Coherence distillation machines are impossible in quantum thermodynamics

Abstract

The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence of a coherence distillation machine, i.e., a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This is related to another fundamental question: Starting from many copies of noisy quantum clocks which are (approximately) synchronized with a reference clock, can one distill synchronized clocks in pure states, at a non-zero rate? Surprisingly, we find that the answer to both questions is negative for generic (full-rank) mixed states. However, at the same time, it is possible to distill a sub-linear number of pure coherent states with a vanishing error.

Close to the published version. 10 pages (3 Figures) + 42 pages of Supplementary Material

References in corpus (16)

• Quantum Resource Theories
• Distillation of secret key and entanglement from quantum states
• Reference frames, superselection rules, and quantum information
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Observable measure of quantum coherence in finite dimensional systems
• Quantum critical scaling of the geometric tensors
• The resource theory of quantum reference frames: manipulations and monotones
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Quantum criticality as a resource for quantum estimation
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Bures metric over thermal state manifolds and quantum criticality
• Relating quantum privacy and quantum coherence: an operational approach
• Generic bound coherence under strictly incoherent operations
• One-Shot Coherence Distillation: Towards Completing the Picture
• Completing the Grand Tour of asymptotic quantum coherence manipulation
• Units of rotational information

Cited by in corpus (24)

• Coherence effects in the performance of the quantum Otto heat engine
• No-Go Theorems for Quantum Resource Purification
• On the Role of Coherence in Shor's Algorithm
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Geometric distinguishability measures limit quantum channel estimation and discrimination
• New perspectives on covariant quantum error correction
• Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices
• Coherence cost for violating conservation laws
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Approximate symmetries and quantum error correction
• Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems
• Partial order on passive states and Hoffman majorization in quantum thermodynamics
• Dynamics of coherence: Maximal quantum Fisher information vs. Loschmidt echo
• Wigner-Araki-Yanase theorem for continuous and unbounded conserved observables
• Fisher information matrix as a resource measure in resource theory of asymmetry with general connected Lie group symmetry
• Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies
• Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma
• Smooth Metric Adjusted Skew Information Rates
• Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information
• Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
• Coordinately Assisted Distillation of Quantum Coherence in Multipartite System
• Coherence revival under the Unruh effect and its metrological advantage
• Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics