Table 1 For a single type of the superposed four-photon decoherence-free states, the operations (circular-polarization flippers (CFs), \(\left| R \right\rangle\)- and \(\left| L \right\rangle\)-phase flippers (RPs and LPs), phase flippers (PPs), and a path switch] by Feed-Forward in parts (1), (2), (3), (4), and (5) should be applied to the output state of the fourth gate, due to the measurement results of the QDs. Here, we assign “O” and “N” to mean “Operation” and “No operation” of the Feed-Forward.
Results of QDs (1, 2, 3, 4) | Operations dependent on results ∵(photon-path) | Result state:\(\left| {\psi_{8} } \right\rangle_{{{\text{ABCD}}}}\) | |||||
|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | |||
\(\left| { +_{{\text{e}}} } \right\rangle_{1} \left| { +_{{\text{e}}} } \right\rangle_{2} \left| { +_{{\text{e}}} } \right\rangle_{3}\) | \(\left| { +_{{\text{e}}} } \right\rangle_{4}\) | N | N | N | (D-1) | O | \(\frac{1}{2}\left| {0_{{\text{ PL}}} } \right\rangle_{{{\text{ABCD}}}}^{1112} + \frac{\sqrt 3 }{2}\left| {1_{{\text{ PL}}} } \right\rangle_{{{\text{ABCD}}}}^{1111}\) |
\(\left| { -_{{\text{e}}} } \right\rangle_{1} \left| { +_{{\text{e}}} } \right\rangle_{2} \left| { +_{{\text{e}}} } \right\rangle_{3}\) | N | N | N | (D-2) | N | ||
\(\left| { +_{{\text{e}}} } \right\rangle_{1} \left| { -_{{\text{e}}} } \right\rangle_{2} \left| { -_{{\text{e}}} } \right\rangle_{3}\) | (A),(B) | (A),(B) | N | (D-1) | O | ||
\(\left| { -_{{\text{e}}} } \right\rangle_{1} \left| { -_{{\text{e}}} } \right\rangle_{2} \left| { -_{{\text{e}}} } \right\rangle_{3}\) | (A),(B) | (A),(B) | N | (D-2) | N | ||
\(\left| { +_{{\text{e}}} } \right\rangle_{1} \left| { -_{{\text{e}}} } \right\rangle_{2} \left| { +_{{\text{e}}} } \right\rangle_{3}\) | (A) | N | (A) | (D-1) | O | ||
\(\left| { -_{{\text{e}}} } \right\rangle_{1} \left| { -_{{\text{e}}} } \right\rangle_{2} \left| { +_{{\text{e}}} } \right\rangle_{3}\) | (A) | N | (A) | (D-2) | N | ||
\(\left| { +_{{\text{e}}} } \right\rangle_{1} \left| { +_{{\text{e}}} } \right\rangle_{2} \left| { -_{{\text{e}}} } \right\rangle_{3}\) | (B) | N | (B) | (D-1) | O | ||
\(\left| { -_{{\text{e}}} } \right\rangle_{1} \left| { +_{{\text{e}}} } \right\rangle_{2} \left| { -_{{\text{e}}} } \right\rangle_{3}\) | (B) | N | (B) | (D-2) | N | ||
\(\left| { +_{{\text{e}}} } \right\rangle_{1} \left| { +_{{\text{e}}} } \right\rangle_{2} \left| { +_{{\text{e}}} } \right\rangle_{3}\) | \(\left| { -_{{\text{e}}} } \right\rangle_{4}\) | N | (C) | N | (D-2) | N | \(\frac{1}{2}\left| {0_{{\text{ PL}}} } \right\rangle_{{{\text{ABCD}}}}^{1122} + \frac{\sqrt 3 }{2}\left| {1_{{\text{ PL}}} } \right\rangle_{{{\text{ABCD}}}}^{1121}\) |
\(\left| { -_{{\text{e}}} } \right\rangle_{1} \left| { +_{{\text{e}}} } \right\rangle_{2} \left| { +_{{\text{e}}} } \right\rangle_{3}\) | N | (C) | N | (D-1) | O | ||
\(\left| { +_{{\text{e}}} } \right\rangle_{1} \left| { -_{{\text{e}}} } \right\rangle_{2} \left| { -_{{\text{e}}} } \right\rangle_{3}\) | (A),(B) | (A),(B),(C) | N | (D-2) | N | ||
\(\left| { -_{{\text{e}}} } \right\rangle_{1} \left| { -_{{\text{e}}} } \right\rangle_{2} \left| { -_{{\text{e}}} } \right\rangle_{3}\) | (A),(B) | (A),(B),(C) | N | (D-1) | O | ||
\(\left| { +_{{\text{e}}} } \right\rangle_{1} \left| { -_{{\text{e}}} } \right\rangle_{2} \left| { +_{{\text{e}}} } \right\rangle_{3}\) | (A) | (C) | (A) | (D-2) | N | ||
\(\left| { -_{{\text{e}}} } \right\rangle_{1} \left| { -_{{\text{e}}} } \right\rangle_{2} \left| { +_{{\text{e}}} } \right\rangle_{3}\) | (A) | (C) | (A) | (D-1) | O | ||
\(\left| { +_{{\text{e}}} } \right\rangle_{1} \left| { +_{{\text{e}}} } \right\rangle_{2} \left| { -_{{\text{e}}} } \right\rangle_{3}\) | (B) | (C) | (B) | (D-2) | N | ||
\(\left| { -_{{\text{e}}} } \right\rangle_{1} \left| { +_{{\text{e}}} } \right\rangle_{2} \left| { -_{{\text{e}}} } \right\rangle_{3}\) | (B) | (C) | (B) | (D-1) | O | ||
