Accessible Quantum Correlations Under Complexity Constraints

Quantum Physics [Submitted on 16 Apr 2026] Accessible Quantum Correlations Under Complexity Constraints Álvaro Yángüez, Noam Avidan, Jan Kochanowski, Thomas A. Hahn 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. Comments: Main paper: 6 pages, 1 figure. Supplementary material: 45 pages Subjects: Quantum Physics (quant-ph); Computational Complexity (cs.CC); Information Theory (cs.IT) Cite as: arXiv:2604.15540 [quant-ph]   (or arXiv:2604.15540v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.15540 Focus to learn more Submission history From: Alvaro Yángüez [view email] [v1] Thu, 16 Apr 2026 21:45:36 UTC (195 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.CC cs.IT math math.IT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)