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Fluctuation theorems for quantum processes
Quantum Physics · Submitted 29 Dec 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control.
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The abstract, sentence by sentence
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. | contribution 0.99 | 0.95 | 0.49 | asserted 1.00 |
| s1 | Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. | result 0.71 | 0.89 | 0.29 | asserted 1.00 |
| s2 | We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. | result 0.92 | 0.93 | 0.21 | asserted 1.00 |
| s3 | We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing. | contribution 0.92 | 0.96 | 0.09 | asserted 1.00 |
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The paper
Original abstract
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
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How the literature uses it
6 arXiv papers cite this in 9 sentences
Papers citing it · 5 sentences without a confident label
Compares with it 1 paper
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My formulations and derivation methods are different from and, in certain respects, complementary to those given in [ref] .
Non-equilibrium equalities with unital quantum channels · Conclusions · 1.00
Cites it as support 1 paper
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After the present paper was submitted I learned about the recent work [ref] , in which the significance of unitality is emphasized as well.
Non-equilibrium equalities with unital quantum channels · Conclusions · 0.96
Cites it as background 2 papers
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It is well-known that unitality is the quantum counterpart of classical microreversibility [ref] .
Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level · Micro-reversibility · 0.87
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Intense research activity recently focused to determine work for closed and open quantum systems (see [ref] ).
Fluctuation Relation for Qubit-Calorimetry · Introduction · 0.98
What it cites · 6 sentences without a confident label
Compares with 2 papers
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Note added: After the appearance of our work on the arXiv, two papers arrived at similar results [ref] .
Non-equilibrium equalities with unital quantum channels · Conclusions · 0.95
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Note added: After the appearance of our work on the arXiv, two papers arrived at similar results [ref] .
Jarzynski equality for quantum stochastic maps · Conclusions · 0.95
Cites as background 1 paper
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We briefly review the generalization of the CJE to the quantum case of thermal states undergoing unitary evolution [ref] , as it will help set the stage for our work (see also [ref]).
Jarzynski Relations for Quantum Systems and Some Applications · Review of Quantum Jarzynski Equality for Closed Systems with Projective Measurements · 0.89
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