Accessible Quantum Correlations Under Complexity Constraints
Álvaro Yángüez, Noam Avidan, Jan Kochanowski, Thomas A. Hahn
Abstract
Quantum systems may contain underlying correlations which are inaccessible to computationally bounded observers. We capture this distinction through a framework that analyses bipartite states only using efficiently implementable quantum channels. This leads to a complexity-constrained max-divergence and a corresponding computational min-entropy. The latter quantity recovers the standard operational meaning of the conditional min-entropy: in the fully quantum case, it quantifies the largest overlap with a maximally entangled state attainable via efficient operations on the conditional subsystem. For classical-quantum states, it further reduces to the optimal guessing probability of a computationally bounded observer with access to side information. Lastly, in the absence of side information, the computational min-entropy simplifies to a computational notion of the operator norm. We then establish strong separations between the information-theoretic and complexity-constrained notions of min-entropy. For pure states, there exist highly entangled families of states with extremal min-entropy whose efficiently accessible entanglement in terms of computational min-entropy is exponentially suppressed. For mixed states, the separation is even sharper: the information-theoretic conditional min-entropy can be highly negative while the complexity-constrained quantity remains nearly maximal. Overall, our results demonstrate that computational constraints can fundamentally limit the quantum correlations that are observable in practice.
AI Impact Assessments
(3 models)Scientific Impact Assessment
1. Core Contribution
This paper develops a unified framework for quantifying quantum correlations accessible to computationally bounded observers. The central objects are a computational max-divergence (Definition C.1) induced by a cone of efficiently implementable Choi operators, and a corresponding computational conditional min-entropy (Definition II.1). The key insight is to replace the full set of quantum channels with those implementable by polynomial-size circuits, then study the resulting restricted order structure on bipartite states.
The framework accomplishes three main goals: (i) it recovers the operational meaning of conditional min-entropy—maximal fidelity with a maximally entangled state via efficient operations on the conditioning system (Theorem II.2); (ii) for classical-quantum states, it reduces to optimal guessing probability under efficient measurements (Lemma II.3); (iii) it establishes strong separations between information-theoretic and computational min-entropy for both pure and mixed states (Theorems III.1–III.3).
The paper also unifies two previously separate lines of work: the computational conditional entropies of Avidan et al. [12, 13] and the efficient-measurement framework of Yángüez et al. [14], showing both arise from the same cone-theoretic construction.
2. Methodological Rigor
The mathematical framework is carefully constructed and technically sound. The cone-theoretic approach is clean: defining the set of efficient Choi operators, forming its conic hull, establishing it as a proper cone under an informational completeness condition (Lemma B.15), and deriving the dual cone and associated partial order. The proof of the main operational theorem (Theorem C.11) uses conic programming duality with explicit verification of Slater's condition, which is rigorous.
The separation results are proven through a combination of representation-theoretic tools (Schur-Weyl duality, entanglement concentration protocols) and probabilistic arguments (Haar-random states, Markov inequality, union bounds). The pure-state separation (Theorem D.5) adapts the Hayashi-Schur concentration protocol via a nontrivial channel reduction lemma (Lemma D.1), while the mixed-state separation (Theorem D.7) uses the generalized Hilbert-Schmidt ensemble with careful moment calculations. Both constructions are technically involved and appear correct.
A notable subtlety: the separations are existential (probabilistic method over Haar measure) rather than constructive, which the authors openly acknowledge as a limitation and direction for future work.
3. Potential Impact
Quantum cryptography: The connection to guessing probability (Lemma II.3) and pseudorandomness extraction [12] gives immediate cryptographic relevance. The framework formalizes when quantum side information is computationally useless, directly relevant to security proofs against bounded adversaries.
Quantum many-body physics: The observation that complexity constraints limit observable entanglement connects to tensor network methods, area laws, and the practical inaccessibility of entanglement in large systems. The mixed-state result (Theorem III.3), showing states can appear maximally uncorrelated to efficient observers despite extensive entanglement, has conceptual implications for many-body physics and potentially for AdS/CFT, where the role of complexity beyond entanglement is debated.
Computational entanglement theory: The paper complements recent work by Leone et al. [16] on computational entanglement cost/distillation, but from the entropy rather than resource-conversion perspective. This provides an independent lens on the same underlying phenomena.
Complexity-constrained thermodynamics: The entropic quantities defined here could feed into one-shot thermodynamic protocols under complexity constraints [17, 22, 23].
4. Timeliness & Relevance
The paper addresses a highly active area at the intersection of quantum information theory and computational complexity. The emergence of pseudoentanglement [5, 6, 11], computational entanglement theory [10, 16], and complexity-constrained resource theories [17, 22, 23] in the past 2-3 years makes this contribution timely. The unification of frameworks from [12-14] is particularly valuable as the field is rapidly producing related but disconnected formalisms.
5. Strengths & Limitations
Strengths:
Limitations:
6. Additional Observations
The paper is well-written for its technical density, with the main text providing accessible summaries and the supplementary material containing full proofs. The figure effectively communicates the conceptual framework. The connection between the cone structure and operational meaning is made transparent. However, the paper would benefit from more discussion of concrete applications where the separations manifest.
Generated Apr 20, 2026
Comparison History (41)
Paper 2 is more conceptually novel, introducing complexity-constrained divergences/min-entropy and proving strong separations between information-theoretic and efficiently accessible correlations. This creates broadly applicable theoretical tools impacting quantum information, cryptography, complexity theory, and foundations, with timeliness given practical limits on quantum operations. While Paper 1 is timely and practically relevant (energy modeling for NISQ/FTQC in HPC) and may influence engineering choices, its impact is likely narrower and more contingent on specific platforms/workloads. Paper 2’s framework and separations are likelier to generalize and be cited across fields.
Paper 1 is more conceptually novel and broadly impactful: it introduces a complexity-constrained entropy/divergence framework tying quantum correlations to computationally bounded observers, with strong separations from information-theoretic notions. This can influence quantum information theory, cryptography, complexity theory, and interpretations of “observable” entanglement. Paper 2 targets an important applied NISQ problem (scalable noise modeling/mitigation) but appears more incremental and simulation-heavy, with impact depending on experimental validation and comparative benchmarks. Overall, Paper 1 has higher cross-field, long-term scientific impact potential.
Paper 1 introduces a broadly applicable complexity-constrained information-theoretic framework (computational max-divergence/min-entropy) with strong separation results showing practical limits on observable quantum correlations. This is conceptually novel, methodologically rigorous, and relevant to quantum cryptography, complexity theory, and foundations, giving wide cross-field impact. Paper 2 targets an interpretable variational quantum regression model with encoding tricks and sample-complexity discussion, but likely faces near-term practicality limits (data loading/encoding overheads, NISQ constraints) and is narrower in scope, with innovation more incremental within QML.
Paper 2 bridges quantum information theory and computational complexity by introducing the concept of computational min-entropy. Its demonstration that computational limits fundamentally restrict observable quantum correlations has profound implications for quantum cryptography, computing, and thermodynamics. While Paper 1 provides valuable methods for engineering non-Hermitian systems, Paper 2 addresses a fundamental theoretical problem with broader, cross-disciplinary applicability and higher potential impact in the rapidly advancing field of quantum technologies.
Paper 1 is more novel and broadly impactful: it introduces complexity-constrained quantum information measures (max-divergence/min-entropy) with clear operational meanings and proves strong separations from information-theoretic quantities, implying fundamental limits on observable entanglement under efficient operations. This connects quantum information, complexity theory, and cryptography, potentially influencing multiple subfields and motivating new computationally grounded resource theories. Paper 2 is rigorous and application-driven, but largely extends established Rydberg-EIT sensing tools (FI/CRLB, cavity enhancement) to low-frequency fields; its impact is likely narrower and more incremental.
Paper 2 has higher potential impact due to its broader conceptual reach and applicability: it introduces a complexity-constrained framework for quantifying “accessible” quantum correlations, connecting quantum information to computational complexity and yielding strong separations between information-theoretic and efficient-access notions. This is timely for near-term quantum technologies where operational limitations matter, and it could influence cryptography, complexity theory, resource theories, and experimental interpretations of entanglement. Paper 1 is novel and relevant for quantum metrology/geometry but is more specialized and likely to affect a narrower community.
Paper 1 bridges quantum information theory and computational complexity, demonstrating that theoretical quantum correlations may be practically inaccessible. This fundamental insight has broad implications across quantum cryptography, quantum computing, and thermodynamics. In contrast, Paper 2, while methodologically rigorous and valuable for quantum error correction theory, is highly specialized in algebraic coding and symmetry groups, likely resulting in a narrower scope of scientific impact.
Paper 2 likely has higher impact due to clear, near-term experimental relevance and broad applicability: deterministic, high-purity few-/multi-photon sources are enabling technology for quantum networking, photonic computing, metrology, and boson-sampling-like platforms. The approach is concrete (cavity-QED with engineered interference and tunable interactions), offers strong performance claims (orders-of-magnitude purity/emission improvements), and suggests scalability/programming of effective nonlinearities. Paper 1 is conceptually novel for complexity-limited quantum correlations, but its impact is more theoretical and may diffuse more slowly without immediate experimental pathways.
Paper 2 addresses a critical, immediate bottleneck in the field of quantum computing: scheduling and executing hybrid workflows on current cloud infrastructure. By optimizing both queue times and circuit fidelity across major heterogeneous providers, Qurator offers immense practical utility that will accelerate experimental research across the entire quantum computing community. While Paper 1 provides a strong, foundational contribution to quantum information theory, Paper 2 has much broader near-term applicability, timeliness, and potential to impact a wider range of interdisciplinary domains utilizing quantum-HPC integration.
Paper 1 experimentally demonstrates fundamental quantum phenomena (a molecular quantum eraser) bridging ultrafast light-matter interactions with quantum information science. This tangible experimental breakthrough, supported by numerical validation, offers broad applicability and methodological innovation. While Paper 2 presents a strong theoretical framework for quantum complexity, Paper 1's experimental realization of complex quantum states in molecular dynamics is likely to have a wider, more immediate scientific impact across multiple physics disciplines.
Paper 2 introduces a novel theoretical framework bridging quantum information theory and computational complexity, establishing strong separations between information-theoretic and complexity-constrained entropies. This has broad implications for quantum cryptography, quantum computing, and complexity theory. Its operational interpretations (guessing probability, entanglement distillation under efficiency constraints) provide concrete applications. Paper 1 offers an interesting reinterpretation of boson correlations via Simpson's paradox, but its impact is narrower, primarily reframing known physics rather than establishing new fundamental limitations. Paper 2's interdisciplinary reach and foundational contributions give it higher potential impact.
Paper 2 introduces a novel theoretical framework connecting quantum information theory with computational complexity, establishing fundamental separations between information-theoretic and complexity-constrained quantum correlations. This bridges quantum cryptography, complexity theory, and quantum information in a broadly impactful way. Paper 1 addresses an important but incremental engineering problem—calibrating flux control lines for superconducting qubits using digital predistortion filters. While practically useful, it represents an engineering refinement rather than a conceptual advance. Paper 2's foundational insights have broader potential to influence multiple research directions.
Paper 2 introduces a fundamental theoretical framework bridging quantum information theory and computational complexity. By defining complexity-constrained min-entropy, it establishes broadly applicable limits on practically observable quantum correlations, which could significantly impact quantum computing, cryptography, and thermodynamics. In contrast, Paper 1 offers a highly specialized theoretical proposal for improving precision force sensing in a specific hybrid magnomechanical setup, which, while valuable for metrology, has a much narrower scope and field of impact.
Paper 1 introduces a broadly applicable framework for “accessible” quantum correlations under computational constraints, defining complexity-constrained divergences/min-entropy and proving strong separations from information-theoretic quantities. This is conceptually novel, timely for quantum complexity/cryptography/foundations, and likely to influence multiple areas (resource theories, operational entanglement, security with bounded adversaries, practical limits of correlation detection). Paper 2 is a useful, modular NISQ-era technique for excited-state calculations with symmetry screening, but is more incremental and narrower in scope (quantum chemistry/VQE methods) and its long-term impact may be constrained by hardware and competing algorithms.
Paper 2 offers a highly practical, timely solution to a critical bottleneck in fault-tolerant quantum computing. By demonstrating a 30-97% reduction in physical resource requirements, it provides immediate, quantifiable value to quantum compiler design and engineering. While Paper 1 presents profound theoretical bounds bridging complexity and quantum information, Paper 2's direct applicability to real-world quantum system optimization suggests a higher and more immediate broader impact across the rapidly growing quantum hardware and software ecosystem.
Paper 2 bridges quantum information theory and computational complexity, offering fundamental insights into the practical accessibility of quantum correlations. This framework has broad implications for quantum cryptography, entanglement theory, and practical quantum computing. Paper 1, while useful for heterogeneous quantum error correction, represents a more specialized advancement in coding theory with a narrower scope of impact.
Paper 1 has higher potential impact due to stronger novelty and cross-field breadth: it introduces complexity-constrained quantum information measures (max-divergence/min-entropy) with clear operational meanings, and proves strong separations between information-theoretic and efficiently accessible correlations—results relevant to quantum cryptography, complexity theory, resource theories, and practical quantum verification. Its applications to bounded adversaries and “observable” entanglement are timely for near-term quantum tech. Paper 2 provides a compelling finite-time thermodynamics bound and optimization insights, but likely impacts a narrower community (stochastic/quantum thermodynamics) and appears more incremental relative to existing information-geometry trade-off literature.
Paper 1 combines two highly relevant and rapidly growing fields: differential privacy and quantum computing. Its focus on answering counting queries offers clear, practical real-world applications for privacy-preserving data analysis and secure quantum server outsourcing. While Paper 2 provides important theoretical insights into quantum correlations under complexity constraints, Paper 1 has broader cross-disciplinary appeal and greater potential for immediate real-world technological impact.
Paper 1 bridges quantum computing and differential privacy, two highly relevant and rapidly growing fields. By providing concrete mechanisms for differentially private counting queries, it offers clear potential for real-world applications in secure data analysis and quantum cloud computing. While Paper 2 presents profound theoretical insights into quantum information and complexity, Paper 1's cross-disciplinary appeal, practical utility, and timeliness give it a higher potential for broad scientific and societal impact.
Paper 2 introduces a novel theoretical framework connecting quantum information theory with computational complexity, establishing fundamental separations between information-theoretic and complexity-constrained quantum correlations. This bridges quantum information, complexity theory, and cryptography in a foundational way with broad implications (e.g., quantum cryptography, entanglement theory, pseudorandomness). Paper 1 presents an incremental improvement to semi-quantum signature protocols with practical but narrower scope. Paper 2's conceptual depth, mathematical rigor, and cross-disciplinary relevance give it substantially higher potential impact.