Table 1 Probability of the (Xi) event occurring.

From: Realizing the measure-device-independent quantum-key-distribution with passive heralded-single photon sources

Case

X1 : s1 = 0, s2 = 0

(1 − d1)(1 − d2)

d1(1 − d2)

d2(1 − d1)

d 1 d 2

X2 : s1 ≠ 0, s2 = 0

0

(1 − d2)

0

d 2

X3 : s1 = 0, s2 ≠ 0

0

0

(1 − d1)

d 1

X4 : s1 ≠ 0, s2 ≠ 0

0

0

0

1