Coherent fluctuation relations: from the abstract to the concrete

Holmes, Zoë; Weidt, Sebastian; Jennings, David; Anders, Janet; Mintert, Florian

doi:10.22331/q-2019-02-25-124

Cited by 33 publications

(49 citation statements)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The coherent fluctuation theorems we develop go beyond traditional relations, such as the Crooks relation, and allow the analysis of quantum coherence in a noisy thermal environment. Because quantum coherence is handled explicitly this also leads to connections to many-body entanglement and our results provide a clean explanatory framework for recent experimental proposals in trapped ion systems [25].…”

Section: Introductionmentioning

confidence: 60%

“…Firstly, it leads to a notion of decomposable and non-decomposable coherence and has an immediate description in terms of recent frameworks for quantum coherence [8-11, 17, 18]. We then extend these considerations in noisy quantum environments and show that this notion of a coherent work process connects naturally with fluctuation relations [19][20][21][22][23][24][25][26]. The coherent fluctuation theorems we develop go beyond traditional relations, such as the Crooks relation, and allow the analysis of quantum coherence in a noisy thermal environment.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Decomposable coherence and quantum fluctuation relations

Mingo

Jennings

2019

Quantum

Self Cite

View full text Add to dashboard Cite

In Newtonian mechanics, any closed-system dynamics of a composite system in a microstate will leave all its individual subsystems in distinct microstates, however this fails dramatically in quantum mechanics due to the existence of quantum entanglement. Here we introduce the notion of a `coherent work process', and show that it is the direct extension of a work process in classical mechanics into quantum theory. This leads to the notion of `decomposable' and `non-decomposable' quantum coherence and gives a new perspective on recent results in the theory of asymmetry as well as early analysis in the theory of classical random variables. Within the context of recent fluctuation relations, originally framed in terms of quantum channels, we show that coherent work processes play the same role as their classical counterparts, and so provide a simple physical primitive for quantum coherence in such systems. We also introduce a pure state effective potential as a tool with which to analyze the coherent component of these fluctuation relations, and which leads to a notion of temperature-dependent mean coherence, provides connections with multi-partite entanglement, and gives a hierarchy of quantum corrections to the classical Crooks relation in powers of inverse temperature.

show abstract

Section: Introductionmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Decomposable coherence and quantum fluctuation relations

Mingo

Jennings

2019

Quantum

Self Cite

View full text Add to dashboard Cite

show abstract

“…This raise the difficulty of a fair comparison between the forward and backward transitions in the same scale. In order to handle this, the coefficients of a density matrix can be weighted differently based on the distribution of the reference states, which we call the reference-rescaling [52,65,66]. In particular, we can choose the rescaling operations (denoted as ∼) for the reverse process to satisfy the relation 1…”

Section: A Pure State Fluctuation Relationmentioning

confidence: 99%

Fluctuation Theorems for a Quantum Channel

Kwon

Kim

2019

Phys. Rev. X

View full text Add to dashboard Cite

We establish the general framework of quantum fluctuation theorems by finding the symmetry between the forward and backward transitions of any given quantum channel. The Petz recovery map is adopted as the reverse quantum channel, and the notion of entropy production in thermodynamics is extended to the quantum regime. Our result shows that the fluctuation theorems, which are normally considered for thermodynamic processes, can be a powerful tool to study the detailed statistics of quantum systems as well as the effect of coherence transfer in an arbitrary non-equilibrium quantum process. We introduce a complex-valued entropy production to fully understand the relation between the forward and backward processes through the quantum channel. We find the physical meaning of the imaginary part of entropy production to witness the broken symmetry of the quantum channel. We also show that the imaginary part plays a crucial role in deriving the second law from the quantum fluctuation theorem. The dissipation and fluctuation of various quantum resources including quantum free energy, asymmetry and entanglement can be coherently understood in our unified framework. Our fluctuation theorem can be applied to a wide range of physical systems and dynamics to query the reversibility of a quantum state for the given quantum processing channel involving coherence and entanglement.

show abstract

“…Some of these results satisfy the first law of thermodynamics but can not recover fluctuation theorems in thermal equilibrium limit [33][34][35], and the others can simultaneously satisfy the first law of thermodynamics and fluctuation theorems, but negative probability appears [36][37][38]. Other efforts based on Bohmian framework [39], autonomous framework [40,41], quantum feedback con- * xbmv@bit.edu.cn † tuzc@bnu.edu.cn ‡ zoujian@bit.edu.cn trol [42], etc., for including the effects of quantum coherence have also been made, and also fluctuation theorems can not be recovered. Recently, Llobet et al proved that for the initial state with quantum coherence, the first law of thermodynamics and fluctuation theorem can not be simultaneously satisfied [43].…”

Section: Introductionmentioning

confidence: 99%

Duality in quantum work

Zou

2020

Phys. Rev. A

View full text Add to dashboard Cite

An open question of fundamental importance in quantum thermodynamics is how to describe the statistics of work for the initial state with quantum coherence. In this paper, work statistics is considered from a fully new perspective of "wave-particle" duality. Based on the generalized quantum work measurement, predictability of energy levels DW and effectiveness of coherence VW are defined, and they obey inequality D 2 W + V 2 W ≤ 1, which is the fundamental tradeoff relations between the contributions of population and coherence to quantum work distribution. As an application, we consider a driven two-level system and discuss the condition of the bound of above tradeoff relation. These results shed light on the effects of quantum coherence in quantum thermodynamics.

show abstract

Coherent fluctuation relations: from the abstract to the concrete

Cited by 33 publications

References 63 publications

Decomposable coherence and quantum fluctuation relations

Decomposable coherence and quantum fluctuation relations

Fluctuation Theorems for a Quantum Channel

Duality in quantum work

Contact Info

Product

Resources

About