Quantum Information Processing

Chen, Ying; Zou, Xiangfu; Wang, Xin; Liu, Jianfeng; Rong, Zhenbang; Huang, Zhiming; Zheng, Shenggen; Liang, Xueying; Wu, Jianxiong

doi: 10.1007/s11128-023-04088-wpmid: N/A

Quantum secure direct communication is an important branch of quantum cryptography. One of the main requirements of quantum secure direct communication is to ensure that no secret information can be stolen. Recently, a bidirectional quantum secure direct communication protocol [Quantum Information Processing 16, 147 (2017)] was proposed. It was believed that the intercept-and-resend attack and information leakage problem can be avoided via this protocol. However, in this paper, we point out that attackers can obtain useful information about the secret messages by constructing two intercept-and-resend attacks on the above protocol. Attackers can obtain Alice’s secret message exclusive OR Bob’s secret message by the first attack and both secret messages by the second attack. To resist the two constructed attacks, we design an improved bidirectional quantum secure direct communication protocol. Furthermore, we show that the designed protocol can resist the two constructed attacks and its efficiency has increased. It is interesting that the designed protocol can publish Alice’s result states, i.e., Bob’s initial states, without affecting its security. The designed protocol can prevent Alice (Bob) from obtaining Bob’s (Alice’s) secret message before Alice (Bob) sends her (his) secret message. This work can notice researchers to avoid similar security problems in constructing quantum cryptography protocols.

Zhang, Yuxia; Tan, Xiangguan; Qiu, Tianhui

doi: 10.1007/s11128-023-04099-7pmid: N/A

The Leggett–Garg inequality (LGI) is used to test incompatibility between the classical world view of macrorealism and quantum mechanics. Except for the LGI, other formulations for testing macrorealism have also been proposed, such as the entropic LGI and the no-signaling-in-time (NSIT) condition. And these formulations of macrorealism are not both the necessary and sufficient conditions for macrorealism. In this paper, analogous to the LGI, an equality for the energy change of a quantum system is given for testing macrorealism. It is called as the energy LG (ELG). Then, we study quantum violations of the ELG, the LGI, the entropic LGI and the NSIT condition for a two-level system. It is shown that for the projective measurement, the ELG can be violated for a wider parameter regime than the NSIT condition, and the NSIT condition can be violated for a wider parameter regime than the LGI and the entropic LGI. For the coarsening measurement reference and coarsening final resolution, we find that the quantum violations of the ELG and the NSIT condition provide the same robustness, which are both the most robust, and the quantum violation of the entropic LGI is the most vulnerable.

Chen, Wei; Yang, Yanmin; Fei, Shao-Ming; Zheng, Zhu-Jun; Wang, Yan-Ling

doi: 10.1007/s11128-023-04090-2pmid: N/A

We study the concurrence for arbitrary N-partite W-class states based on the (N-1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(N-1)$$\end{document}-partite partitions of subsystems by taking account to the structures of W-class states. By using the method of permutation and combination, we give some analytical formulas of concurrence and elegant relations between the N-partite concurrence and the (N-1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(N-1)$$\end{document}-partite concurrence for arbitrary N-partite W-class states. Applying these relations, we present better lower bounds of concurrence for some multipartite mixed states. An example is given to demonstrate that our lower bounds can detect more entanglements.

Lin, Da; Xiang, Zejun; Xu, Runqing; Zhang, Shasha; Zeng, Xiangyong

doi: 10.1007/s11128-023-04043-9pmid: N/A

This work researches the implementation of the AES family with Pauli-X gates, CNOT gates and Toffoli gates as the underlying quantum logic gate set. First, the properties of quantum circuits are investigated, as well as the influence of Pauli-X gates, CNOT gates and Toffoli gates on the performance of the circuits constructed with those gates. Based on these properties and the observations on the hardware circuits built by Boyar et al. and Zou et al., it is possible to construct quantum circuits for AES’s Substitution-box (S-box) and its inverse (S-box-1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$^{-1}$$\end{document}) by rearranging the classical implementation to three parts. Since the second part is treated as a 4-bit S-box in this paper and can be dealt with by existing tools, a heuristic is proposed to search optimized quantum circuits for the first and the third parts. In addition, considering the number of parallelly executed S-boxes, the trade-offs between the qubit consumption and T·M\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$T\cdot M$$\end{document} values for the round function and key schedule of AES are studied. As a result, quantum circuits of AES-128, AES-192 and AES-256 can be constructed with 269, 333 and 397 qubits, respectively. If more qubits are allowed, quantum circuits that outperform state-of-the-art schemes in the metric of T·M\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$T\cdot M$$\end{document} value for the AES family can be reported, and it needs only 474, 538 and 602 qubits for AES-128, AES-192 and AES-256, respectively.

Zhou, Jian; Wu, Leixin; Feng, Yanyan; Li, Hui; Shi, Jinjing; Shi, Ronghua

doi: 10.1007/s11128-023-04111-0pmid: N/A

In this paper, a modified four-state continuous variable quantum key distribution protocol is proposed by adding a hybrid linear amplifier to Bob’s output. The heralded hybrid linear amplifier is composed by an ideal deterministic linear amplifier and a probabilistic noiseless linear amplifier. The degradation of signal-to-noise ratio caused by deterministic linear amplifier during the amplification of quantum light states can be surmounted by the probabilistic amplification process. The hybrid linear amplifier allows us to tune between the regimes of high gain or high noise reduction and control the trade-off between the amplification coefficient and a finite heralding probability flexibly. We examine how the new protocol is affected by the hybrid amplifier’s G and g parameters. By adjusting the characteristics of the hybrid linear amplifier, it is possible to optimize the key at a specific distance. In order to improve the simulation’s reality value, we take into account the role of finite-size while examining the key rate and simulation. The application for the hybrid linear amplifier is increased by its use in the four-state protocol.

Jiang, Yinghua; Chen, Liquan; Gong, Ximing; Zhu, Yaqing; Gao, Yuan

doi: 10.1007/s11128-023-04102-1pmid: N/A

To address the risk of spoofing the information exchanged by users and reduce the trustworthiness of third party, we propose a quantum information fair exchange protocol based on three-particle GHZ states. This protocol achieves quantum multi-party fair exchange of secret information through the utilization of three-particle GHZ states, Pauli matrix, a semi-trusted third party, and polarization state of a single photon. By leveraging the unique physical properties of the GHZ state, this protocol achieves fair exchange of secret information with experimental results that align with theoretical derivation, thus demonstrating its feasibility. Additionally, it provides superdense coding which enhances transmission efficiency while also being resistant to false signal attacks, interception retransmission attacks, and entanglement attacks, ultimately improving security. Furthermore, compared with the classic fair exchange protocol, which requires a trusted third party, it only requires a semi-trusted third party, which raises the security from “computational security” to “unconditional security”. The implementation of this protocol resolves the risk of users who hand over information first, presenting a novel solution for digital currency trading, information swapping, and multi-party secure computing.

Chang, Shoukang; Ye, Wei; Rao, Xuan; Liu, Min; Zhang, Huan; Huang, Liqing; Luo, Mengmeng; Chen, Yuetao; Gao, Shaoyan

doi: 10.1007/s11128-023-04093-zpmid: N/A

Most of the studies have focused on the single-angular displacement estimation, while the multiple angular displacement estimation in ideal and noisy scenarios is still elusive. In this paper, we investigate the simultaneous multiple angular displacement estimation based on an orbital angular momentum (OAM), together with inputting (d+1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(d+1)$$\end{document}-mode NOON-like states as the probe state. By revealing the role of the intramode correlation of the probe state, this allows us to give a reasonable explanation for the corresponding quantum Cramér-Rao bound (QCRB) behaviors. Our analyses suggest that the QCRB for multiple angular displacement estimation is always positively related to the intramode correlation, especially for the multimode entangled squeezed vacuum state showing the best performance compared to another probe state. More importantly, strengthening the robustness of multiple angular-displacement estimation systems can be achieved by increasing the OAM quantum number.

Xiao, Yu-Xiang; Zhou, Lan; Zhong, Wei; Du, Ming-Ming; Sheng, Yu-Bo

doi: 10.1007/s11128-023-04097-9pmid: N/A

Quantum secure direct communication (QSDC) can directly transmit secret messages through quantum channel without keys. The typical entanglement-based QSDC protocol encodes in one degree of freedom and requires the Bell state measurement (BSM). In the paper, we propose a hyperentanglement-based QSDC protocol with the single-photon measurement. Comparing with the BSM, the single-photon measurement is easier to implement and has higher success probability. The adoption of hyperentanglement can increase the capacity of each photon pair, and thus increase the secret message capacity. The message sender can transmit 2 bits of messages with a hyperentangled photon pair in theory. We make the numerical simulations to study the secret message capacity against the collective attack and photon number splitting attack. Our QSDC protocol has potential applications in the future quantum communication field.

Grigoryan, Artyom M.; Agaian, Sos S.

doi: 10.1007/s11128-023-04091-1pmid: N/A

Quantum computing algorithms offer the potential to revolutionize computational efficiency across a wide range of applications. However, one significant challenge that has impeded progress in color image processing is the difficulty of representing color relationships in quantum computers. In addition to this challenge, another major hurdle is efficiently representing data in quantum computers and performing quantum operations or arithmetic. To overcome these challenges, researchers have proposed various novel approaches, including using qubit lattices and flexible representations of quantum images. Despite these advancements, the quantum color image processing field is still in its early stages. This paper proposes a new arithmetic for processing quantum color images using novel operations for 2-qubits and the concept of quantum quaternion Fourier transform. We first study arithmetic operations in the 2-qubit setting, such as multiplication, inverse, and division on 2-qubits in quantum computation. The space of 2-qubits with real amplitudes is considered, and prototypes of power and exponent operations are also defined. The presented operations are applied to quantum superpositions of 2-qubits, to enable processing of quaternion images, which are 4-dimensional vectors and can be represented by 2-qubits at each pixel. The proposed methods and tools are designed to be embedded in a quantum device, which allows them to be used in various applications in the 2-qubits domain. To facilitate practical applications, the paper also introduces a tool for processing color images that can be used for color image filtering. Furthermore, this work provides a foundation to explore theoretical and practical aspects of color image processing on quantum computers.

Sun, Yuan-Hao; Guo, Yu-Qing; Cao, Cong

doi: 10.1007/s11128-023-04101-2pmid: N/A

Hyperentangled Bell-state analysis (HBSA) for two-photon systems and hyperentangled Greenberger–Horne–Zeilinger-state analysis (HGSA) for multi-photon systems play significant roles in quantum information processing. In this paper, we propose a complete and fidelity-robust spatial-polarization two-photon HBSA scheme and generalize it to unambiguous multi-photon HGSA based on the interaction between single photons and singly charged quantum dots (QDs) in optical microcavities under the balance condition. Under the balance condition, the requirement for side-leakage rate and coupling strength for the QD-cavity system can be relaxed and the noise brought on by the unbalanced reflectance of coupled and uncoupled QD-cavity systems is effectively suppressed, raising the fidelity of our schemes to unity in theory. When generalizing to the multi-photon HGSA, our scheme can effectively suppress the decrease in efficiency resulting from the increase in the number of photons. In addition, our schemes simplify the discrimination process and reduce the required light–matter interaction by using self-assisted mechanism. These advantages make our schemes more universal and feasible for high-capacity quantum communications and quantum networks based on hyperentanglement with currently available techniques.