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Table 1 \(TP_{1}\)’s operations under different Cases

From: Hybrid protocols for multi-party semiquantum private comparison, multiplication and summation without a pre-shared key based on d-dimensional single-particle states

Case

The preparation basis of \(TP_{1}\)

The mode of \(P_{n}\)

The operations of \(TP_{1}\)

Case 1

The \(T_{1}\) basis

The REFLECT mode

Measuring \(S_{n}^{l'}\) with the \(T_{1}\) basis

Case 2

The \(T_{2}\) basis

The REFLECT mode

Measuring \(S_{n}^{l'}\) with the \(T_{2}\) basis

Case 3

The \(T_{2}\) basis

The MEASURE mode

Ignoring \(S_{n}^{l'}\)

Case 4

The \(T_{1}\) basis

The MEASURE mode

Measuring \(S_{n}^{l'}\) with the \(T_{1}\) basis