v této bázi se projevuje tak, že v některých případech jeden foton aktivuje fialový detektor, zatímco foton druhý aktivuje oranžový detektor. |
| Data | |
| Burimi | Punë e juaja |
| Autori | JozumBjada |
Licencim
Unë, krijuesi i kësaj pune, e publikoj këtu në bazë të licensës në vijim:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
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Source code
This animation was created using Wolfram language 12.0.0 for Microsoft Windows (64-bit) (April 6, 2019). Source code follows.
(* ::Package:: *)
(* ::Title:: *)
(*Rotating disks*)
(* ::Code:: *)
(*"Created in Wolfram language - version: 12.0.0 for Microsoft Windows (64-bit) (April 6, 2019)"*)
(* ::Chapter:: *)
(*Photon sequences*)
(* ::Input::Initialization:: *)
ClearAll[probsEnt]
(*probability of detection of an entangled photon pair in one of four \
outputs, when detectors are rotated through angle \[Theta]*)
probsEnt[\[Theta]_] := {0.5, 0, 0, 0.5}
(* ::Input::Initialization:: *)
ClearAll[probsSep]
(*probability of detection of a separable photon pair in one of four \
outputs, when detectors are rotated through angle \[Theta]*)
probsSep[\[Theta]_] := {1/8. (3 + Cos[4 \[Theta]]),Cos[\[Theta]]^2 Sin[\[Theta]]^2, Cos[\[Theta]]^2 Sin[\[Theta]]^2,1/8. (3 + Cos[4 \[Theta]])}
(* ::Input::Initialization:: *)
ClearAll[generateSinglePhotonSequence]
(*generate a train of photons according to probabilities probs*)
generateSinglePhotonSequence[probs_, numOfPairs_] :=
Module[{samples,seqPh},
\[NonBreakingSpace]\[NonBreakingSpace]samples= Prepend[RandomChoice[probs->{{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}},numOfPairs], {0, 0, 0, 0}];
seqPh=Rest[samples]/.{{0,0,0,1}->{True,True},{0,0,1,0}->{True,False},{0,1,0,0}->{False,True},{1,0,0,0}->{False,False}};
AppendTo[seqPh, {False, False}]
]
(* ::Chapter:: *)
(*Images*)
(* ::Input:: *)
(*(*figures in the animation are made in Blender; here simple substitutes are generated in Mathematica*)*)
(* ::Input::Initialization:: *)
{radius,width}={.9,.6};
rect=Rectangle[{-.1,radius-width},{.1,radius}];
(* ::Input::Initialization:: *)
{grayCol,redCol,greenCol}={GrayLevel[.7],Purple(*Red*),Orange(*Green*)};
brownCol=Blend[{redCol,greenCol},.5];
(* ::Input::Initialization:: *)
thickness=Thickness[.1];
connRR=Graphics[{Lighter[redCol],thickness,Line[{{0,-1},{0,1}}]}];
connRG=Graphics[{brownCol,thickness,Circle[.7{-1,1},.7,{3\[Pi]/2.,2.\[Pi]}]},PlotRange->1];
connGR=Graphics[{brownCol,thickness,Circle[.7{1,-1},.7,{\[Pi]/2.,\[Pi]}]},PlotRange->1];
connGG=Graphics[{Lighter[greenCol],thickness,Line[{{-1,0},{1,0}}]}];
(* ::Input::Initialization:: *)
ClearAll[imgDisk]
imgDisk[col1_:grayCol,col2_:grayCol,col3_:grayCol,col4_:grayCol,conn_:Graphics@{}]:=Module[{gr},
gr=Graphics[{
{Inset[conn,Center,Center,1]},
{GrayLevel[.55],
Annulus[{0,0},{radius-.6width,radius},{0,\[Pi]/2.}],
Annulus[{0,0},{radius-.6width,radius},{\[Pi],3.\[Pi]/2}]
},
{col1,Rotate[rect,0\[Pi]/2,{0,0}]},
{col2,Rotate[rect,1\[Pi]/2,{0,0}]},
{col3,Rotate[rect,2\[Pi]/2,{0,0}]},
{col4,Rotate[rect,3\[Pi]/2,{0,0}]}
},PlotRange->1];
Rasterize[gr,Background->None,ImageResolution->50]
]
(* ::Input::Initialization:: *)
(*images themselves stored in variable imgs*)
imgEmpty=imgDisk[];
imgs[False,False]=imgDisk[redCol,grayCol,redCol,grayCol,connRR];
imgs[False,True]=imgDisk[redCol,greenCol,grayCol,grayCol,connRG];
imgs[True,False]=imgDisk[grayCol,grayCol,redCol,greenCol,connGR];
imgs[True,True]=imgDisk[grayCol,greenCol,grayCol,greenCol,connGG];
(* ::Input:: *)
(*(*Append[BooleanTable[imgs[i,j],{i,j}],imgEmpty]*)*)
(* ::Chapter:: *)
(*Scene*)
(* ::Input::Initialization:: *)
ClearAll[imgFun]
imgFun[ang_,flash_,cols_]:=Module[{img},
img=If[flash,imgs@@cols,imgEmpty];
Graphics[Inset[img,Center,Center,2,AngleVector@ang],PlotRange->1,ImageSize->400]
]
(* ::Input:: *)
(*(*Manipulate[imgFun[ang,flash,{col1,col2}],{ang,0,2\[Pi]},{flash,{True,False}},{col1,{True,False}},{col2,{True,False}},Deployed->True]*)*)
(* ::Chapter:: *)
(*Animation*)
(* ::Input::Initialization:: *)
ClearAll[generateAnimation]
generateAnimation[numShots_:4]:=Module[{seqsEnt,seqsSep,animationFun,shotDuration=1./numShots,fireRat=.7,
numPhotonsPerShot=15,fontFamily="Adobe Devanagari",lab1,lab2,labelCol=GrayLevel[0.29],angleFun},
seqsEnt = generateSinglePhotonSequence[probsEnt[#], numPhotonsPerShot] & /@ Most@Subdivide[0.,(*2.*)\[Pi],numShots];
seqsSep = generateSinglePhotonSequence[probsSep[#], numPhotonsPerShot] & /@ Most@Subdivide[0.,(*2.*)\[Pi],numShots];
lab1=Text[Style[Ket["\[Psi]"],Bold,labelCol,50,FontFamily->fontFamily]];
lab2=Text[Style["\[Rho]",Bold,labelCol,60,FontFamily->fontFamily]];
animationFun[ratIn_]:=Module[{rat=ratIn,ang,flash,idx,idx2=1,rat2,len},
rat=Clip[rat,{0,1.-1*^-6}];
{rat,idx}={numShots Mod[rat, 1/numShots], Floor[rat numShots] + 1};
ang=(*2*)\[Pi] shotDuration (idx-1);
flash=(rat<fireRat);
If[flash,
idx2= Floor[rat numPhotonsPerShot/fireRat] + 1;
,
ang+=(*2*)\[Pi] shotDuration Rescale[rat,{fireRat,1.},{0.,1}];
];
Grid[{{imgFun[ang,flash,seqsEnt[[idx,idx2]]],imgFun[ang,flash,seqsSep[[idx,idx2]]]},{lab1,lab2}}]
];
animationFun
]
(* ::Chapter:: *)
(*Rasterization*)
(* ::Input::Initialization:: *)
ClearAll[rasterizeFrameSequence]
rasterizeFrameSequence[fun_, numOfFrames_ : 10, imgResolution_ : 70] :=
Module[{time, frames},
{time, frames} = AbsoluteTiming[
Map[
Rasterize[fun[#], Background->None,ImageResolution->imgResolution]&,
Subdivide[0, 1., numOfFrames - 1]
]
];
Print["execution time: ",DateString[time, {"Minute", " m ", "Second", " s"}]];
Print["size: ", ByteCount[frames]/1024/1024., " MB"];
frames
]
(* ::Chapter:: *)
(*Export*)
(* ::Input::Initialization:: *)
filename = "test2.gif";
anim = generateAnimation[4];
(* ::Input::Initialization:: *)
frames =rasterizeFrameSequence[anim,30,50];
(* ::Input:: *)
(*(*ListAnimate[frames, AnimationRate -> 3.]*)*)
(* ::Input::Initialization:: *)
SetDirectory[NotebookDirectory[]]
Export[filename,frames,
"DisplayDurations" -> 0.2,
"ColorMapLength" -> 256/2,
AnimationRepetitions -> Infinity,
Dithering -> None]
Historiku skedës
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| Data/Koha | Miniaturë | Përmasat | Përdoruesi | Koment | |
|---|---|---|---|---|---|
| e tanishme | 9 dhjetor 2020 21:21 | | 562 × 341 (1,49 MB) | JozumBjada | Cross-wiki upload from cs.wikipedia.org |
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