Multi-Photon States with Minimal Polarization

The table below summarizes the maximal degree M of extremal unpolarized, pure states with N photons (or, equivalently, spin S=N/2). For those states, all multipoles up to order M vanishes, corresponding to isotropic moments of the Stoke's variables up to Mth order. Furthermore, the cumulative squared lengths A(S)M vanishes.

So far, in all case for which we have found solutions, the maximal degree M of unpolarization matches the largest degree t for which a spherical t design with N points is known to exist.

Click on the number of photons to get more detailed information (more solutions will be added).
NM
   
   
21
3 1
4 2
5 1
6 3
7 2
8 3
9 2
NM
103
113
125
133
144
153
165
174
185
194
NM
205
214
225
235
247
255
266
275
286
29 
NM
307
316
327
336
347
356
368
37 
387
397
NM
408
417
428
43 
448
45 
468
47 
489
49 
NM
509
51 
52 
53 
549
55 
569
57 
58 
59 
NM
6010
61 
62 
63 
64 
65 
66 
67 
68 
69 
NM
7011
71 
7211
73 
7411
75 
76 
77 
7811
79 
NM
8011
81 
82 
83 
8412
85 
86 
87 
88 
89 
NM
90 
91 
92 
93 
94 
95 
96 
97 
98 
99 
NM
100 
101 
102 
103 
104 
105 
106 
107 
108 
109 
NM
110 
111 
112 
113 
114 
115 
116 
117 
118 
119 
 
NM
12015
  
13215
  
21219

References:


Markus Grassl (Markus.Grassl[at]mpl.mpg.de)