Robust and efficient quantum private comparison of equality with collective detection over collective-noise channels

We present a protocol for quantum private comparison of equality (QPCE) with the help of a semi-honest third party (TP). Instead of employing the entanglement, we use single photons to achieve the comparison in this protocol. By utilizing collective eavesdropping detection strategy, our protocol has the advantage of higher qubit efficiency and lower cost of implementation. In addition to this protocol, we further introduce three robust versions which can be immune to collective dephasing noise, collective-rotation noise and all types of unitary collective noise, respectively. Finally, we show that our protocols can be secure against the attacks from both the outside eavesdroppers and the inside participants by using the theorems on quantum operation discrimination.