Problem
Research questions and friction points this paper is trying to address.
Quantum information
Local state transformation
Non-interacting subsystems
Impossibility of Local State Transformation via Hypercontractivity
🤖 AI Summary
This study addresses the feasibility and fundamental limitations of deterministic quantum state transformations under local operations in multipartite systems without direct interactions. To tackle local irreversibility, we systematically introduce the theory of hypercontraction and establish a quantitative information-decay criterion based on the hypercontraction constant. Employing hypercontraction inequalities, quantum channel analysis, entropy methods, and operator norm estimates, we rigorously prove the impossibility of deterministic local quantum operations converting several paradigmatic entangled states—including pure states of varying dimensions, W states, and GHZ-type states. Our results uncover an intrinsic connection between the depth of information erasure and the hypercontraction constant, thereby providing a novel inconvertibility criterion and an analytical framework for quantum resource theory. This work advances the understanding of locality-induced constraints on quantum state manipulation and offers a principled tool for assessing transformation capabilities in distributed quantum systems.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Quantification of Limits
Non-Interacting System Transformations
Computational Methods
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