Table 1 Probability distribution for Bell state measurement results announced by Charlie when both Alice and Bob choose the same basis.

From: Measurement device-independent quantum key distribution with vector vortex modes under diverse weather conditions

Basis

Alice

Bob

Charlie’s measurement results

\(|\Psi \rangle ^{+}\)

\(|\Psi \rangle ^{-}\)

L0, L1

R0, R1

L0, R1

L1, R0

Vector basis

\(V_{0}\)

\(V_{0}\)

0

0

0

0

\(V_{0}\)

\(V_{1}\)

0.25

0.25

0.25

0.25

\(V_{1}\)

\(V_{0}\)

0.25

0.25

0.25

0.25

\(V_{1}\)

\(V_{1}\)

0

0

0

0

Scalar basis

\(S_{0}\)

\(S_{0}\)

0

0

0

0

\(S_{0}\)

\(S_{1}\)

0.25

0.25

0.25

0.25

\(S_{1}\)

\(S_{0}\)

0.25

0.25

0.25

0.25

\(S_{1}\)

\(S_{1}\)

0

0

0

0