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Keywords = information-theoretic approaches to the quantum state

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16 pages, 334 KB  
Article
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
Viewed by 666
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 [...] Read more.
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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67 pages, 2605 KB  
Article
Polar Codes for 6G and Beyond Wireless Quantum Optical Communications
by Peter Jung, Kushtrim Dini, Faris Abdel Rehim and Hamza Almujahed
Electronics 2025, 14(17), 3563; https://doi.org/10.3390/electronics14173563 - 8 Sep 2025
Viewed by 824
Abstract
Wireless communication applications above 300 GHz need careful analog electronics design that takes into account the frequency-dependent nature of ohmic resistance at these frequencies. The cumbersome development of electronics brings quantum optical communication solutions for the sixth generation (6G) THz band located between [...] Read more.
Wireless communication applications above 300 GHz need careful analog electronics design that takes into account the frequency-dependent nature of ohmic resistance at these frequencies. The cumbersome development of electronics brings quantum optical communication solutions for the sixth generation (6G) THz band located between 300 GHz and 10 THz into focus. In this manuscript, the authors propose to replace the classical radio frequency based inner physical layer transceiver blocks used in classical channel coded short range wireless communication systems by wireless quantum optical communication concepts. In addition to discussing the resulting generic concept of the wireless quantum optical communications and illustrating optimum quantum data detection schemes, novel reduced state quantum data detection and novel Kohonen maps-based quantum data detection, will be addressed. All the considered quantum data detection schemes provide soft outputs required for the lowest possible block error ratio (BLER) at the output of the channel decoding. Furthermore, a novel polar codes design approach determining the polar sequence by appropriately combining already available polar sequences tailored for low BLER is presented for the first time after illustrating the basics of polar codes. In addition, turbo equalization for wireless quantum optical communications using polar codes will be presented, for the first time explicitly stating the generation of soft information associated with the codebits and introducing a novel scheme for the computation of extrinsic soft outputs to be used in the turbo equalization iterations. New simulation results emphasize the viability of the theoretical concepts. Full article
(This article belongs to the Special Issue Channel Coding and Measurements for 6G Wireless Communications)
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29 pages, 569 KB  
Article
Born’s Rule from Contextual Relative-Entropy Minimization
by Arash Zaghi
Entropy 2025, 27(9), 898; https://doi.org/10.3390/e27090898 - 25 Aug 2025
Viewed by 2105
Abstract
We give a variational characterization of the Born rule. For each measurement context, we project a quantum state ρ onto the corresponding abelian algebra by minimizing Umegaki relative entropy; Petz’s Pythagorean identity makes the dephased state the unique local minimizer, so the Born [...] Read more.
We give a variational characterization of the Born rule. For each measurement context, we project a quantum state ρ onto the corresponding abelian algebra by minimizing Umegaki relative entropy; Petz’s Pythagorean identity makes the dephased state the unique local minimizer, so the Born weights pC(i)=Tr(ρPi) arise as a consequence, not an assumption. Globally, we measure contextuality by the minimum classical Kullback–Leibler distance from the bundle {pC(ρ)} to the noncontextual polytope, yielding a convex objective Φ(ρ). Thus, Φ(ρ)=0 exactly when a sheaf-theoretic global section exists (noncontextuality), and Φ(ρ)>0 otherwise; the closest noncontextual model is the classical I-projection of the Born bundle. Assuming finite dimension, full-rank states, and rank-1 projective contexts, the construction is unique and non-circular; it extends to degenerate PVMs and POVMs (via Naimark dilation) without change to the statements. Conceptually, the work unifies information-geometric projection, the presheaf view of contextuality, and categorical classical structure into a single optimization principle. Compared with Gleason-type, decision-theoretic, or envariance approaches, our scope is narrower but more explicit about contextuality and the relational, context-dependent status of quantum probabilities. Full article
(This article belongs to the Special Issue Quantum Foundations: 100 Years of Born’s Rule)
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18 pages, 912 KB  
Article
A Guiding Principle for Quantum State Discrimination in the Real-Spectrum Phase of P-Pseudo-Hermitian Systems
by Qinliang Dong, Xueer Gao, Zhihang Liu, Hui Li, Jingwei Wen and Chao Zheng
Entropy 2025, 27(8), 836; https://doi.org/10.3390/e27080836 - 6 Aug 2025
Viewed by 827
Abstract
Quantum state discrimination (QSD) is a fundamental task in quantum information processing, improving the computation efficiency and communication security. Non-Hermitian (NH) PT-symmetric systems were found to be able to discriminate two quantum states better than the Hermitian strategy. In this work, we propose [...] Read more.
Quantum state discrimination (QSD) is a fundamental task in quantum information processing, improving the computation efficiency and communication security. Non-Hermitian (NH) PT-symmetric systems were found to be able to discriminate two quantum states better than the Hermitian strategy. In this work, we propose a QSD approach based on P-pseudo-Hermitian systems with real spectra. We theoretically prove the feasibility of realizing QSD in the real-spectrum phase of a P-pseudo-Hermitian system, i.e., two arbitrary non-orthogonal quantum states can be discriminated by a suitable P-pseudo-Hermitian Hamiltonian. In detail, we decide the minimal angular separation between two non-orthogonal quantum states for a fixed P-pseudo-Hermitian Hamiltonian, and we find the orthogonal evolution time is able to approach zero under suitable conditions, while both the trace distance and the quantum relative entropy are employed to judge their orthogonality. We give a criterion to choose the parameters of a P-pseudo-Hermitian Hamiltonian that evolves the two initial orthogonal states faster than a fixed arbitrary PT-symmetric one with an identical energy difference. Our work expands the NH family for QSD, and can be used to explore real quantum systems in the future. Full article
(This article belongs to the Topic Quantum Systems and Their Applications)
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15 pages, 712 KB  
Article
Extracting Correlations in Arbitrary Diagonal Quantum States via Weak Couplings and Auxiliary Systems
by Hui Li, Chao Zheng, Yansong Li and Xian Lu
Symmetry 2025, 17(8), 1233; https://doi.org/10.3390/sym17081233 - 4 Aug 2025
Viewed by 536
Abstract
In this work, we introduce a novel method to extract correlations in diagonal quantum states in multi-particle quantum systems, addressing a significant limitation of traditional approaches that require prior knowledge of the density matrices of quantum states. Instead of relying on classical information [...] Read more.
In this work, we introduce a novel method to extract correlations in diagonal quantum states in multi-particle quantum systems, addressing a significant limitation of traditional approaches that require prior knowledge of the density matrices of quantum states. Instead of relying on classical information processing, our method is based on weak couplings and ancillary systems, eliminating the need for classical communication, optimization, and complex calculations. The concept of mutually unbiased bases is intrinsically linked to symmetry, as it entails the uniform distribution of quantum states across distinct bases. Within the framework of our theoretical model, mutually unbiased bases are employed to facilitate weak measurements and to function as the post-selected states. To quantify the correlations in the initial state, we employ the trace distance between the initial state and the product of its marginal states, and illustrate the feasibility and effectiveness of our approach. We generalize the approach to accommodate high-dimensional multi-particle systems for potential applications in quantum information processing and quantum networks. Full article
(This article belongs to the Topic Quantum Systems and Their Applications)
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17 pages, 3307 KB  
Article
Direct Generation and Non-Hermitian Regulation of Energy-Time-Polarization-Hyper-Entangled Quadphotons
by Rui Zhuang, Siqiang Zhang, Guobin Liu, Zhou Feng, Qingyu Chen, Sinong Liu and Yanpeng Zhang
Sensors 2025, 25(11), 3425; https://doi.org/10.3390/s25113425 - 29 May 2025
Viewed by 683
Abstract
Entangled multiphoton is an ideal resource for quantum information technology. Here, narrow-bandwidth hyper-entangled quadphoton is theoretically demonstrated by quantizing degenerate Zeeman sub states through spontaneous eight-wave mixing (EWM) in a hot 85Rb. Polarization-based energy-time entanglement (output) under multiple polarized dressings is presented [...] Read more.
Entangled multiphoton is an ideal resource for quantum information technology. Here, narrow-bandwidth hyper-entangled quadphoton is theoretically demonstrated by quantizing degenerate Zeeman sub states through spontaneous eight-wave mixing (EWM) in a hot 85Rb. Polarization-based energy-time entanglement (output) under multiple polarized dressings is presented in detail with uncorrelated photons and Raman scattering suppressed. High-dimensional entanglement is contrived by passive non-Hermitian characteristic, and EWM-based quadphoton is genuine quadphoton with quadripartite entanglement. High quadphoton production rate is achieved from co-action of four strong input fields, and electromagnetically induced transparency (EIT) slow light effect. Atomic passive non-Hermitian characteristic provides the system with acute coherent tunability around exceptional points (EPs). The results unveil multiple coherent channels (~8) inducing oscillations with multiple periods (~19) in quantum correlations, and high-dimensional (~8) four-body entangled quantum network (capacity ~65536). Coexistent hyper and high-dimensional entanglements facilitate high quantum information capacity. The system can be converted among three working states under regulating passive non-Hermitian characteristic via triple polarized dressing. The research provides a promising approach for applying hyper-entangled multiphoton to tunable quantum networks with high information capacity, whose multi-partite entanglement and multiple-degree-of-freedom properties help optimize the accuracy of quantum sensors. Full article
(This article belongs to the Special Issue Quantum-Enabled Optical Communications and Networks)
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16 pages, 1709 KB  
Article
Phase Space Insights: Wigner Functions for Qubits and Beyond
by Luis L. Sánchez-Soto, Ariana Muñoz, Pablo de la Hoz, Andrei B. Klimov and Gerd Leuchs
Appl. Sci. 2025, 15(9), 5155; https://doi.org/10.3390/app15095155 - 6 May 2025
Cited by 1 | Viewed by 3284
Abstract
Phase space methods, particularly Wigner functions, provide intuitive tools for representing and analyzing quantum states. We focus on systems with SU(2) dynamical symmetry, which naturally describes spin and a wide range of two-mode quantum models. We present a unified phase space framework tailored [...] Read more.
Phase space methods, particularly Wigner functions, provide intuitive tools for representing and analyzing quantum states. We focus on systems with SU(2) dynamical symmetry, which naturally describes spin and a wide range of two-mode quantum models. We present a unified phase space framework tailored to these systems, highlighting its broad applicability in quantum optics, metrology, and information. After reviewing the core SU(2) phase-space formalism, we apply it to states designed for optimal quantum sensing, where their nonclassical features are clearly revealed in the Wigner representation. We then extend the approach to systems with an indefinite number of excitations, introducing a generalized framework that captures correlations across multiple SU(2)-invariant subspaces. These results offer practical tools for understanding both theoretical and experimental developments in quantum science. Full article
(This article belongs to the Special Issue Quantum Optics: Theory, Methods and Applications)
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21 pages, 326 KB  
Article
Quantum-Inspired Latent Variable Modeling in Multivariate Analysis
by Theodoros Kyriazos and Mary Poga
Stats 2025, 8(1), 20; https://doi.org/10.3390/stats8010020 - 28 Feb 2025
Cited by 1 | Viewed by 1660
Abstract
Latent variables play a crucial role in psychometric research, yet traditional models often struggle to address context-dependent effects, ambivalent states, and non-commutative measurement processes. This study proposes a quantum-inspired framework for latent variable modeling that employs Hilbert space representations, allowing questionnaire items to [...] Read more.
Latent variables play a crucial role in psychometric research, yet traditional models often struggle to address context-dependent effects, ambivalent states, and non-commutative measurement processes. This study proposes a quantum-inspired framework for latent variable modeling that employs Hilbert space representations, allowing questionnaire items to be treated as pure or mixed quantum states. By integrating concepts such as superposition, interference, and non-commutative probabilities, the framework captures cognitive and behavioral phenomena that extend beyond the capabilities of classical methods. To illustrate its potential, we introduce quantum-specific metrics—fidelity, overlap, and von Neumann entropy—as complements to correlation-based measures. We also outline a machine-learning pipeline using complex and real-valued neural networks to handle amplitude and phase information. Results highlight the capacity of quantum-inspired models to reveal order effects, ambivalent responses, and multimodal distributions that remain elusive in standard psychometric approaches. This framework broadens the multivariate analysis theoretical and methodological toolkit, offering a dynamic and context-sensitive perspective on latent constructs while inviting further empirical validation in diverse research settings. Full article
(This article belongs to the Section Multivariate Analysis)
28 pages, 558 KB  
Article
Leakage Benchmarking for Universal Gate Sets
by Bujiao Wu, Xiaoyang Wang, Xiao Yuan, Cupjin Huang and Jianxin Chen
Entropy 2024, 26(1), 71; https://doi.org/10.3390/e26010071 - 13 Jan 2024
Cited by 3 | Viewed by 2474
Abstract
Errors are common issues in quantum computing platforms, among which leakage is one of the most-challenging to address. This is because leakage, i.e., the loss of information stored in the computational subspace to undesired subspaces in a larger Hilbert space, is more difficult [...] Read more.
Errors are common issues in quantum computing platforms, among which leakage is one of the most-challenging to address. This is because leakage, i.e., the loss of information stored in the computational subspace to undesired subspaces in a larger Hilbert space, is more difficult to detect and correct than errors that preserve the computational subspace. As a result, leakage presents a significant obstacle to the development of fault-tolerant quantum computation. In this paper, we propose an efficient and accurate benchmarking framework called leakage randomized benchmarking (LRB), for measuring leakage rates on multi-qubit quantum systems. Our approach is more insensitive to state preparation and measurement (SPAM) noise than existing leakage benchmarking protocols, requires fewer assumptions about the gate set itself, and can be used to benchmark multi-qubit leakages, which has not been achieved previously. We also extended the LRB protocol to an interleaved variant called interleaved LRB (iLRB), which can benchmark the average leakage rate of generic n-site quantum gates with reasonable noise assumptions. We demonstrate the iLRB protocol on benchmarking generic two-qubit gates realized using flux tuning and analyzed the behavior of iLRB under corresponding leakage models. Our numerical experiments showed good agreement with the theoretical estimations, indicating the feasibility of both the LRB and iLRB protocols. Full article
(This article belongs to the Special Issue Quantum Computing in the NISQ Era)
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29 pages, 1783 KB  
Article
An Architecture Superposing Indefinite Causal Order and Path Superposition Improving Pauli Channels’ Parameter Estimation
by Carlos Cardoso-Isidoro and Francisco Delgado
Symmetry 2024, 16(1), 74; https://doi.org/10.3390/sym16010074 - 5 Jan 2024
Viewed by 1909
Abstract
Quantum Parameter Estimation (QPE) is commonly led using quantum probe states for the characterization of quantum systems. For these purposes, Quantum Fisher Information (QFI) plays a crucial role by imposing a lower bound for the parametric estimation of quantum channels. Several schemes for [...] Read more.
Quantum Parameter Estimation (QPE) is commonly led using quantum probe states for the characterization of quantum systems. For these purposes, Quantum Fisher Information (QFI) plays a crucial role by imposing a lower bound for the parametric estimation of quantum channels. Several schemes for obtaining QFI lower bounds have been proposed, particularly for Pauli channels regarding qubits. Those schemes commonly employ either the individual channel, multiple copies of it, or arrangements including communication architectures. The present work aims to propose an architecture involving path superposition and causal indefinite order in superposition. Thus, by controlling the symmetry balance of this superposition, it reaches notable improvements in quantum parameter estimation. The proposed architecture has been tested to find the best possible QPE bounds for a representative and emblematic set of Pauli channels. Further, for the most reluctant channels, it was revisited testing the architecture again under a primary path superposition (using double teleportation) and also using entangled probe states to recombine their outputs with the original undisturbed state. Notable outcomes practically near zero were found for the QPE bounds, stating a hierarchy between the approaches, but anyway reaching a perfect theoretical QPE, particularly for the last path superposition including the proposed architecture. Full article
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15 pages, 752 KB  
Article
Tunneling between Multiple Histories as a Solution to the Information Loss Paradox
by Pisin Chen, Misao Sasaki, Dong-han Yeom and Junggi Yoon
Entropy 2023, 25(12), 1663; https://doi.org/10.3390/e25121663 - 15 Dec 2023
Cited by 5 | Viewed by 1864
Abstract
The information loss paradox associated with black hole Hawking evaporation is an unresolved problem in modern theoretical physics. In a recent brief essay, we revisited the evolution of the black hole entanglement entropy via the Euclidean path integral (EPI) of the quantum state [...] Read more.
The information loss paradox associated with black hole Hawking evaporation is an unresolved problem in modern theoretical physics. In a recent brief essay, we revisited the evolution of the black hole entanglement entropy via the Euclidean path integral (EPI) of the quantum state and allow for the branching of semi-classical histories along the Lorentzian evolution. We posited that there exist at least two histories that contribute to EPI, where one is an information-losing history, while the other is an information-preserving one. At early times, the former dominates EPI, while at the late times, the latter becomes dominant. By doing so, we recovered the essence of the Page curve, and thus, the unitarity, albeit with the turning point, i.e., the Page time, much shifted toward the late time. In this full-length paper, we fill in the details of our arguments and calculations to strengthen our notion. One implication of this modified Page curve is that the entropy bound may thus be violated. We comment on the similarity and difference between our approach and that of the replica wormholes and the islands’ conjectures. Full article
(This article belongs to the Special Issue The Black Hole Information Problem)
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10 pages, 283 KB  
Article
Information-Theoretic Models for Physical Observables
by D. Bernal-Casas and J. M. Oller
Entropy 2023, 25(10), 1448; https://doi.org/10.3390/e25101448 - 14 Oct 2023
Cited by 4 | Viewed by 2360
Abstract
This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular Riemannian metric, defined in the parameter space [...] Read more.
This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular Riemannian metric, defined in the parameter space of a smooth statistical manifold of normal probability distributions. Following this approach, we study the stationary states with the time-independent Schrödinger’s equation to discover that the information could be represented and distributed over a set of quantum harmonic oscillators, one for each independent source of data, whose coordinate for each oscillator is a parameter of the smooth statistical manifold to estimate. We observe that the estimator’s variance equals the energy levels of the quantum harmonic oscillator, proving that the estimator’s variance is definitively quantized, being the minimum variance at the minimum energy level of the oscillator. Interestingly, we demonstrate that quantum harmonic oscillators reach the Cramér–Rao lower bound on the estimator’s variance at the lowest energy level. In parallel, we find that the global probability density function of the collective mode of a set of quantum harmonic oscillators at the lowest energy level equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. Interestingly, the opposite is also true, as the prior is constant. Altogether, these results suggest that we can break the sources of information into little elements: quantum harmonic oscillators, with the square modulus of the collective mode at the lowest energy representing the most likely reality, supporting A. Zeilinger’s recent statement that the world is not broken into physical but informational parts. Full article
14 pages, 1885 KB  
Article
Dynamics of Dispersive Measurements of Flux-Qubit States: Energy-Level Splitting Connected to Quantum Wave Mechanics
by Jeong Ryeol Choi
Nanomaterials 2023, 13(17), 2395; https://doi.org/10.3390/nano13172395 - 23 Aug 2023
Viewed by 1897
Abstract
Superconducting flux qubits have many advantages as a storage of quantum information, such as broad range tunability of frequency, small-size fabricability, and high controllability. In the flux qubit–oscillator, qubits are connected to SQUID resonators for the purpose of performing dispersive non-destructive readouts of [...] Read more.
Superconducting flux qubits have many advantages as a storage of quantum information, such as broad range tunability of frequency, small-size fabricability, and high controllability. In the flux qubit–oscillator, qubits are connected to SQUID resonators for the purpose of performing dispersive non-destructive readouts of qubit signals with high fidelity. In this work, we propose a theoretical model for analyzing quantum characteristics of a flux qubit–oscillator on the basis of quantum solutions obtained using a unitary transformation approach. The energy levels of the combined system (qubit + resonator) are analyzed in detail. Equally spaced each energy level of the resonator splits into two parts depending on qubit states. Besides, coupling of the qubit to the resonator brings about an additional modification in the split energy levels. So long as the coupling strength and the tunnel splitting are not zero but finite values, the energy-level splitting of the resonator does not disappear. We conclude that quantum nondemolition dispersive measurements of the qubit states are possible by inducing bifurcation of the resonator states through the coupling. Full article
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21 pages, 4928 KB  
Article
Quantum Computing Meets Deep Learning: A Promising Approach for Diabetic Retinopathy Classification
by Shtwai Alsubai, Abdullah Alqahtani, Adel Binbusayyis, Mohemmed Sha, Abdu Gumaei and Shuihua Wang
Mathematics 2023, 11(9), 2008; https://doi.org/10.3390/math11092008 - 24 Apr 2023
Cited by 20 | Viewed by 4137
Abstract
Diabetic retinopathy seems to be the cause of micro-vascular retinal alterations. It remains a leading reason for blindness and vision loss in adults around the age of 20 to 74. Screening for this disease has become vital in identifying referable cases that require [...] Read more.
Diabetic retinopathy seems to be the cause of micro-vascular retinal alterations. It remains a leading reason for blindness and vision loss in adults around the age of 20 to 74. Screening for this disease has become vital in identifying referable cases that require complete ophthalmic evaluation and treatment to avoid permanent loss of vision. The computer-aided design could ease this screening process, which requires limited time, and assist clinicians. The main complexity in classifying images involves huge computation, leading to slow classification. Certain image classification approaches integrating quantum computing have recently evolved to resolve this. With its parallel computing ability, quantum computing could assist in effective classification. The notion of integrating quantum computing with conventional image classification methods is theoretically feasible and advantageous. However, as existing image classification techniques have failed to procure high accuracy in classification, a robust approach is needed. The present research proposes a quantum-based deep convolutional neural network to avert these pitfalls and identify disease grades from the Indian Diabetic Retinopathy Image Dataset. Typically, quantum computing could make use of the maximum number of entangled qubits for image reconstruction without any additional information. This study involves conceptual enhancement by proposing an optimized structural system termed an optimized multiple-qbit gate quantum neural network for the classification of DR. In this case, multiple qubits are regarded as the ability of qubits in multiple states to exist concurrently, which permits performance improvement with the distinct additional qubit. The overall performance of this system is validated in accordance with performance metrics, and the proposed method achieves 100% accuracy, 100% precision, 100% recall, 100% specificity, and 100% f1-score. Full article
(This article belongs to the Special Issue Quantum Computing for Industrial Applications)
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22 pages, 4410 KB  
Article
Enhanced Solid-State Fluorescence of Flavin Derivatives by Incorporation in the Metal-Organic Frameworks MIL-53(Al) and MOF-5
by Dietrich Püschel, Simon Hédé, Iván Maisuls, Simon-Patrick Höfert, Dennis Woschko, Ralf Kühnemuth, Suren Felekyan, Claus A. M. Seidel, Constantin Czekelius, Oliver Weingart, Cristian A. Strassert and Christoph Janiak
Molecules 2023, 28(6), 2877; https://doi.org/10.3390/molecules28062877 - 22 Mar 2023
Cited by 10 | Viewed by 4697
Abstract
The flavin derivatives 10-methyl-isoalloxazine (MIA) and 6-fluoro-10-methyl-isoalloxazine (6F-MIA) were incorporated in two alternative metal-organic frameworks, (MOFs) MIL-53(Al) and MOF-5. We used a post-synthetic, diffusion-based incorporation into microcrystalline MIL-53 powders with one-dimensional (1D) pores and an in-situ approach during the synthesis of MOF-5 with [...] Read more.
The flavin derivatives 10-methyl-isoalloxazine (MIA) and 6-fluoro-10-methyl-isoalloxazine (6F-MIA) were incorporated in two alternative metal-organic frameworks, (MOFs) MIL-53(Al) and MOF-5. We used a post-synthetic, diffusion-based incorporation into microcrystalline MIL-53 powders with one-dimensional (1D) pores and an in-situ approach during the synthesis of MOF-5 with its 3D channel network. The maximum amount of flavin dye incorporation is 3.9 wt% for MIA@MIL-53(Al) and 1.5 wt% for 6F-MIA@MIL-53(Al), 0.85 wt% for MIA@MOF-5 and 5.2 wt% for 6F-MIA@MOF-5. For the high incorporation yields the probability to have more than one dye molecule in a pore volume is significant. As compared to the flavins in solution, the fluorescence spectrum of these flavin@MOF composites is broadened at the bathocromic side especially for MIA. Time-resolved spectroscopy showed that multi-exponential fluorescence lifetimes were needed to describe the decays. The fluorescence-weighted lifetime of flavin@MOF of 4 ± 1 ns also corresponds to those in solution but is significantly prolonged compared to the solid flavin dyes with less than 1 ns, thereby confirming the concept of “solid solutions” for dye@MOF composites. The fluorescence quantum yield (ΦF) of the flavin@MOF composites is about half of the solution but is significantly higher compared to the solid flavin dyes. Both the fluorescence lifetime and quantum yield of flavin@MOF decrease with the flavin loading in MIL-53 due to the formation of various J-aggregates. Theoretical calculations using plane-wave and QM/MM methods are in good correspondence with the experimental results and explain the electronic structures as well as the photophysical properties of crystalline MIA and the flavin@MOF composites. In the solid flavins, π-stacking interactions of the molecules lead to a charge transfer state with low oscillator strength resulting in aggregation-caused quenching (ACQ) with low lifetimes and quantum yields. In the MOF pores, single flavin molecules represent a major population and the computed MIA@MOF structures do not find π-stacking interactions with the pore walls but only weak van-der-Waals contacts which reasons the enhanced fluorescence lifetime and quantum yield of the flavins in the composites compared to their neat solid state. To analyze the orientation of flavins in MOFs, we measured fluorescence anisotropy images of single flavin@MOF-5 crystals and a static ensemble flavin@MIL53 microcrystals, respectively. Based on image information, anisotropy distributions and overall curve of the time-resolved anisotropy curves combined with theoretical calculations, we can prove that all fluorescent flavins species have a defined and rather homogeneous orientation in the MOF framework. In MIL-53, the transition dipole moments of flavins are orientated along the 1D channel axis, whereas in MOF-5 we resolved an average orientation that is tilted with respect to the cubic crystal lattice. Notably, the more hydrophobic 6F-MIA exhibits a higher degree order than MIA. The flexible MOF MIL-53(Al) was optimized essentially to the experimental large-pore form in the guest-free state with QuantumEspresso (QE) and with MIA molecules in the pores the structure contracted to close to the experimental narrow-pore form which was also confirmed by PXRD. In summary, the incorporation of flavins in MOFs yields solid-state materials with enhanced rigidity, stabilized conformation, defined orientation and reduced aggregations of the flavins, leading to increased fluorescence lifetime and quantum yield as controllable photo-luminescent and photo-physical properties. Full article
(This article belongs to the Special Issue Porous Materials: Synthetic Strategies and Applications)
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