Entanglement Percolation in Two Types of Irregular Quantum Networks

Figures & Tables

	CEP
Series rule	p = p₁p₂ ⋯
Parallel rule	1 − p = (1 − p₁)(1 − p₂) ⋯

c	C_SC	∂2CSC∂c2 {{{\partial^2}{C_{SC}}} \over {\partial {c^2}}}	P_SC	∂2PSC∂c2 {{{\partial^2}{P_{SC}}} \over {\partial {c^2}}}	PSCConPT P_{SC}^{\rm{ConPT}}
0.60	0.5551	2.8157	0.0277	4.6301	0.168216
0.62	0.6142	0.4345	0.0369	5.6487	0.210849
0.64	0.6734	−2.2899	0.0487	6.7974	0.260721
0.66	0.7317	−5.3403	0.0634	8.0677	0.318373
0.68	0.7878	−8.6893	0.0816	9.4416	0.384068
0.70	0.8405	−12.2992	0.1039	10.89	0.458188
0.72	0.8882	−16.1206	0.1308	12.3698	0.540542
0.74	0.9294	−20.0926	0.163	13.821	0.630925
0.76	0.9627	−24.1425	0.201	15.1645	0.729428
0.78	0.9863	−28.1861	0.2452	16.298	0.835038
0.80	0.9986	−32.1289	0.2962	17.0934	0.947103
0.82	1	−36.1567	0.3541	17.3919	1
0.84	1	−40.1238	0.4189	16.9994	1
0.92	1	−55.7857	0.7331	2.745	1
0.94	1	−59.7285	0.8166	−6.4183	1
0.96	1	−63.6713	0.895	−20.064	1

c	C_SC	∂2CSC∂c2 {{{\partial^2}{C_{SC}}} \over {\partial {c^2}}}	P_SC	∂2PSC∂c2 {{{\partial^2}{P_{SC}}} \over {\partial {c^2}}}	PSCConPT P_{SC}^{\rm{ConPT}}
0.66	0.543678214	0.0013	0.0598251	7.1932	0.160706
0.68	0.584345788	0.0006	0.0733271	9.1772	0.188495
0.70	0.626347348	0.0004	0.0895879	10.3325	0.220455
0.72	0.668926005	−0.0005	0.108726	11.7100	0.256671
0.74	0.711917832	−0.00038694	0.131535	13.6725	0.297737
0.76	0.754400424	−0.0014	0.158477	15.3625	0.343585
0.78	0.796496077	−0.0021	0.190103	17.7075	0.395356
0.92	0.99929325	−0.0069	0.605555	20.2300	0.962410
0.94	1	−0.0094	0.699814	9.1200	1
0.96	1	−0.0094	0.802165	−35.4075	1

	ConPT
Series rule	C = c₁ c₂ ⋯
Parallel rule	1+1−C22=max12,1+1−c1221+1−c222… {{1 + \sqrt {1 - {C^2}}} \over 2} = \max \left\{{{1 \over 2},{{1 + \sqrt {1 - c_1^2}} \over 2}{{1 + \sqrt {1 - c_2^2}} \over 2} \ldots} \right\}