-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathKirkwood-Dirac Distribution.nb
15852 lines (15786 loc) · 899 KB
/
Kirkwood-Dirac Distribution.nb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 13.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 920704, 15844]
NotebookOptionsPosition[ 915534, 15751]
NotebookOutlinePosition[ 916155, 15773]
CellTagsIndexPosition[ 916112, 15770]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["\<\
Conditions tighter than noncommutation needed for nonclassicality\
\>", "Title",
CellChangeTimes->{{3.868494374102778*^9, 3.868494503859474*^9}, {
3.8684946742546597`*^9, 3.868494931688478*^9}, {3.868495039765729*^9,
3.868495045182228*^9}, {3.868495079303303*^9, 3.868495155580761*^9}, {
3.8684952248215647`*^9, 3.868495275998229*^9}, {3.8684954635360928`*^9,
3.868495597424655*^9}, {3.868495670392705*^9, 3.868495689345199*^9}, {
3.868495733272902*^9, 3.868495763716963*^9}, {3.868495818951961*^9,
3.8684958522908897`*^9}, {3.868495890928649*^9, 3.8684958996674147`*^9}, {
3.868495996473661*^9, 3.868496016963809*^9}, {3.8685102383824997`*^9,
3.8685102669075127`*^9}, {3.8685112642136*^9, 3.86851126863762*^9}, {
3.868625081707698*^9, 3.8686250821835012`*^9}, {3.868625309172742*^9,
3.868625320892551*^9}, {3.8686692386139708`*^9, 3.868669284062008*^9},
3.8686705917881947`*^9},
Background->GrayLevel[
0.85],ExpressionUUID->"87103a5b-1b0c-486d-a6fb-a4bef04e43f0"],
Cell["\<\
SUPPLEMENTARY MATERIAL
Appendix A: Example KD distributions
Calculations\
\>", "Subtitle",
CellChangeTimes->{{3.868494374102778*^9, 3.868494503859474*^9}, {
3.8684946742546597`*^9, 3.868494931688478*^9}, {3.868495039765729*^9,
3.868495045182228*^9}, {3.868495079303303*^9, 3.868495155580761*^9}, {
3.8684952248215647`*^9, 3.868495275998229*^9}, {3.8684954635360928`*^9,
3.868495597424655*^9}, {3.868495670392705*^9, 3.868495689345199*^9}, {
3.868495733272902*^9, 3.868495763716963*^9}, {3.868495818951961*^9,
3.8684958522908897`*^9}, {3.868495890928649*^9, 3.8684958996674147`*^9}, {
3.868495996473661*^9, 3.868496016963809*^9}, {3.8685102383824997`*^9,
3.8685102669075127`*^9}, {3.8685112642136*^9, 3.86851126863762*^9}, {
3.868625081707698*^9, 3.8686250821835012`*^9}, {3.868625309172742*^9,
3.868625320892551*^9}, 3.8686692386139708`*^9, {3.868669289736228*^9,
3.868669328071748*^9}, {3.8686705777418957`*^9, 3.86867058972232*^9}, {
3.8686731552991877`*^9,
3.868673161030785*^9}},ExpressionUUID->"a1fcd143-fe67-4587-bba3-\
9ae3590c48de"],
Cell["\<\
widely used for representing complex and negative quasiprobabilities, \
although in many cases there might be just a few complex or negative values\
\>", "Subitem",
GeneratedCell->False,
CellAutoOverwrite->False,
CellChangeTimes->{{3.5143080983732347`*^9, 3.514308102892667*^9}, {
3.514308469349834*^9, 3.5143084713580437`*^9}, {3.514308507511819*^9,
3.514308539833797*^9}, 3.78801374153763*^9, 3.788020189532795*^9,
3.8707345096401997`*^9, {3.870734552892797*^9, 3.870734596012597*^9}, {
3.8707394144887857`*^9, 3.8707394211312933`*^9}, {3.87073947032516*^9,
3.8707394924500637`*^9}, {3.87073958312317*^9, 3.8707396250396833`*^9}, {
3.870739676436349*^9, 3.87073972239883*^9}, {3.870739791958743*^9,
3.87073991197686*^9}, {3.8707400851153173`*^9, 3.870740085682619*^9}, {
3.8707401525550737`*^9, 3.870740164625453*^9}, {3.8707402364767523`*^9,
3.870740313921801*^9}, {3.870740346874797*^9, 3.8707403707808657`*^9}, {
3.870740536339136*^9,
3.870740545995434*^9}},ExpressionUUID->"3c41945c-7fd3-4940-89ca-\
da22bf95f7a4"],
Cell["\<\
negative quasiprobabilities can be used to focus the energy of the \
distribution and provide quantum advantage in computation, work extraction \
and parameter estimation\
\>", "Subitem",
GeneratedCell->False,
CellAutoOverwrite->False,
CellChangeTimes->{{3.5143080983732347`*^9, 3.514308102892667*^9}, {
3.514308469349834*^9, 3.5143084713580437`*^9}, {3.514308507511819*^9,
3.514308539833797*^9}, 3.78801374153763*^9, 3.788020189532795*^9,
3.8707345096401997`*^9, {3.870734552892797*^9, 3.870734596012597*^9}, {
3.8707394144887857`*^9, 3.8707394211312933`*^9}, {3.87073947032516*^9,
3.8707394924500637`*^9}, {3.87073958312317*^9, 3.8707396250396833`*^9}, {
3.870739676436349*^9, 3.87073972239883*^9}, {3.870739791958743*^9,
3.87073991197686*^9}, {3.8707400851153173`*^9, 3.870740085682619*^9}, {
3.8707401525550737`*^9, 3.870740164625453*^9}, {3.8707402364767523`*^9,
3.8707403242273273`*^9}, {3.870740395334783*^9, 3.870740478839408*^9}, {
3.87074150003051*^9, 3.8707415000322733`*^9}, {3.872640317022418*^9,
3.872640317023185*^9}},ExpressionUUID->"9b11df26-0c71-464f-b613-\
883173ba1ae1"],
Cell[BoxData[
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
"We", " ", "assume", " ", "that", " ", "all", " ",
"operators", " ", "on", " ", "a", " ", "Hilbert", " ",
"space", " ", "with", " ", "finite", " ", "dimensions",
StyleBox["d",
FontSlant->"Italic"], "and", " ", "consider", " ", "two",
" ", "orthonormal",
FormBox[
RowBox[{"bases", ",",
RowBox[{"{",
RowBox[{"|",
SubscriptBox["a", "i"]}]}]}],
TraditionalForm]}], "\[RightAngleBracket]"}], "}"}], " ",
"and",
FormBox[
RowBox[{"{",
RowBox[{"|",
SubscriptBox["f", "i"]}]}],
TraditionalForm]}], "\[RightAngleBracket]"}], "}"}], ".",
"\[LineSeparator]", "We"}], " ", "regard", " ", "these", " ",
"bases", " ", "as", " ", "eigenbases", " ", "of", " ",
"observables", " ", "\[CapitalAHat]"}], "=",
RowBox[{
RowBox[{
FormBox[
SubscriptBox["\[Sum]",
RowBox[{" ", "i"}]],
TraditionalForm], " ",
FormBox[
SubscriptBox["a",
RowBox[{"i", " "}]],
TraditionalForm]}], " ", "|",
FormBox[
SubscriptBox["a",
RowBox[{"i", " "}]],
TraditionalForm]}]}], "\[RightAngleBracket]"}], " ",
RowBox[{"\[LeftAngleBracket]",
RowBox[{
RowBox[{
FormBox[
SubscriptBox["a",
RowBox[{"i", " "}]],
TraditionalForm], "|",
RowBox[{"and",
FormBox[
OverscriptBox["F", "^"],
TraditionalForm]}]}], " ", "=",
RowBox[{
RowBox[{
FormBox[
SubscriptBox["\[Sum]",
RowBox[{" ", "i"}]],
TraditionalForm], " ",
FormBox[
SubscriptBox["f",
RowBox[{"i", " "}]],
TraditionalForm]}], " ", "|",
FormBox[
SubscriptBox["f",
RowBox[{"i", " "}]],
TraditionalForm]}]}], "\[RightAngleBracket]"}], " ",
RowBox[{"\[LeftAngleBracket]",
RowBox[{
RowBox[{
FormBox[
SubscriptBox["f",
RowBox[{"i", " "}]],
TraditionalForm], "|",
RowBox[{
RowBox[{".", "\[LineSeparator]", "In"}], " ", "terms", " ", "of",
" ", "these", " ", "bases"}]}], ",",
RowBox[{"a", " ", "state",
FormBox[
OverscriptBox["\[Rho]", "^"],
TraditionalForm], "can", " ", "be", " ", "represented", " ",
"by", " ", "the", " ", "KD", " ",
RowBox[{"Distribution", ":", "\[LineSeparator]",
RowBox[{
RowBox[{"{",
FormBox[
SubsuperscriptBox["q",
RowBox[{"i", ",", "j"}],
OverscriptBox["\[Rho]", "^"]],
TraditionalForm], "}"}], "\[Congruent]",
RowBox[{"{",
FormBox[
RowBox[{"\[LeftAngleBracket]",
RowBox[{
FormBox[
SubscriptBox["f",
RowBox[{"i", " "}]],
TraditionalForm], "|",
SubscriptBox["a",
RowBox[{"i", " "}]]}]}],
TraditionalForm]}]}]}]}]}]}]}], "\[RightAngleBracket]"}], " ",
RowBox[{"\[LeftAngleBracket]",
RowBox[{
FormBox[
SubscriptBox["a",
RowBox[{"i", " "}]],
TraditionalForm], "|",
FormBox[
RowBox[{" ",
OverscriptBox["\[Rho]", "^"]}],
TraditionalForm], " ", "|",
FormBox[
SubscriptBox["f",
RowBox[{"i", " "}]],
TraditionalForm]}], "\[RightAngleBracket]"}]}], "}"}], "=",
RowBox[{"{",
RowBox[{"Tr",
RowBox[{"(",
RowBox[{
FormBox[
SubscriptBox[
OverscriptBox[
OverscriptBox["\[Product]",
RowBox[{" ", "f"}]], "^"], "j"],
TraditionalForm], " ",
RowBox[{
FormBox[
SubscriptBox[
OverscriptBox[
OverscriptBox["\[Product]",
RowBox[{" ", "a"}]], "^"], "i"],
TraditionalForm], " ",
FormBox[
RowBox[{
OverscriptBox["\[Rho]", "^"], " "}],
TraditionalForm]}]}], ")"}]}], "}"}]}], ",",
RowBox[{
RowBox[{
RowBox[{"where",
FormBox[
SubscriptBox[
OverscriptBox[
OverscriptBox["\[Product]",
RowBox[{" ", "a"}]], "^"], "i"],
TraditionalForm]}], " ", "\[Congruent]"}], " ", "|",
FormBox[
SubscriptBox["a",
RowBox[{"i", " "}]],
TraditionalForm]}]}], "\[RightAngleBracket]"}], " ",
RowBox[{"\[LeftAngleBracket]",
RowBox[{
RowBox[{
FormBox[
SubscriptBox["a",
RowBox[{"i", " "}]],
TraditionalForm], "|"}], ",",
RowBox[{
RowBox[{
RowBox[{"etc", ".", "\[LineSeparator]", "The"}], " ", "distribution",
" ", "can", " ", "be", " ", "used", " ", "to", " ", "calculate", " ",
"expectation", " ", "values", " ", "and", " ", "measurement"}], "-",
RowBox[{"outcome", " ",
RowBox[{"probabilities", ".", "\[LineSeparator]",
RowBox[{"{",
FormBox[
SubsuperscriptBox["q",
RowBox[{"i", ",", "j"}],
OverscriptBox["\[Rho]", "^"]],
TraditionalForm], "}"}]}], " ", "satisfies", " ", "some", " ", "of",
" ",
RowBox[{"Kolmogorov", "'"}], "s", " ", "axioms", " ", "for", " ",
"joint", " ", "probability", " ",
RowBox[{"distributions", "."}]}]}]}]}]}]], "Subitem",
CellChangeTimes->{{3.868494374102778*^9, 3.868494503859474*^9}, {
3.8684946742546597`*^9, 3.868494931688478*^9}, {3.868495039765729*^9,
3.868495045182228*^9}, {3.868495079303303*^9, 3.868495155580761*^9}, {
3.8684952248215647`*^9, 3.868495275998229*^9}, {3.8684954635360928`*^9,
3.868495597424655*^9}, {3.868495670392705*^9, 3.868495689345199*^9}, {
3.868495733272902*^9, 3.868495763716963*^9}, {3.868495818951961*^9,
3.8684958522908897`*^9}, {3.868495890928649*^9, 3.8684958996674147`*^9}, {
3.868495996473661*^9, 3.868496016963809*^9}, {3.8685102383824997`*^9,
3.8685102669075127`*^9}, {3.8685112642136*^9, 3.86851126863762*^9}, {
3.868625081707698*^9, 3.8686250821835012`*^9}, {3.868625309172742*^9,
3.868625320892551*^9}, 3.8686692386139708`*^9, 3.868669289736228*^9, {
3.8686693401820507`*^9, 3.868669364986142*^9}, {3.868669399802484*^9,
3.868669414875289*^9}, {3.874712391401877*^9, 3.874712489248678*^9}, {
3.874712542400723*^9, 3.874712576530356*^9}, {3.8747126480548363`*^9,
3.874712654567048*^9}},ExpressionUUID->"b5b81038-a903-447c-8093-\
3b17d90ab9f6"],
Cell["\<\
See Arvidsson-Shukur,David R.M.,Drori,Jacob Chevalier and Nicole Yunger \
Halpern 2021 (https://arxiv.org/pdf/2009.04468.pdf)\
\>", "Subitem",
CellChangeTimes->{{3.868494374102778*^9, 3.868494503859474*^9}, {
3.8684946742546597`*^9, 3.868494931688478*^9}, {3.868495039765729*^9,
3.868495045182228*^9}, {3.868495079303303*^9, 3.868495155580761*^9}, {
3.8684952248215647`*^9, 3.868495275998229*^9}, {3.8684954635360928`*^9,
3.868495597424655*^9}, {3.868495670392705*^9, 3.868495689345199*^9}, {
3.868495733272902*^9, 3.868495763716963*^9}, {3.868495818951961*^9,
3.8684958522908897`*^9}, {3.868495890928649*^9, 3.8684958996674147`*^9}, {
3.868495996473661*^9, 3.868496016963809*^9}, {3.8685102383824997`*^9,
3.8685102669075127`*^9}, {3.8685112642136*^9, 3.86851126863762*^9}, {
3.868625081707698*^9, 3.8686250821835012`*^9}, {3.868625309172742*^9,
3.868625320892551*^9}, 3.8686692386139708`*^9, 3.868669289736228*^9, {
3.8686693401820507`*^9, 3.868669364986142*^9}, {3.868669399802484*^9,
3.868669414875289*^9}, {3.874712391401877*^9,
3.874712477208975*^9}},ExpressionUUID->"19a6e8df-2b6e-457a-8ff8-\
3a1414907d29"],
Cell[CellGroupData[{
Cell["Example 1", "Section",
CellChangeTimes->{{3.868576112566503*^9, 3.8685761150264397`*^9}, {
3.86862498009269*^9, 3.868624983568787*^9}, {3.868625049291687*^9,
3.868625063758182*^9}},ExpressionUUID->"bcce5bb0-713c-498b-adff-\
3da33f87a901"],
Cell[TextData[{
Cell[BoxData[
GraphicsBox[
TagBox[RasterBox[CompressedData["
1:eJzsvXecFrX2+D+w1EU6LL13EBABUZEm0gXp0quwVOlNmoA0pQgovVxAipdL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