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This study establishes an analytical framework for optimal quantum transport by generalizing classical Monge theory using density matrices and completely positive maps. By introducing the "stote" mathematical object, researchers demonstrate a fundamental qualitative difference between resource distribution in quantum versus classical systems. This work advances the theoretical foundations of quantum information processing and thermodynamics without relying on experimental data.

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Researchers calculate optimal quantum transport analytically

Quantum ZeitgeistOctober 14, 20264 min read

Researchers calculated costs for quantum transport, generalizing classical theory with density matrices and completely positive maps.

Matt Hoogsteder-Riera, John Calsamiglia, and Andreas Winter have calculated optimal quantum transport analytically by generalizing a classical cost theory. The researchers built on Monge’s classical work, replacing probability densities with and transport plans with “completely positive and trace preserving maps”. This work introduces a mathematical object called a “stote”, a combination of quantum state and process, to integrate these elements. The team demonstrates that this quantum transport cost differs from its classical counterpart, suggesting a fundamental departure in understanding…

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