Advantage of flexible catalysis for entanglement and quantum thermodynamics

Abstract

Understanding the fundamental limits of state convertibility is crucial for establishing the boundaries of quantum information processing and thermodynamic efficiency. While auxiliary systems, catalysts, can facilitate otherwise impossible transformations, standard catalysis rigidly requires the auxiliary system to return to its exact initial state. In this work, we investigate the power of flexible catalysis, where the catalyst evolves through a cycle of states, restoring its initial configuration only after a finite number of steps. Focusing on the regime of fixed, finite dimensions, we analyze the capabilities of flexible catalysis within the resource theories of entanglement and quantum thermodynamics. In the context of entanglement, we derive conditions limiting flexible catalysts and demonstrate that they offer a strict advantage in the success probability of stochastic local operations and classical communication. Conversely, in quantum thermodynamics, we prove that flexible catalysis strictly outperforms standard catalysis even in deterministic settings. We provide an example identifying state transformations that are impossible with any standard catalyst of fixed dimension and Hamiltonian but become achievable via a flexible cycle.

Figures (2)

• Figure 1: Success probability landscape for a 2-step flexible catalysis of $k=2$. The heatmap illustrates $P_{\text{flex}}$ as a function of the catalyst parameters $c_1$ and $c_2$ for the transformation $\vec{x} \to \vec{y}$. The dashed diagonal line marks the regime of standard catalysis ($c_1 = c_2$), where the maximum value is $P_{\text{std}} \approx 0.730$. The global maximum $P_{\text{flex}} \approx 0.767$ is achieved at an off-diagonal position (green star), proving the existence of a strict advantage $P_{\text{flex}} > P_{\text{std}}$.
• Figure 2: Solution landscapes for flexible thermo-majorization. Parameter space of a 2-cycle flexible catalyst pair $(c_1, c_2)$ for the transition $\vec{p} \to \vec{q}$. (a) For a non-trivial catalyst Hamiltonian $E_C=\{0,1\}$, a valid solution space (green region) exists off the diagonal ($c_1 \neq c_2$). The dashed diagonal line representing standard catalysis does not intersect this region. (b) For a degenerate Hamiltonian $E_C=\{0,0\}$, the valid region is empty.

Theorems & Definitions (23)

• Definition 1: Flexible Catalysis
• Theorem 1
• proof
• Conjecture 1
• Theorem 2
• Theorem 3: Equivalence of Thermodynamic Transitions PRXQuantum.3.040323Gour_2025
• Theorem 4
• Lemma 1
• proof
• Theorem 5