Accessible Quantum Correlations Under Complexity Constraints

2026-04-16

AI Summary

This work addresses the gap between theoretical predictions and experimentally accessible quantities in quantum systems, arising from observers’ limited computational power, which prevents full detection of underlying correlations. The authors propose a complexity-constrained framework based on minimal entropy and maximal divergence, characterizing practically accessible bipartite correlations using only efficiently implementable quantum channels. Key contributions include demonstrating an exponential decay of observable entanglement under computational constraints, showing that while the information-theoretic conditional min-entropy of mixed states can be extremely negative, its computationally bounded counterpart remains close to maximal, and establishing a strong separation between computational and information-theoretic measures of correlation—both for pure and mixed quantum states.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Large-scale security measurements
• Social Networks and Social Media: Computational social science
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation

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.

Problem

• quantum correlations
• computational constraints
• min-entropy
• accessible entanglement
• complexity-constrained

Innovation

• computational min-entropy
• complexity-constrained quantum correlations
• efficiently implementable quantum channels
• max-divergence
• accessible entanglement