File:Unambiguous quantum state discrimination - animation.gif
Original file (972 × 972 pixels, file size: 666 KB, MIME type: image/gif, looped, 55 frames, 6.5 s)
Captions
Summary
[edit]DescriptionUnambiguous quantum state discrimination - animation.gif |
English: Construction of measurement operators for unambiguous quantum state discrimination for the case of two pure equiprobable states. At first, vectors and are found that are orthogonal to the (orange) initial states and , respectively. From these, (blue) non-normalized vectors and are obtained, such that the POVM measurement operators for unambiguous discrimination read for . Using these the third operator is found , which corresponds to the inconclusive result and whose eigenvector is also shown. Čeština: Konstrukce měřicích operátorů pro jednoznačné rozlišení kvantových stavů pro případ dvou čistých stavů, které mají stejnou pravděpodobnost výskytu. Nejprve jsou nalezeny vektory a , které jsou po řadě ortogonální k počátečním (oranžovým) stavům a . Z těchto jsou zkonstruovány (modré) nenormalizované vektory a tak, že POVM měřicí operátory nabývají tvaru pro . S jejich pomocí je vytvořen třetí operátor , který odpovídá neprůkaznému výsledku a jehož vlastní vektor je také vyobrazen. |
Date | |
Source | Own work |
Author | JozumBjada |
Licensing
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- to remix – to adapt the work
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Source code
[edit]This animation was created using Wolfram language 12.0.0 for Microsoft Windows (64-bit) (April 6, 2019). The source code follows.
(* ::Package:: *)
(* ::Title:: *)
(*Unambiguous quantum state discrimination \[LongDash] animation*)
(* ::Input::Initialization:: *)
vec[char_,idx_,ang_,italic_:True,len_:1,off_:.15]:={Arrow[{{0,0},len AngleVector[ang ]}],Text[Style[ToString[Ket[Subscript[char,idx]],TraditionalForm],If[italic,Italic,Plain],30,FontFamily->"Times",Background->White],(1+off)AngleVector[ang],{0,0},AngleVector[ang]]}
(* ::Input::Initialization:: *)
grUSD[ang1_,ang2_,stage_]:=Module[{angavg=(ang1+ang2)/2,sceneAux1,sceneAux2,scenePro,prefac,prefacI,off},
prefac=1/Sqrt[1+Abs[Cos[ang2-ang1]]];
prefacI=prefac Sqrt[2Abs[Cos[ang2-ang1]]];
off=prefac-1+0.15;
sceneAux1={RGBColor[0.4, 0.4, 1.],Disk[{0,0},.12,{ang2,ang2-\[Pi]/2}],vec["x",1,ang2-\[Pi]/2]};
sceneAux2={RGBColor[0.4, 0.4, 1.],Disk[{0,0},.14,{ang1,ang1+\[Pi]/2}],vec["x",2,ang1+\[Pi]/2]};
scenePro={Blue,Disk[{0,0},.14,{ang1,ang1+\[Pi]/2}],Disk[{0,0},.12,{ang2,ang2-\[Pi]/2}],vec["e",2,ang1+\[Pi]/2,True,prefac,off],vec["e",1,ang2-\[Pi]/2,True,prefac,off],vec["e","?",(ang1+ang2)/2,True,prefacI,Min[prefacI-1+0.2,0.15]]};
Graphics[{
{Circle[{0,0},1]},
{Thickness[0.003],Dashing[0.02],Line[{{{-1,0},{1,0}},{{0,-1},{0,1}}}]},
{Thickness[0.005],Arrowheads[0.05],
{Orange,vec["\[Psi]",1,ang1,False],vec["\[Psi]",2,ang2,False]},
Switch[stage,
1,{},
2,{sceneAux1},
3,{sceneAux1,sceneAux2},
4,{scenePro}
],
{Black,PointSize[0.02],Point[{0,0}]}
}
},ImageSize->700,PlotRange->1.25,Background->None]
];
(* ::Input::Initialization:: *)
animationUSD[t_]:=Module[{tstages=0.5,ang1=0.2,ang2=0.8,t1,t2},
{t1,t2}=tstages+(1-tstages){3,6}/7;
Which[
t<tstages,grUSD[ang1,ang2,Quotient[Rescale[t,{0,tstages},{1,5}],1]],
tstages<=t<t1,grUSD[ang1+\[Pi]/6 UnitTriangle[Rescale[t,{tstages,t1},1.2{-1,1}]],ang2,4],
t1<=t<t2,grUSD[ang1,ang2+\[Pi]/4 UnitTriangle[Rescale[t,{t1,t2},1.2{-1,1}]],4],
t2<=t,grUSD[ang1,ang2,4]
]
]
(* ::Input::Initialization:: *)
exportAnimation[fun_,name_,resolution_:100]:=Module[{init,fin,seq,durs},
SetDirectory[NotebookDirectory[]];
init=fun/@{0,.2,.3,.4};
fin=Table[fun[t],{t,.5,1,.01}];
seq=Join[init,fin];
durs=Join[Table[1.5,Length[init]],Table[0.01,Length[fin]]];
Export[name<>".gif",seq,AnimationRepetitions->Infinity,"DisplayDurations"->durs,"TransparentColor"->Automatic,"ColorMapLength"->8,"QuantizationMethod"->"MedianCut",Dithering->None,ImageResolution->resolution]
]
(* ::Input:: *)
(*Manipulate[animationUSD[t],{t,0,1},SaveDefinitions->True]*)
(* ::Input:: *)
(*exportAnimation[animationUSD,"animUSD"]*)
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 18:33, 4 December 2021 | 972 × 972 (666 KB) | JozumBjada (talk | contribs) | Cross-wiki upload from cs.wikipedia.org |
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GIF file comment | Created with the Wolfram Language : www.wolfram.com |
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