File:Minimum error quantum state discrimination - animation.gif

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Original file (972 × 972 pixels, file size: 624 KB, MIME type: image/gif, looped, 55 frames, 6.5 s)

Captions

Captions

Minimum error quantum state discrimination for two pure states

Summary

[edit]
Description
English: Construction of measurement operators for minimum error quantum state discrimination for the case of two pure equiprobable states. At first, vectors and are found that form a new orthonormal basis in which (orange) initial states and are symmetrically situated around . By rotating this basis, another orthonormal basis is created that comprises (blue) vectors and . From these vectors one constructs projectors for .
Čeština: Konstrukce měřicích operátorů pro rozlišení kvantových stavů s minimální chybou pro případ dvou čistých stavů, které mají stejnou pravděpodobnost výskytu. Nejprve jsou nalezeny vektory a , které tvoří novou ortonormální bázi, v níž jsou počáteční (oranžové) stavy a souměrně rozmístěny kolem . Natočením této báze je vytvořena další ortonormální báze sestávající z (modrých) vektorů a . Z těchto vektorů jsou zkonstruovány projektory pro .
Date
Source Own work
Author JozumBjada

Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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:: *)
(*Minimum error 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:: *)
grME[ang1_,ang2_,stage_]:=Module[{angavg=(ang1+ang2)/2,sceneAng,sceneAux,scenePro},
sceneAng={Orange,Circle[{0,0},.5,{ang1,ang2}],Text[Style["\[Theta]",30,FontFamily->"Times"],.6AngleVector[(angavg+#)/2],{0,0},AngleVector[(angavg+#)/2]]&/@{ang1,ang2}};
sceneAux={RGBColor[0.4, 0.4, 1.],vec["x",1,angavg],vec["x",2,angavg-\[Pi]/2],Disk[{0,0},.12,{angavg,angavg-\[Pi]/2}]};
scenePro={Blue,vec["e",1,angavg-\[Pi]/4],vec["e",2,angavg+\[Pi]/4],Disk[{0,0},.1,{angavg+\[Pi]/4,angavg-\[Pi]/4}]};

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,{sceneAng,sceneAux},
3,{sceneAng,sceneAux,scenePro},
4,{scenePro}
],

{Black,PointSize[0.02],Point[{0,0}]}
}
},ImageSize->700,PlotRange->1.25,Background->None]
];


(* ::Input::Initialization:: *)
animationME[t_]:=Module[{tstages=0.5,ang1=0.2,ang2=0.8,t1,t2},
{t1,t2}=tstages+(1-tstages){3,6}/7;
Which[
t<tstages,grME[ang1,ang2,Quotient[Rescale[t,{0,tstages},{1,5}],1]],
tstages<=t<t1,grME[ang1+\[Pi]/6 UnitTriangle[Rescale[t,{tstages,t1},1.2{-1,1}]],ang2,4],
t1<=t<t2,grME[ang1,ang2+\[Pi]/4 UnitTriangle[Rescale[t,{t1,t2},1.2{-1,1}]],4],
t2<=t,grME[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[animationME[t],{t,0,1},SaveDefinitions->True]*)


(* ::Input:: *)
(*exportAnimation[animationME,"animME"]*)

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Date/TimeThumbnailDimensionsUserComment
current18:37, 4 December 2021Thumbnail for version as of 18:37, 4 December 2021972 × 972 (624 KB)JozumBjada (talk | contribs)Cross-wiki upload from cs.wikipedia.org

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