Impossibility of universal work extraction from coherence: Reconciling axiomatic and resource-theory approaches (2404.07786v1)

Abstract: We compare how the impossibility of a universal work extractor from coherence arises from different approaches to quantum thermodynamics: an explicit protocol accounting for all relevant quantum resources, and axiomatic, information-theoretic constraints imposed by constructor theory. We first explain how the impossibility of a universal work extractor from coherence is directly implied by a recently proposed constructor-theoretic theorem based on distinguishability, which is scale- and dynamics- independent. Then we give an explicit demonstration of this result within quantum theory, by proving the impossibility of generalising a proposed quantum protocol for deterministically extracting work from coherence. We demonstrate a new connection between the impossibility of universal work extractors and constructor-based irreversibility, which was recently shown using the quantum homogenizer. Finally we discuss additional avenues for applying the constructor-theoretic formulation of work extraction to quantum thermodynamics, including the irreversibility of quantum computation and thermodynamics of multiple conserved quantities.

• The paper establishes that universal work extraction from quantum coherence is impossible within both resource-theory and constructor-theory frameworks.
• It demonstrates that deterministic work extraction requires orthogonal initial states due to the inherent limitations in distinguishing non-orthogonal states, leading to the work-locking phenomenon.
• The analysis paves the way for extending quantum thermodynamic principles to other conserved quantities and unifying disparate theoretical approaches.

Overview of "Impossibility of Universal Work Extraction from Coherence: Reconciling Axiomatic and Resource-theory Approaches"

This paper examines two prominent frameworks in quantum thermodynamics—resource theories and constructor theory—to address the challenges in universal work extraction from quantum coherence. The authors, Plesnik and Violaris, explore the intricacies of these frameworks to understand the limitations of work extraction protocols in quantum systems, grounding their investigation in both dynamical and axiomatic thermodynamics.

Key Contributions

The paper's primary contribution is establishing the impossibility of devising a universal work extraction mechanism from quantum coherence within the frameworks of both resource theories and constructor theory. The authors explore and compare these approaches:

1. Resource Theories vs. Constructor Theory: The paper contrasts the resource-theoretic and constructor-theoretic views on thermodynamics. Resource theories focus on transformations permissible under existing physical laws and are instrumental in quantifying resources such as coherence. Conversely, constructor theory posits a more foundational perspective, emphasizing possible and impossible tasks without presupposing specific dynamical laws.
2. Theorem on Distinguishability: A crucial result from the constructor-theoretic framework is that deterministic work extraction demands initial quantum states to be orthogonal, as inferred from a dynamics-independent theorem. This restriction stems from the inability to perfectly distinguish non-orthogonal states in a single shot, thereby constraining universal work extraction processes.
3. Analysis of Work-locking Phenomenon: The authors address the "work-locking" phenomenon, wherein the additional free energy in coherent states is not accessible without auxiliary coherent resources. By analyzing a proposed protocol for work extraction \cite{korzekwa2016extraction}, they demonstrate its failure to generalize across non-orthogonal input states, supporting their impossibility theorem.
4. Implications of Quantum Homogenizers: They explore the potential of quantum homogenizers as a candidate for constructing devices capable of approximating the task under discussion. The results indicate that even with the introduction of sophisticated resources like homogenizers, transforming arbitrary mixed to pure states remains constructor-theoretically impossible, reinforcing the constraints established by their theorem.

Implications and Future Directions

The implications of this research are significant for theoretical advancements in quantum thermodynamics and practical quantum computing:

• Entropy and Irreversibility: The constraints indicate fundamental limits on entropy changes in non-classical computation tasks, hinting at an underlying form of irreversibility. Future research could further explore the intersection of these constraints with known limits like Landauer's principle, potentially yielding a broader framework for understanding the irreversibility inherent in quantum computation.
• Extension to General Conserved Quantities: The paper suggests that the approach could facilitate the extension of thermodynamic principles to other conserved quantities beyond energy. This could unravel new connections between distinct resources conserved in quantum systems and unify current isolated observations under a broader thermodynamic perspective.
• Potential for Unification: By illustrating converging conclusions from disparate frameworks, this work paves the way for reconciling resource-theoretic and axiomatic approaches with constructive principles, moving towards a cohesive theory of quantum thermodynamics.

This paper thus advances our understanding of the theoretical limitations inherent in quantum resource manipulation and sets a foundation for further inquiry into both the fundamental laws governing quantum systems and their practical utility in emerging quantum technologies.