Hierarchy of Qubit Dynamical Maps in the Presence of Symmetry and Coherence

• URL: http://arxiv.org/abs/2509.04790v1
• Date: Fri, 05 Sep 2025 04:04:34 GMT
• Title: Hierarchy of Qubit Dynamical Maps in the Presence of Symmetry and Coherence
• Authors: Unnati Akhouri,
• Abstract summary: We prove that U(1) conservation constrains quantum thermodynamic operations through charge conservation of Pauli strings.<n>Our no-go theorem shows that U(1) dynamics cannot generate local coherence from diagonal thermal states.<n>We demonstrate measurable thermodynamic advantages in work extraction and state distinguishability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the relationship between symmetries and thermodynamic transformations by analyzing how global energy conservation and coherence resources affect the local dynamics of subsystems. We prove that U(1) conservation fundamentally constrains quantum thermodynamic operations through charge conservation of Pauli strings. Our no-go theorem shows that U(1) dynamics cannot generate local coherence from diagonal thermal states, restricting thermal operations to phase-covariant maps. Breaking this hierarchy requires environmental coherence with odd charge parity that couples unequal energy states. We establish the minimal resource requirements through a two-qubit construction that achieves Gibbs-preserving transformations beyond thermal operations. We demonstrate measurable thermodynamic advantages in work extraction and state distinguishability, revealing the fundamental role of quantum coherence in enhancing thermodynamic performance.

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