Table 1 The corresponding measurement results.
From: Cryptanalysis of efficient controlled semi-quantum secret sharing protocol with entangled state
\(Bob_{1}\)’s, \(\cdots\), \(Bob_{n}\)’s states | \(\hbox {Bob}_{{1}}\)’s operation | Alice’s operation | Alice’s basis | Alice’s state (\(a_{1}a_{2}\)R) |
|---|---|---|---|---|
\(|0\rangle |0\rangle ^{\otimes (n-1)}\) | M(REF) | Z | I | \(|00\rangle (|0\rangle )\) |
\(|0\rangle |1\rangle ^{\otimes (n-1)}\) | M(REF) | Z | I | \(|01\rangle (|0\rangle )\) |
\(|1\rangle |0\rangle ^{\otimes (n-1)}\) | M(REF) | Z | I | \(|10\rangle (|1\rangle )\) |
\(|1\rangle |1\rangle ^{\otimes (n-1)}\) | M(REF) | Z | I | \(|11\rangle (|1\rangle )\) |
\(|0\rangle ^{\otimes (n)} \texttt {or}|1\rangle ^{\otimes (n)}\) | M | X | H | \(|{+}{+}\rangle\) |
\(|0\rangle ^{\otimes (n)} \texttt {or}|1\rangle ^{\otimes (n)}\) | M | X | H | \(|{+}{-}\rangle\) |
\(|0\rangle ^{\otimes (n)} \texttt {or}|1\rangle ^{\otimes (n)}\) | M | X | H | \(|{-}{+}\rangle\) |
\(|0\rangle ^{\otimes (n)} \texttt {or}|1\rangle ^{\otimes (n)}\) | M | X | H | \(|{-}{-}\rangle\) |
\(|0\rangle ^{\otimes (n-1)} \texttt {or}|1\rangle ^{\otimes (n-1)}\) | REF | X | H | \(|{+}{+}\rangle (|+\rangle )\) |
\(|0\rangle ^{\otimes (n-1)} \texttt {or}|1\rangle ^{\otimes (n-1)}\) | REF | X | H | \(|{+}{-}\rangle (|+\rangle )\) |
\(|0\rangle ^{\otimes (n-1)} \texttt {or}|1\rangle ^{\otimes (n-1)}\) | REF | X | H | \(|{-}{+}\rangle (|-\rangle )\) |
\(|0\rangle ^{\otimes (n-1)} \texttt {or}|1\rangle ^{\otimes (n-1)}\) | REF | X | H | \(|{-}{-}\rangle (|-\rangle )\) |
