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IEEJ Transactions on Electronics Information and Systems

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

Published Nov 30, 2020• 3 citations
Publisher

Abstract

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.

DOI
10.1541/ieejeiss.140.1328

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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.
Quantum reading is one of application protocols of entanglement. This protocol uses entanglement for reading of a digital memory such as a CD or DVD. O. Hirota showed that in a noiseless environment, quantum reading using a quasi-Bell state that has maximum entanglement is error free. Moreover, K. Kato and O. Hirota considered equal losses for amplitudes of modes A and B of this state in determining energy-loss effects. However, in real settings, the loss associated with the amplitude of mode B is greater than that of mode A. Therefore, we consider non-symmetric loss and its effect on quantum reading using a quasi-Bell state. In this paper, we show the analytical solution of the error probability in this case, and investigate the amplitude of mode A that minimizes the error probability when the amplitude of mode B is fixed. Moreover, we consider the robustness against alignment mismatch.
Non-classical states of light field have been exploited to provide marvellous results in quantum information science. Effectiveness of nonclassical states depends on whether physical parameter as signal is continuous or digital. Here we present an investigation on the potential of quasi Bell state of entangled coherent states in quantum reading of the classical digital memory which was pioneered by Pirandola. This is a typical example of discrete quantum discrimination. We show that the quasi Bell state gives the error free performance in the quantum reading that cannot be obtained by any classical state.
Quantum illumination proposed by Lloyd is a protocol that detects the existence of a target by using entangled light of two-mode. Quantum illumination was first proposed using the Bell state, and then the use of a two-mode Gaussian state was proposed. On the other hand, there are many impact studies using the quasi-Bell state. However, as far as we know, there are no studies that analyze quantum illumination using the quasi-Bell state. Therefore, we focused on the performance evaluation of quantum illumination using the quasi-Bell state in this paper. We compared and considered the effects using the Bell state, the two-mode Gaussian state, the maximum quasi-Bell state, the non-maximum quasi-Bell state, and the coherent state (i.e., a laser radar) on the attenuated channel. In particular, we derived the exact solutions of the error probabilities when using the maximum and non-maximum quasi-Bell states. Then we clarified that quantum illumination using the quasi-Bell state offers a clear advantage over that using the other entangled states under almost situations and always offers a clear advantage over the laser radar.
Abstract Nonclassical states of light field have been exploited to provide marvellous results in quantum information science. Usefulness of nonclassical states in quantum information science depends on whether a physical parameter as a signal is continuous or discrete. Here we present an investigation of the potential of quasi Bell states of entangled coherent states in quantum reading of the classical digital memory which was pioneered by Pirandola (Phys.Rev.Lett.,106,090504,2011). This is a typical example of discrimination for discrete quantum parameters. We show that the quasi Bell state gives the error free performance in the quantum reading that cannot be obtained by any classical state.
It has been reported that error-free quantum reading of a classical digital memory is possible when the entangled coherent state |a〉 |a〉– |– a〉|–a〉 is used as the probe state for quantum reading with binary phase shift keying format under the assumption that the channel is noiseless [quant-ph/1108.4163v2]. In this paper, the theoretical performance limits of the minimum error probability and classical capacity of quantum reading with binary phase shift keying entangled coherent state signal are investigated in the presence of channel loss.
We propose an amplitude shift keying-type asymmetric quantum communication (AQC) system that uses an entangled state. As a first step toward development of this system, we evaluated and considered the communication performance of the proposed receiver when applied to the AQC system using a two-mode squeezed vacuum state (TSVS), the maximum quasi-Bell state, and the non-maximum quasi-Bell state, along with an asymmetric classical communication (ACC) system using the coherent state. Specifically, we derived an analytical expression for the error probability of the AQC system using the quasi-Bell state. Comparison of the error probabilities of the ACC system and the AQC systems when using the TSVS and the quasi-Bell state shows that the AQC system using the quasi-Bell state offers a clear performance advantage under specific conditions. Additionally, it was clarified that there are cases where the universal lower bound on the error probability for the AQC system was almost achieved when using the quasi-Bell state, unlike the case in which the TSVS was used.