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A Special Issue of Entropy (ISSN 1099-4300) belonging to the section "Quantum Information".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 8975

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Dr. Wei Yang

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Guest Editor

School of Computer Science and Technology, University of Science and Technology of China, Hefei 230026, China
Interests: quantum computing; quantum information processing; information security; machine learning; ubiquitous computing

Special Issue Information

Dear Colleagues,

The rapid advancement of quantum computing poses both unprecedented challenges and transformative opportunities for information security. While quantum technologies promise significant breakthroughs in computational power, they also threaten to undermine classical cryptographic systems that form the backbone of modern digital security. In response, quantum information security has emerged as a double-edged sword, both leveraging quantum principles to strengthen security and countering the threats posed by quantum-enabled attacks.

We invite contributions that explore quantum and quantum-resistant cryptography, security models for quantum networks, and post-quantum cryptographic algorithms. Additionally, we welcome research on quantum attack strategies, cryptographic protocols resilient to quantum threats, and novel quantum-based secure multi-party computation schemes. Submissions may also address integrating quantum security into existing infrastructures and standardization efforts for post-quantum security frameworks.

This Special Issue will provide a comprehensive overview of the evolving landscape of quantum information security, fostering collaboration between researchers in quantum computing, cryptography, and cybersecurity. Both theoretical and experimental studies, as well as survey papers offering new insights into the field, are encouraged for submission.

This Special Issue will accept unpublished original papers and comprehensive reviews focused on (but not restricted to) the following research areas:

Quantum Cryptography and Protocols;
Post-Quantum Cryptography;
Secure Multi-party Quantum Computation;
Security of Quantum Networks and the Quantum Internet;
Quantum Attacks and Security Analysis;
Quantum Machine Learning for Security Applications;
Privacy and Secure Computation in Quantum Environments;
Quantum-Secured Blockchain and Distributed Systems;
Formal Verification of Quantum Security;
Quantum-Safe Infrastructure and Hybrid Systems;
Quantum Hardware Security.

Dr. Wei Yang
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

quantum computing
information security
cryptography
secure computation
attacks
machine learning

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Published Papers (9 papers)

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Research

35 pages, 714 KB

Open AccessArticle

Quantitative Assessment and Verification of Quantum Neural Network Security Based on Violations of the Bell Inequality

by Yulu Zhang

Entropy 2026, 28(8), 860; https://doi.org/10.3390/e28080860 - 1 Aug 2026

Viewed by 332

Abstract

In response to the current research landscape, which lacks unified quantitative standards and a reproducible verification framework for assessing the security of quantum neural networks (QNNs), this paper proposes a quantitative evaluation system and verification scheme for QNN security based on the violation characteristics of CHSH-type Bell inequalities. This method treats quantum entanglement as the core element of intrinsic security and establishes a controlled-variable controlled experiment involving purely classical models, non-entangled QNNs, weakly entangled QNNs, and strongly entangled QNNs. Numerical simulations were conducted using the Iris dataset; the presence of quantum entanglement was determined using the CHSH statistic, and a quantitative metric system centered on the normalized CHSH observation metric Q was constructed. Based on the theoretical limits of Bell’s inequalities, a normalization derivation was performed to establish the theoretical constraint interval of

0 \leq Q \leq 1

; the threshold values of 0.3 and 0.7 obtained from the simulations are applicable only to the experimental scenarios described in this paper and serve solely as a reference for grouping data within the experiment; they do not possess universal validity for determination. Simulation results show that the CHSH values for the weakly and strongly entangled QNN experimental groups can reach 2.8284, significantly exceeding the theoretical limits of classical locality. These values correspond to an observation metric of

Q = 0.9838

and a privacy protection strength of

P = 0.8854

, with the security level rated as high. The CHSH values of the non-entangled QNN and the purely classical model do not exceed the classical threshold of 2; they exhibit no quantum nonlocality or quantum advantage, and their security level is rated as low. This paper advances the security evaluation of QNNs from qualitative, empirical judgments to verifiable quantitative classification, providing a theoretical basis and evaluation framework for the practical application of quantum neural networks in highly security-sensitive scenarios such as privacy-preserving computing. Full article

(This article belongs to the Special Issue Quantum Information Security)

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29 pages, 2965 KB

Open AccessArticle

Security as a Natural Law: A Quantum-Inspired Hypothesis for Information Persistence

by Pete Herzog, Michael Sletten, Šarūnas Grigaliūnas and Rasa Brūzgienė

Entropy 2026, 28(7), 770; https://doi.org/10.3390/e28070770 - 7 Jul 2026

Viewed by 1596

Abstract

This paper proposes a quantum-inspired hypothesis that cybersecurity can be modeled as information persistence: the maintenance of separation between protected and adverse system states under entropy, latency, and control cost. The objective is to provide a time- and energy-aware framework for comparing security architectures without claiming that cybersecurity is literally quantum or that a universal law has been proven. We define a dimensionless Security Persistence Index,

P = Δ / (E + L + S)

, and map controls across three temporal phases—Intent, React, and Resolve—within a

5 \times 3

Control Lattice. The resulting Principle of Energetic Asymmetry predicts that React-dominated architectures should require greater energy, latency, and residual-entropy cost than architectures that shift control weight toward Intent and Resolve. We evaluate this prediction through a simulation of four architectures—Intent-heavy, Balanced, Misaligned, and React-heavy—using 1000 trials per condition. The expected pattern was observed: Intent-heavy achieved the highest simulated persistence,

P_{sim} = 5.93

, vs.

3.45

for React-heavy, and lower normalized energy cost, CPU load, false positives, latency, and residual entropy. These results provide simulation-based internal-consistency evidence only; the framework remains a hypothesis requiring hardware-level measurement, independent replication, and field validation. Full article

(This article belongs to the Special Issue Quantum Information Security)

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20 pages, 708 KB

Open AccessArticle

Decoupling the Dual Impact of NISQ Noise on Quantum Adversarial Robustness

by Haoran Wang, Shaoliang Ye, Shaowei Wang, Hanyi Wang, Zhenbo Shi and Wei Yang

Entropy 2026, 28(7), 719; https://doi.org/10.3390/e28070719 - 24 Jun 2026

Viewed by 387

Abstract

As quantum machine learning modules become increasingly integrated into NISQ-era infrastructures, it remains unclear whether intrinsic device noise can be regarded as a passive defense against adversarial examples, or whether it in fact introduces a new attack surface. To answer this question, we propose a noise-aware four-path evaluation protocol that decouples the noise assumed at attack generation from the noise present at inference, and we systematically test it on a 4-qubit variational quantum classifier over four datasets with depolarizing probabilities in the range

p \in [0, 0.3]

, using both standard gradient attacks and expectation over transformation (EOT)-based attacks. The results show that for some datasets, higher noise does suppress attacks, whereas for others attacks remain effective even at

p = 0.3

, and in several cases a moderate noise level even maximizes the attack success rate. Moreover, we find that adversarial examples generated under moderate noise often attack the clean model more successfully than those generated in an ideal setting, demonstrating that noise can be actively exploited by an adversary to discover more transferable adversarial directions. Therefore, ambient noise should not be treated as a built-in security guarantee, and future quantum machine learning (QML) robustness evaluations must explicitly model such noise-aware threats. Full article

(This article belongs to the Special Issue Quantum Information Security)

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22 pages, 1045 KB

Open AccessArticle

Efficient Semi-Quantum Secure Multi-Party Summation Protocol Based on Cancelable Random Masks and Its Applications

by Dan Wang, Diedie Yang and Haibin Wang

Entropy 2026, 28(7), 716; https://doi.org/10.3390/e28070716 - 23 Jun 2026

Viewed by 349

Abstract

Quantum Secure Multi-party Summation (QSMS) is a fundamental primitive of Quantum Secure Multi-party Computation (QSMC), enabling multiple participants to jointly compute the sum of their private inputs without disclosing individual data. However, most existing QSMS protocols require all participants to possess full quantum capabilities and often rely on pre-shared keys, auxiliary mask transmission, or multiple trusted third parties, resulting in high communication overhead and limited practicality. To address these limitations, we propose an efficient Semi-Quantum Secure Multi-party Summation (SQSMS) protocol based on d-dimensional n-particle entangled states. By exploiting the global correlation properties of high-dimensional entangled states, the proposed protocol generates correlated random masks directly from quantum measurement outcomes. These masks cancel automatically during the aggregation process, eliminating the need for additional mask distribution and transmission. Compared with existing QSMS schemes, the proposed protocol reduces communication overhead, improves quantum efficiency, and avoids reliance on pre-shared keys or multiple trusted third parties. Moreover, only simple measurement operations are required from classical participants, making the protocol more practical for semi-quantum environments. We further provide formal correctness and security analyses of the proposed protocol and conduct quantum circuit simulations using the IBM Qiskit platform to demonstrate its feasibility. Moreover, based on the proposed summation protocol, we design several extended application protocols, including anonymous voting, anonymous auction, and anonymous ranking, which further illustrate the scalability and practical applicability of the proposed scheme. Full article

(This article belongs to the Special Issue Quantum Information Security)

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21 pages, 1781 KB

Open AccessEditor’s ChoiceArticle

A Post-Quantum Authentication and Key Agreement Protocol Based on Lattice-Based KEM for Secure Network Environments

by Xiaoping Chen, Wangyu Wu, Guangmin Liang, Haonan Tan and Yicheng Yu

Entropy 2026, 28(5), 490; https://doi.org/10.3390/e28050490 - 24 Apr 2026

Cited by 1 | Viewed by 796

Abstract

In emerging environments such as cloud computing and the Internet of Things (IoT), secure authentication and key negotiation play a crucial role in protecting data transmitted over public networks. However, many existing authentication protocols are still designed based on classical public-key cryptography primitives, and quantum computing may threaten their security. To address this challenge, we propose a post-quantum authentication and key agreement protocol that uses the lattice-based Kyber key encapsulation mechanism (KEM). Our proposed protocol integrates cryptographic authentication, smart card protection, and post-quantum key encapsulation mechanisms, enabling mutual authentication between users and servers and securely establishing session keys. The security of the protocol is formally analyzed in the Real-or-Random (ROR) model under the random oracle assumption and the IND-CCA security of the underlying KEM scheme. Furthermore, through informal security analysis, we have further demonstrated that the protocol possesses important security properties, including anonymity, untraceability, perfect forward confidentiality, and resistance to known attacks. In addition, the computational cost and communication overhead of the proposed scheme are evaluated and compared with several representative authentication protocols. The results show that the proposed protocol can provide strong security while maintaining low computational cost and communication overhead. Full article

(This article belongs to the Special Issue Quantum Information Security)

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26 pages, 911 KB

Open AccessArticle

Logarithmic-Size Post-Quantum Linkable Ring Signatures Based on Aggregation Operations

by Minghui Zheng, Shicheng Huang, Deju Kong, Xing Fu, Qiancheng Yao and Wenyi Hou

Entropy 2026, 28(1), 130; https://doi.org/10.3390/e28010130 - 22 Jan 2026

Viewed by 796

Abstract

Linkable ring signatures are a type of ring signature scheme that can protect the anonymity of signers while allowing the public to verify whether the same signer has signed the same message multiple times. This functionality makes linkable ring signatures suitable for applications such as cryptocurrencies and anonymous voting systems, achieving the dual goals of identity privacy protection and misuse prevention. However, existing post-quantum linkable ring signature schemes often suffer from issues such as excessive linear data growth the adoption of post-quantum signature algorithms, and high circuit complexity resulting from the use of post-quantum zero-knowledge proof protocols. To address these issues, a logarithmic-size post-quantum linkable ring signature scheme based on aggregation operations is proposed. The scheme constructs a Merkle tree from ring members’ public keys via a hash algorithm to achieve logarithmic-scale signing and verification operations. Moreover, it introduces, for the first time, a post-quantum aggregate signature scheme to replace post-quantum zero-knowledge proof protocols, thereby effectively avoiding the construction of complex circuits. Scheme analysis confirms that the proposed scheme meets the correctness requirements of linkable ring signatures. In terms of security, the scheme satisfies the anonymity, unforgeability, and linkability requirements of linkable ring signatures. Moreover, the aggregation process does not leak information about the signing members, ensuring strong privacy protection. Experimental results demonstrate that, when the ring size scales to 1024 members, our scheme outperforms the existing Dilithium-based logarithmic post-quantum ring signature scheme, with nearly 98.25% lower signing time, 98.90% lower verification time, and 99.81% smaller signature size. Full article

(This article belongs to the Special Issue Quantum Information Security)

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21 pages, 876 KB

Open AccessArticle

Multi-Party Semi-Quantum Simultaneous Ascending Auction Protocol Based on Single-Particle States

by Xiuqi Wu, Yu Yang, Baichang Wang, Yue Zhang and Yunguang Han

Entropy 2026, 28(1), 39; https://doi.org/10.3390/e28010039 - 28 Dec 2025

Viewed by 740

Abstract

Simultaneous ascending auctions find extensive applications in spectrum licensing and advertising space allocation. However, existing quantum sealed-bid auction protocols suffer from dual limitations: they cannot support multi-item simultaneous bidding scenarios, and their reliance on complex quantum resources along with requiring full quantum operational capabilities from bidders fails to accommodate practical constraints of quantum resource-limited users. To address these challenges, this paper proposes a multi-party semi-quantum simultaneous ascending auction protocol based on single-particle states. The protocol employs a trusted honest third party (HTP) responsible for quantum state generation, distribution, and security verification. Bidders determine their groups through quantum measurements and privately encode their bid vectors. Upon successful HTP authentication, each bidder obtains a unique identity code. During the bidding phase, HTP dynamically updates quantum sequences, allowing bidders to submit bids for multiple items by performing only simple unitary operations. HTP announces the highest bid for each item in real time and iteratively generates auction sequences until no new highest bid emerges, thereby achieving simultaneous ascending auctions for multiple items. It acts as a quantum-secured signaling layer, ensuring unconditional security for bid transmission and identity verification while maintaining classical auction logic. Quantum circuit simulations validate the protocol’s feasibility with current technology while satisfying critical security requirements, including anonymity, verifiability, non-repudiation, and privacy preservation. It provides a scalable semi-quantum auction solution for resource-constrained scenarios. Full article

(This article belongs to the Special Issue Quantum Information Security)

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16 pages, 334 KB

Open AccessArticle

An Efficient and Secure Semi-Quantum Secret Sharing Scheme Based on W State Sharing of Specific Bits

by Kai Xing, Rongbo Lu, Sihai Liu and Lu Lan

Entropy 2025, 27(11), 1107; https://doi.org/10.3390/e27111107 - 26 Oct 2025

Cited by 1 | Viewed by 1550

Abstract

This paper presents a semi-quantum secret sharing (SQSS) protocol based on three-particle W states, designed for efficient and secure secret sharing in quantum-resource-constrained scenarios. In the protocol, a fully quantum-capable sender encodes binary secrets using W, while receivers with limited quantum capabilities reconstruct the secret through collaborative Z basis measurements and classical communication, ensuring no single participant can obtain the complete information independently. The protocol employs a four-state decoy photon technique (

{| 0 ⟩, | 1 ⟩, | + ⟩, | - ⟩}

) and position randomization, combined with photon number splitting (PNS) and wavelength filtering (WF) technologies, to resist intercept–resend, entanglement–measurement, and double controlled-NOT(CNOT) attacks. Theoretical analysis shows that the detection probability of intercept–resend attacks increases exponentially with the number of decoy photons (approaching 1). For entanglement–measurement attacks, any illegal operation by an attacker introduces detectable quantum state disturbances. Double CNOT attacks are rendered ineffective by the untraceability of particle positions and mixed-basis strategies. Leveraging the robust entanglement of W states, the protocol proves that the mutual information between secret bits and single-participant measurement results is strictly zero, ensuring lossless reconstruction only through authorized collaboration. Full article

(This article belongs to the Special Issue Quantum Information Security)

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18 pages, 712 KB

Open AccessArticle

Lightweight Quantum Authentication and Key Agreement Scheme in the Smart Grid Environment

by Zehui Jiang and Run-Hua Shi

Entropy 2025, 27(9), 957; https://doi.org/10.3390/e27090957 - 14 Sep 2025

Cited by 2 | Viewed by 1218

Abstract

Smart grids leverage smart terminal devices to collect information from the user side, achieving accurate load forecasting and optimized dispatching of power systems, effectively improving power supply efficiency and reliability while reducing energy consumption. However, the development of quantum technology poses severe challenges to the communication security of smart grids that rely on traditional cryptography. To address this security risk in the quantum era, this paper draws on the core idea of quantum private comparison and proposes a quantum-secure identity authentication and key agreement scheme suitable for smart grids. This scheme uses Bell states as quantum resources, combines hash functions and XOR operations, and can adapt to resource-constrained terminal devices. Through a security proof, it verifies the scheme’s ability to resist various attacks; the experimental results further show that the scheme still has good robustness in different noise environments, providing a feasible technical path for the secure communication of smart grids in the quantum environment and having clear practical engineering value. Full article

(This article belongs to the Special Issue Quantum Information Security)

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