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Reachable Sets from Toy Models to Controlled Markovian Quantum Systems
Optimization and Control · Submitted 3 May 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We completely characterize the case $T=0$ and present inclusions for $T>0$.
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The abstract, sentence by sentence
In the framework of bilinear control systems, we present reachable sets of coherently controllable open quantum systems with switchable coupling to a thermal bath of arbitrary temperature $T geq 0$. The core problem boils down to studying points in the standard simplex amenable to two types of controls that can be used interleaved: (i) permutations within the simplex, (ii) contractions by a dissipative one-parameter semigroup. Our work illustrates how the solutions of the core problem pertain to the reachable set of the original controlled Markovian quantum system. We completely characterize the case $T=0$ and present inclusions for $T>0$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the framework of bilinear control systems, we present reachable sets of coherently controllable open quantum systems with switchable coupling to a thermal bath of arbitrary temperature $T geq 0$. | contribution 0.99 | 0.92 | 0.15 | asserted 1.00 |
| s1 | The core problem boils down to studying points in the standard simplex amenable to two types of controls that can be used interleaved: (i) permutations within the simplex, (ii) contractions by a dissipative one-parameter semigroup. | method 0.71 | 0.44 | 0.11 | asserted 1.00 |
| s2 | Our work illustrates how the solutions of the core problem pertain to the reachable set of the original controlled Markovian quantum system. | interpretation 0.78 | 0.89 | 0.17 | asserted 0.99 |
| s3 | We completely characterize the case $T=0$ and present inclusions for $T>0$. | result 0.61 | 0.95 | 0.36 | asserted 1.00 |
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The paper
Original abstract
In the framework of bilinear control systems, we present reachable sets of coherently controllable open quantum systems with switchable coupling to a thermal bath of arbitrary temperature $T geq 0$. The core problem boils down to studying points in the standard simplex amenable to two types of controls that can be used interleaved: (i) permutations within the simplex, (ii) contractions by a dissipative one-parameter semigroup. Our work illustrates how the solutions of the core problem pertain to the reachable set of the original controlled Markovian quantum system. We completely characterize the case $T=0$ and present inclusions for $T>0$.
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How the literature uses it
2 arXiv papers cite this in 3 sentences
Papers citing it · 2 sentences without a confident label
Builds on it 1 paper
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Our recent toy-model results in [ref] thus extend (the diagonal part of) the qubit picture previously analysed by [ref] to $n$-level systems, and even more generally to systems of $m$ qudits.
Exploring the Limits of Open Quantum Dynamics I: Motivation, New Results from Toy Models to Applications · State-of-the-Art · 1.00
What it cites · 1 sentence without a confident label
Builds on 1 paper
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The current results extend the qubit picture of [ref] to $n$-level systems, and even more generally to systems of $m$ qudits.
Arbitrary n-Qubit State Transfer Implemented by Coherent Control and Simplest Switchable Local Noise · Main Results · 1.00
Cites as support 1 paper
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Our first results show that there exists a rich class of physically relevant models motivated by quantum dynamical qubit systems [ref] which are relaxing and satisfy the invariance condition IN.
Arbitrary n-Qubit State Transfer Implemented by Coherent Control and Simplest Switchable Local Noise · Toy Models with Unique Attractive Fixed Point · 0.96
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