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Non-equilibrium equalities with unital quantum channels
Quantum Physics · Submitted 5 Jan 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is essential that the representing quantum channel be unital.
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The abstract, sentence by sentence
A general tool for description of open quantum systems is given by the formalism of quantum operations. Most important of them are trace-preserving maps also known as quantum channels. We discuss those conditions on quantum channels under which the Jarzynski equality and related fluctuation theorems hold. It is essential that the representing quantum channel be unital. Under the mentioned condition, we first derive the corresponding Jarzynski equality. For bistochastic map and its adjoint, we further formulate a theorem of Tasaki-Crooks type. In the context of unital channels, some notes on heat transfer between two quantum systems are given. We also consider the case of a finite system operated by an external agent with a feedback control. When unital channels are applied at the first stage and, for a mutual-information form, at the further ones, we obtain quantum Jarzynski-Sagawa-Ueda relations. These are extension of the previously given results to unital quantum operations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A general tool for description of open quantum systems is given by the formalism of quantum operations. | background 1.00 | 0.12 | 0.03 | asserted 1.00 |
| s1 | Most important of them are trace-preserving maps also known as quantum channels. | background 1.00 | 0.05 | 0.03 | asserted 1.00 |
| s2 | We discuss those conditions on quantum channels under which the Jarzynski equality and related fluctuation theorems hold. | contribution 0.97 | 0.67 | 0.11 | asserted 0.65 |
| s3 | It is essential that the representing quantum channel be unital. | result 0.79 | 0.58 | 0.45 | asserted 1.00 |
| s4 | Under the mentioned condition, we first derive the corresponding Jarzynski equality. | result 0.52 | 0.93 | 0.19 | asserted 1.00 |
| s5 | For bistochastic map and its adjoint, we further formulate a theorem of Tasaki-Crooks type. | result 0.67 | 0.88 | 0.11 | asserted 1.00 |
| s6 | In the context of unital channels, some notes on heat transfer between two quantum systems are given. | contribution 0.92 | 0.73 | 0.04 | asserted 0.72 |
| s7 | We also consider the case of a finite system operated by an external agent with a feedback control. | contribution 1.00 | 0.75 | 0.03 | asserted 0.86 |
| s8 | When unital channels are applied at the first stage and, for a mutual-information form, at the further ones, we obtain quantum Jarzynski-Sagawa-Ueda relations. | result 0.86 | 0.88 | 0.26 | asserted 1.00 |
| s9 | These are extension of the previously given results to unital quantum operations. | interpretation 0.74 | 0.71 | 0.23 | asserted 1.00 |
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The paper
Original abstract
A general tool for description of open quantum systems is given by the formalism of quantum operations. Most important of them are trace-preserving maps also known as quantum channels. We discuss those conditions on quantum channels under which the Jarzynski equality and related fluctuation theorems hold. It is essential that the representing quantum channel be unital. Under the mentioned condition, we first derive the corresponding Jarzynski equality. For bistochastic map and its adjoint, we further formulate a theorem of Tasaki-Crooks type. In the context of unital channels, some notes on heat transfer between two quantum systems are given. We also consider the case of a finite system operated by an external agent with a feedback control. When unital channels are applied at the first stage and, for a mutual-information form, at the further ones, we obtain quantum Jarzynski-Sagawa-Ueda relations. These are extension of the previously given results to unital quantum operations.
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How the literature uses it
4 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Compares with it 1 paper
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Note added: After the appearance of our work on the arXiv, two papers arrived at similar results [ref] .
Fluctuation theorems for quantum processes · Conclusions · 0.95
What it cites · 11 sentences without a confident label
Builds on 1 paper
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Assuming unitary evolution, the relation ([ref]) has been derived by Tasaki [ref] .
Jarzynski Relations for Quantum Systems and Some Applications · Jarzynski's equality with unital quantum channels · 0.90
Compares with 1 paper
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My formulations and derivation methods are different from and, in certain respects, complementary to those given in [ref] .
Fluctuation theorems for quantum processes · Conclusions · 1.00
Cites 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.
Fluctuation theorems for quantum processes · Conclusions · 0.96
Cites as background 1 paper
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In the quantum regime, many approaches were done with somewhat particular assumptions such as description by Schrödinger [ref] or master equation [ref] , unitary evolution [ref] , or the time-reversal symmetry [ref] .
Jarzynski Relations for Quantum Systems and Some Applications · Introduction · 0.91
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