Comparison of Performances on Quantum Reading in Non-symmetric Loss Using Maximum and Non-maximum Quasi-Bell States
Keita Ishikawa, Tiancheng Wang, Tsuyoshi Sasaki Usuda · IEEJ Transactions on Electronics Information and Systems · 2020
Quantum reading is the protocol that uses entanglement for reading a bit stored in digital memory. By using entanglement, it was shown by S. Pirandola that the data rate was improved. O. Hirota showed that in noiseless environments, error-free reading is possible by using a quasi-Bell state that has maximum entanglement. After that, some non-ideal cases were considered, such as symmetric loss and incomplete phase shift. In this study, we would like to clarify properties of the protocol in more realistic situations for experiment. In this paper, we compare and consider the effects using maximum and non-maximum quasi-Bell states on quantum reading with (1) only non-symmetric loss, (2) non-symmetric loss and incomplete phase shift, and (3) non-symmetric loss and phase noise. In the case (1), we derive the exact solutions of the error probabilities when using maximum and non-maximum quasi-Bell states. Then we clarify that the error probability using maximum quasi-Bell states is always lower than that using non-maximum quasi-Bell states. In the other two cases, we compute error probabilities numerically. In cases (2) and (3), the results are different from that of the case (1). That is, both maximum and non-maximum quasi-Bell states are not always supremer than the other.