A universal protocol for bidirectional controlled teleportation with network coding
Meng-Yao He,Song-Ya Ma,Kun-Peng Kang
Table 1. The expressions for $| {f}_{{p}_{1}{q}_{1}{p}_{2}{q}_{2}}^{l}\rangle $ and the recovery operations (RO).
p1q1, p2q2lp1q1, p2q2l$| {f}_{{p}_{1}{q}_{1}{p}_{2}{q}_{2}}^{l}\rangle $RO
00,00010,101α0∣00⟩ + α1∣01⟩ + α2∣10⟩ + α3∣11⟩I ⨂ I
00,01010,111α0∣01⟩ + α1∣00⟩ + α2∣11⟩ + α3∣10⟩I ⨂ X
00,10010,001α0∣00⟩ − α1∣01⟩ + α2∣10⟩ − α3∣11⟩I ⨂ Z
00,11010,011α0∣01⟩ − α1∣00⟩ + α2∣11⟩ − α3∣10⟩I ⨂ (ZX)
01,00011,101α0∣10⟩ + α1∣11⟩ + α2∣00⟩ + α3∣01⟩X ⨂ I
01,01011,111α0∣11⟩ + α1∣10⟩ + α2∣01⟩ + α3∣00⟩X ⨂ X
01,10011,001α0∣10⟩ − α1∣11⟩ + α2∣00⟩ − α3∣01⟩X ⨂ Z
01,11011,011α0∣11⟩ − α1∣10⟩ + α2∣01⟩ − α3∣00⟩X ⨂ (ZX)
10,00000,101α0∣00⟩ + α1∣01⟩ − α2∣10⟩ − α3∣11⟩Z ⨂ I
10,01000,111α0∣01⟩ + α1∣00⟩ − α2∣11⟩ − α3∣10⟩Z ⨂ X
10,10000,001α0∣00⟩ − α1∣01⟩ − α2∣10⟩ + α3∣11⟩Z ⨂ Z
10,11000,011α0∣01⟩ − α1∣00⟩ − α2∣11⟩ + α3∣10⟩Z ⨂ (ZX)
11,00001,101α0∣10⟩ + α1∣11⟩ − α2∣00⟩ − α3∣01⟩(ZX) ⨂ I
11,01001,111α0∣11⟩ + α1∣10⟩ − α2∣01⟩ − α3∣00⟩(ZX) ⨂ X
11,10001,001α0∣10⟩ − α1∣11⟩ − α2∣00⟩ + α3∣01⟩(ZX) ⨂ Z
11,11001,011α0∣11⟩ − α1∣10⟩ − α2∣01⟩ + α3∣00⟩(ZX) ⨂ (ZX)