Table 2 The relation between the X quadrature measurements results of probe coherent beams \(|\alpha {\rangle }_{1}\), \(|\alpha {\rangle }_{3}\), the state of four photons after the X quadrature measurements and corresponding operation with which Alice and Bob can transform state of photons \({A}_{1},{A}_{2},{B}_{2},{B}_{1}\) to \(|{\psi }_{1}\rangle \) in accordance with the X quadrature measurement results.
From: Hyper-parallel nonlocal CNOT operation with hyperentanglement assisted by cross-Kerr nonlinearity
R 1 | R 3 | State | U t |
|---|---|---|---|
\(|\alpha {e}^{\pm i\theta }{\rangle }_{1}\) | \(|\alpha {e}^{\pm i\theta }{\rangle }_{3}\) | \(|{\psi }_{1}\rangle \) | I |
\(|\alpha {e}^{\pm i\theta }{\rangle }_{1}\) | \(|\alpha {\rangle }_{3}\) | \({({\sigma }_{x}^{p})}_{{B}_{2}}{({\sigma }_{z}^{p})}_{{A}_{2}}|{\psi }_{1}\rangle \) | \({({\sigma }_{x}^{p})}_{{B}_{2}}{({\sigma }_{z}^{p})}_{{A}_{2}}\) |
\(|\alpha {\rangle }_{1}\) | \(|\alpha {e}^{\pm i\theta }{\rangle }_{3}\) | \({({\sigma }_{x}^{s})}_{{a^{\prime} }_{2}{a}_{2}}{({\sigma }_{x}^{s})}_{{b^{\prime} }_{2}{b}_{2}}{({\sigma }_{z}^{p})}_{{A}_{2}}|{\psi }_{1}\rangle \) | \({({\sigma }_{x}^{s})}_{{a^{\prime} }_{2}{a}_{2}}{({\sigma }_{x}^{s})}_{{b^{\prime} }_{2}{b}_{2}}{({\sigma }_{z}^{p})}_{{A}_{2}}\) |
\(|\alpha {\rangle }_{1}\) | \(|\alpha {\rangle }_{3}\) | \({({\sigma }_{x}^{s})}_{{a^{\prime} }_{2}{a}_{2}}{({\sigma }_{x}^{s})}_{{b^{\prime} }_{2}{b}_{2}}{({\sigma }_{x}^{p})}_{{B}_{2}}|{\psi }_{1}\rangle \) | \({({\sigma }_{x}^{s})}_{{a^{\prime} }_{2}{a}_{2}}{({\sigma }_{x}^{s})}_{{b^{\prime} }_{2}{b}_{2}}{({\sigma }_{x}^{p})}_{{B}_{2}}\) |
