Tsallis relative entropy of coherence dynamics in Grover's search algorithm
Linlin Ye, Zhaoqi Wu, Shao-Ming Fe
Abstract
Quantum coherence plays a central role in Grover's search algorithm. We study the Tsallis relative entropy of coherence dynamics of the evolved state in Grover's search algorithm. We prove that the Tsallis relative entropy of coherence decreases with the increase of the success probability, and derive the complementarity relations between the coherence and the success probability. We show that the operator coherence of the first relies on the size of the database , the success probability and the target states. Moreover, we illustrate the relationships between coherence and entanglement of the superposition state of targets, as well as the production and deletion of coherence in Grover iterations.
AI Impact Assessments
(3 models)Scientific Impact Assessment
Core Contribution
This paper studies the dynamics of quantum coherence in Grover's search algorithm (GSA) using the Tsallis relative α entropy as the coherence quantifier. The main contributions are: (1) proving that Tsallis relative α entropy of coherence decreases as success probability increases, (2) deriving complementarity relations between coherence and success probability, (3) analyzing how each basic operator (O, P, H⊗n) contributes to coherence production/depletion, and (4) examining how the entanglement structure of target states affects coherence for different α regimes.
The paper extends prior work by Pan and Qiu [69], who studied similar dynamics using the l₁ norm of coherence, and Pan, Situ and Zheng [72], who derived complementarity relations via the l₁ norm. The novelty lies in using a parametric family of coherence measures (Tsallis relative α entropy) that interpolates between the relative entropy of coherence (α→1) and the skew information of coherence (α=1/2), providing a more unified and parameterized view.
Methodological Rigor
The mathematical derivations appear technically sound but largely straightforward. The proofs rely on direct substitution and algebraic manipulation of known formulas for the Grover state evolution and the Tsallis relative α entropy of coherence. The key approximation throughout is t≪N (few targets relative to database size), which is the standard regime of interest for Grover's algorithm.
Several concerns regarding rigor:
Potential Impact
The paper's impact is primarily within the niche intersection of quantum resource theory and quantum algorithm analysis. The practical implications are limited:
1. Understanding quantum speedup: The complementarity between coherence and success probability adds to our understanding of how coherence is consumed during Grover's algorithm, but the relationship is not surprising—it essentially reformulates the known geometry of Grover's rotation in coherence-theoretic language.
2. Algorithm design insights: The observation that coherence oscillates (depletes and produces alternately) with a turning point mirrors the known entanglement dynamics in GSA. The paper suggests this could inform new algorithm design, but provides no concrete mechanism for how.
3. Unification across measures: The parametric nature of Tsallis relative α entropy allows recovery of results for relative entropy and skew information as special cases. This provides some economy of expression but limited new physical insight.
4. Target state entanglement effects: The observation that entangled target states affect coherence differently depending on whether α∈(0,1) or α∈(1,2] is potentially interesting, suggesting measure-dependent behavior, but this is not explored deeply.
Timeliness & Relevance
The topic sits within an active research area—understanding the resource-theoretic underpinnings of quantum algorithms. However, the field has matured considerably, and incremental extensions using different coherence measures (from l₁ norm to relative entropy to Tsallis entropy) face diminishing returns in terms of new insights. The paper from 2026 follows a sequence of closely related works [69, 70, 71, 72, 73] that have largely established the main qualitative picture. The key question the community is moving toward—whether coherence (or any specific resource) is truly *necessary and sufficient* for quantum speedup—is not addressed here.
Strengths
Limitations
Overall Assessment
This is a technically competent but incremental contribution that extends the analysis of coherence dynamics in Grover's algorithm to the Tsallis relative α entropy measure. While the mathematics is correct and the treatment systematic, the paper does not substantially advance our understanding of why Grover's algorithm works or how coherence could be leveraged for new algorithmic advantages. The main results parallel those already established with simpler coherence measures.
Generated Apr 16, 2026
Comparison History (33)
Paper 2 likely has higher impact due to a more experimentally relevant and device-oriented proposal: nonreciprocal magnon-magnon entanglement in a realistic cavity-magnon platform (YIG + spinning WGM cavity), leveraging Kerr nonlinearity and Sagnac physics. It targets timely goals in quantum technologies (nonreciprocal components, robust entanglement) and claims thermal robustness (up to 100 mK), improving applicability. Paper 1 is more formal/analytical, refining coherence measures and complementarity in Grover’s algorithm, but its advances are narrower and less directly enabling new hardware or cross-field applications.
Paper 1 introduces a novel verification framework (Linear Chain Logic) for spatial/size-dependent properties of periodic MPS, leveraging CP-map transfer-operator structure and proposing scalable approximate model-checking with sound bounds and asymptotic analysis. This is methodologically and conceptually innovative, broadly relevant across quantum many-body physics, tensor networks, and formal methods, with clear potential applications to reliable analysis of large-system simulations. Paper 2 provides coherence/entropy relations for Grover’s algorithm using Tsallis measures—interesting but more incremental, narrower in scope, and with limited downstream methodological or cross-field impact.
Paper 2 addresses the emerging and highly relevant field of quantum batteries, linking battery capacity to a comprehensive set of quantum resources. Its focus on quantum energy storage offers clear future real-world applications in quantum thermodynamics, whereas Paper 1 presents a more specialized theoretical analysis of a specific entropy measure within an established algorithm.
Paper 1 is likely higher impact: it introduces a versatile, tunable generalized-measurement protocol for probe preparation starting from thermal states, directly targeting quantum sensing and thermometry with explicit QFI enhancement and an analytical link between QFI, susceptibilities, and Hamiltonian variance (broad relevance to quantum metrology and nonequilibrium thermodynamics). It also discusses experimental implementation (NMR), strengthening real-world applicability. Paper 2 analyzes coherence measures in Grover’s algorithm with complementarity relations; useful conceptually but more specialized, with limited immediate applications and less methodological/experimental depth.
Paper 1 addresses fundamental conceptual questions in quantum foundations regarding the Wigner's friend scenario and Frauchiger-Renner thought experiment, which have generated significant debate across the physics community. It offers novel philosophical and interpretive insights about subjective collapse, quantum erasure, and single-world vs many-world interpretations. Paper 2 provides a more incremental analysis applying a specific coherence measure (Tsallis relative α entropy) to Grover's algorithm. While technically sound, it is narrower in scope and less likely to influence broader debates. Paper 1's engagement with foundational interpretation questions gives it wider impact potential.
Paper 2 has higher potential impact due to its clearer real-world relevance (carbon fixation/formic acid chemistry, carbon footprint) and broader interdisciplinary reach (quantum algorithms + computational chemistry + quantum-inspired/classical methods). It targets timely challenges like near-term VQE and barren plateaus and proposes integrating a “discrete quantum exhaustive search” based on mutually unbiased bases into molecular analysis workflows. Paper 1 is more niche and primarily theoretical—refining coherence measures and relations within Grover’s algorithm—valuable but with narrower applications and incremental impact on quantum algorithm understanding.
Paper 1 presents a novel, scalable quantum framework for molecular generation with practical applications in drug discovery and materials science. It combines quantum circuit design with GPU-accelerated tensor-network simulation, demonstrating significant speedups and scalability to 40 heavy atoms. It addresses real-world problems (de novo generation, scaffold decoration, linker design) with methodological rigor. Paper 2 provides theoretical analysis of coherence dynamics in Grover's algorithm, which, while mathematically interesting, is more incremental and narrow in scope, analyzing well-studied quantum phenomena without clear practical applications.
Paper 2 is more likely to have higher scientific impact because it contributes quantitative, testable results on coherence dynamics in a widely used quantum algorithm (Grover), with clear applicability to quantum information processing and resource theories. It presents specific theorems (monotonicity with success probability, complementarity relations) that can be built upon in related algorithmic and experimental studies. Paper 1 is primarily interpretational/philosophical; while potentially influential conceptually, its impact is typically narrower and less directly actionable scientifically than new formal results tied to quantum computing practice.
Paper 1 is more novel and broadly impactful: it extends quantum thermodynamic resource theories to realistic equilibrium uncertainty, proves a sharp no-go theorem, and develops two battery models with exact one-shot and asymptotic characterizations, revealing new irreversibility phenomena (bound-thermo analogs) persisting under small uncertainty. This is timely and potentially foundational for nanoscale thermodynamics and experimental implementations with imperfect calibration. Paper 2 mainly analyzes coherence measures (Tsallis α) within a well-studied algorithm (Grover), yielding complementarity relations but with narrower conceptual and application scope and likely incremental impact.
Paper 1 addresses a critical infrastructure challenge for the highly anticipated quantum Internet (quantum memory dimensioning and EPR pair storage). Its focus on system design and practical architectural optimization provides broad, real-world applicability in quantum networking. In contrast, Paper 2 offers a niche, purely theoretical analysis of coherence dynamics in a specific algorithm, which, while rigorous, has a narrower scope and less immediate technological application.
Paper 2 is a comprehensive review of response theory for isolated quantum fields, covering fundamental topics like causality, spectral representations, fluctuation-dissipation relations, and conservation laws. Its broad scope spanning quantum field theory, nonequilibrium physics, and statistical mechanics gives it wider applicability and potential to serve as a reference work across multiple subfields. Paper 1, while technically sound, addresses a relatively narrow topic—coherence dynamics in Grover's algorithm using a specific entropy measure—with more limited breadth of impact.
Paper 2 addresses specific, measurable dynamics within Grover's search algorithm, a cornerstone of quantum computing. Its findings on coherence and entanglement have direct implications for quantum information processing and algorithm optimization, ensuring high relevance and practical impact. In contrast, Paper 1 presents an alternative, highly theoretical approach to quantum foundations that, while intellectually interesting, is likely to remain niche and have less immediate influence on active, applied research fields.
Paper 2 has higher potential impact due to its broader applicability and direct relevance to experimental quantum technologies. While Paper 1 offers a specific theoretical analysis of coherence in a well-established algorithm, Paper 2 provides a novel theoretical framework for inhomogeneous spin ensembles that yields exact expressions for fundamental limits like the quantum speed limit. Its explicit connection to the design of quantum components using NV centers, nuclear spins, or ultracold atoms gives it significant potential for real-world application and broader impact across both theoretical and experimental physics.
Paper 1 proposes a physical solution to valley degeneracy in silicon spin qubits, a critical hardware bottleneck in quantum computing. Its focus on strain engineering in SiGe heterostructures offers highly practical implications for building scalable quantum processors, bridging materials science and quantum engineering. Paper 2, while theoretically rigorous, focuses on a niche mathematical analysis (Tsallis entropy) of a well-established algorithm (Grover's), which is less likely to drive immediate technological breakthroughs. Therefore, Paper 1 has higher potential for real-world application and broader scientific impact.
Paper 2 is more likely to have higher scientific impact: it provides quantitative, testable results on coherence measures (Tsallis relative α-entropy) within a widely used quantum algorithm (Grover), linking coherence to success probability and entanglement. This is timely for quantum information science and can inform algorithm analysis, resource theories, and near-term experimental demonstrations. Paper 1 is conceptually interesting but primarily interpretive/metaphysical; its applications (e.g., Zeno paradox “resolution”) are less likely to drive broad, cumulative research uptake or practical advances compared to operationally grounded results in quantum computing.
Paper 2 bridges quantum measurement theory with classical image processing, offering a highly innovative, cross-disciplinary approach with immediate real-world applications in computer vision. Its quantum-inspired framework provides tunable parameters for image transformation, demonstrating practical utility. In contrast, Paper 1 presents a narrow, highly theoretical analysis of quantum coherence in a specific search algorithm, which, while rigorous, lacks the broader applicability and near-term impact potential of Paper 2.
Paper 1 is a comprehensive review covering entangled-photon photoemission and absorption, bridging quantum optics with materials science and spectroscopy. It addresses experimentally observed phenomena with broad applications in microscopy and spectroscopy (ETPFM, ETPS), and provides both theoretical models and experimental validation. Paper 2 offers a narrower contribution analyzing a specific coherence measure in Grover's algorithm, which, while mathematically interesting, has more limited scope and practical impact. Paper 1's breadth across quantum optics, photonics, and spectroscopy gives it significantly wider potential influence.
Paper 2 has higher potential impact: it introduces a general, structural reachability constraint for variational quantum algorithms, clarifying when exact ground states are unattainable without prior module-weight information. This is novel and timely given widespread VQA use, and it yields actionable implications (identifying regimes with efficient classical surrogates, e.g., matchgates/MaxCut) that affect algorithm design, benchmarking, and claims of quantum advantage across multiple domains (quantum algorithms, complexity, simulation). Paper 1 is a solid, rigorous resource-theoretic analysis but is narrower (Grover-specific coherence metrics) with more limited cross-field applicability.
Paper 1 addresses a fundamental question in quantum optics—the conditions under which independent two-level emitters produce thermal light statistics—providing rigorous analytical conditions (Gaussian Moment Theorem criteria) with broad relevance to cold atom experiments and photon statistics. Paper 2 studies coherence dynamics in Grover's algorithm using a specific entropic measure, which is more incremental and narrower in scope, primarily extending known coherence-algorithm relationships to Tsallis entropy without clear new algorithmic insights or experimental implications.
Paper 1 has higher potential impact: it targets quantum information/algorithms and provides quantitative coherence–success-probability relations in Grover search, a foundational algorithm with ongoing relevance for resource theories and algorithm design/analysis. Its results could influence broader studies of quantum resources (coherence/entanglement) and practical benchmarking of search implementations. Paper 2 is elegant and rigorous but is primarily a conceptual/educational bridge between solvable quantum systems and the Wallis formula, with narrower direct applicability and likely more limited cross-field uptake.