Operational impact of quantum resources in chemical dynamics

Abstract

Quantum coherence and other non-classical features are widely discussed in chemical dynamics, yet it remains difficult to quantify when such resources are operationally relevant for a given process and observable. While quantum resource theories provide a comprehensive framework for comparing free and resourceful settings, existing approaches typically rely on resource monotones or on performance bounds under free operations, and do not directly quantify the maximal influence a chosen resource can exert on a fixed chemical dynamics. Here, we introduce task specific, process level quantifiers that upper bound the largest change a quantum resource can induce in a target figure of merit. Central is a resource impact functional $\mathcal{C}_M(Λ)$, defined by comparing a state with its paired resource-free counterpart under the same quantum channel $Λ$, which admits an operational interpretation in binary hypothesis testing. We derive variation and time bounds that constrain how rapidly a resource can modify a target signal, providing resource-aware analogues of quantum speed limits. Moreover, we show that open system dynamics can be decomposed into free and resourceful components such that only the resourceful component contributes to $\mathcal{C}_M(Λ)$, thereby isolating the parts of a generator responsible for resource-induced changes in the observable. We illustrate the framework exemplary for energy transfer in a donor-acceptor dimer in two analytically solvable regimes. Our results provide a general toolbox for diagnosing and benchmarking quantum resource effects in molecular processes.

Figures (5)

• Figure 1: Schematic illustration of the geometric picture behind the post-processing bound in Eq. \ref{['eq:CM-postprocessing']} and Corollary \ref{['cor:capacity-geometry']}. (See main text for details.)
• Figure 2: Schematic illustration of the uniform time and feasibility bounds in Corollary \ref{['cor:time-bound']}. The horizontal axis shows the evolution time $\Delta\tau$ and the vertical axis the change $|\Delta\mathcal{C}_M|$. For a uniform generator bound $\|\mathcal{L}_s\|_{1\to 1}\le L_{\max}$, the light and dark gray regions below the line $|\Delta\mathcal{C}_M| = c_{M,\mathcal{G}}L_{\max}\Delta\tau$ contain all admissible pairs. A time budget $T_{\max}$ limits the achievable change to $|\Delta\mathcal{C}_M|\leq T_{\max}c_{M,\mathcal{G}}L_{\max}$ (dark gray), while a target change $\Delta\mathcal{C}_M^*$ defines a minimal time $\Delta\tau^*$ via Eq. \ref{['eq:min-time']}.
• Figure 3: Illustration of the three-site donor-acceptor model and the three processes described by the quantum channel in Eq. \ref{['eq:Lambda-conc']} (see text for more details).
• Figure 4: Illustration of the coherence-induced task advantage and its variation bound in the donor--acceptor model. We plot the exact task advantage $|\Delta\mathcal{C}_M|$ (dark red) and the integrated variation bound $\int_0^t\Gamma_M(s)\,\mathrm{d}s$ (light red) from Theorem \ref{['thm:variation-bound']} for $M = |A\rangle\!\langle A|$, starting at $t_1=0$, for parameters $\Delta=130$, $J=100$, and $\gamma=5$ (in arbitrary but consistent units).
• Figure 5: Change in the coherence-induced resource impact functional in the donor-acceptor model for zero detuning and $J=100$, $\gamma=5$. We plot the exact change $|\Delta\mathcal{C}_M|$ for $M=\hbox{$| A \rangle$}\!\hbox{$\langle A |$}$ (dark red solid: underdamped with $\gamma_\varphi=50$; dark blue dashed: overdamped with $\gamma_\varphi=500$), the corresponding variation bounds $\int_0^t\Gamma_M(s)\,\mathrm{d}s$ (medium red solid/medium blue dashed), and the analytic uniform bounds from Eq. \ref{['eq:DC-Zdet']} (light red solid/light blue dashed). We choose $t_1=0$ such that $\Delta\tau = t_2$.

Theorems & Definitions (23)

• Theorem 1
• Corollary 2
• Theorem 3
• Theorem 4
• Corollary 5
• Corollary 6: Polar characterization of $\mathcal{C}_M(\Lambda)$
• Theorem 7: Variation bound and Dini derivatives
• Lemma 8
• Corollary 9: Time and feasibility bounds
• Theorem 10: Decomposition with respect to a resource-destroying map