Accessible Quantum Correlations Under Complexity Constraints

• URL: http://arxiv.org/abs/2604.15540v1
• Date: Thu, 16 Apr 2026 21:45:36 GMT
• Title: Accessible Quantum Correlations Under Complexity Constraints
• Abstract summary: We show that computational constraints can fundamentally limit the quantum correlations that are observable in practice.<n>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.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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