Philippe Faist
@phfaist.bsky.social
Tenured senior researcher in quantum information at the Freie Universität Berlin (previously: PhD at ETH Zurich & post-doc at IQIM Caltech) https://phfaist.com/
Note to self: avoid transparent PNG's in social media posts 😅
August 7, 2025 at 10:51 AM
Note to self: avoid transparent PNG's in social media posts 😅
Our short paper (you want to get straight to the point): arxiv.org/abs/2508.03993
Our technical companion paper (you want a careful mathematical construction with all the details): arxiv.org/abs/2508.03994
Thanks for reading!
Our technical companion paper (you want a careful mathematical construction with all the details): arxiv.org/abs/2508.03994
Thanks for reading!
August 7, 2025 at 10:33 AM
Our short paper (you want to get straight to the point): arxiv.org/abs/2508.03993
Our technical companion paper (you want a careful mathematical construction with all the details): arxiv.org/abs/2508.03994
Thanks for reading!
Our technical companion paper (you want a careful mathematical construction with all the details): arxiv.org/abs/2508.03994
Thanks for reading!
The thermal state is so ubiquitous throughout physics, information theory, and algorithms; wouldn't it be fun if the thermal quantum channel had as broad a range of applicability? I think we've only begun to scratch the surface of what it can do.
August 7, 2025 at 10:33 AM
The thermal state is so ubiquitous throughout physics, information theory, and algorithms; wouldn't it be fun if the thermal quantum channel had as broad a range of applicability? I think we've only begun to scratch the surface of what it can do.
All of our methods are detailed in our technical paper arxiv.org/abs/2508.03994 . We use lots of Lagrange duality of convex problems, Schur-Weyl duality, typicality techniques for noncommuting operators and channels, and develop an extended postselection theorem for quantum channels.
August 7, 2025 at 10:33 AM
All of our methods are detailed in our technical paper arxiv.org/abs/2508.03994 . We use lots of Lagrange duality of convex problems, Schur-Weyl duality, typicality techniques for noncommuting operators and channels, and develop an extended postselection theorem for quantum channels.
Are there any uses of the thermal quantum channel in quantum learning algorithms? We think that state learning algorithms based on maximum entropy arguments can naturally be extended to channels, and they do seem to converge to the correct channel for some simple examples.
August 7, 2025 at 10:33 AM
Are there any uses of the thermal quantum channel in quantum learning algorithms? We think that state learning algorithms based on maximum entropy arguments can naturally be extended to channels, and they do seem to converge to the correct channel for some simple examples.
Except that now, we can account for arbitrary correlations and constraints the dynamics must obey, which may correlate input and output systems. In this sense, the thermal quantum channel represents thermalizing dynamics with arbitrary “partial information.”
August 7, 2025 at 10:33 AM
Except that now, we can account for arbitrary correlations and constraints the dynamics must obey, which may correlate input and output systems. In this sense, the thermal quantum channel represents thermalizing dynamics with arbitrary “partial information.”
What's the thermal quantum channel good for? Much like how we often replace a complex or unknown quantum microstate by a thermal state in a many-body system [(a)], I'd like to think that we could often replace complex or unknown evolution 𝒰 by the thermal quantum channel [(b)].
![Much like how we replace a complex or unknown quantum state by a thermal state in a many-body system [(a)], I'd like to think that we can replace complex or unknown evolution 𝒰 by the thermal quantum channel [(b)]](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:geqpszldclrgztwi2lhlldwr/bafkreiesoti3s2d36wx6baqkur2yzuofukitfogc6dfm632klvisybxcly@jpeg)
August 7, 2025 at 10:33 AM
What's the thermal quantum channel good for? Much like how we often replace a complex or unknown quantum microstate by a thermal state in a many-body system [(a)], I'd like to think that we could often replace complex or unknown evolution 𝒰 by the thermal quantum channel [(b)].
Therefore, we have two independent arguments that identify the same *thermal quantum channel*.
August 7, 2025 at 10:33 AM
Therefore, we have two independent arguments that identify the same *thermal quantum channel*.
We find a *microcanonical channel* Ω that represents a global channel on the system and a large environment and which obeys a global conservation law represented by a set of constraints. On a single system, Ω looks the same as the channel defined from the maximum channel entropy principle!
August 7, 2025 at 10:33 AM
We find a *microcanonical channel* Ω that represents a global channel on the system and a large environment and which obeys a global conservation law represented by a set of constraints. On a single system, Ω looks the same as the channel defined from the maximum channel entropy principle!
So Jaynes' maximum entropy principle extends naturally to channels. But what happens if we extend other definitions of the thermal state to channels? It would be worrying if different approaches to define of the thermal quantum channel led to different channels.
August 7, 2025 at 10:33 AM
So Jaynes' maximum entropy principle extends naturally to channels. But what happens if we extend other definitions of the thermal state to channels? It would be worrying if different approaches to define of the thermal quantum channel led to different channels.
For *average* energy conservation, the thermal quantum channel outputs, for each input energy eigenstate |E⟩, a thermal state with temperature such that the state has energy E. This channel is thermalizing (it outputs thermal states) but conserves memory of its input (the average energy)!
August 7, 2025 at 10:33 AM
For *average* energy conservation, the thermal quantum channel outputs, for each input energy eigenstate |E⟩, a thermal state with temperature such that the state has energy E. This channel is thermalizing (it outputs thermal states) but conserves memory of its input (the average energy)!
The expectation values of physically accessible quantities imposed as constraints can be arbitrary general linear constraints on the channel. E.g., for strict energy conservation, the thermal quantum channel is maximally depolarizing within each energy subspace.
August 7, 2025 at 10:33 AM
The expectation values of physically accessible quantities imposed as constraints can be arbitrary general linear constraints on the channel. E.g., for strict energy conservation, the thermal quantum channel is maximally depolarizing within each energy subspace.
The entropy of a channel 𝒩 measures “how thermalizing” 𝒩 is. It quantifies how entropic 𝒩's output is guaranteed to be, for any input state, and even using a reference system as side information. Specifically: if 𝒩 acts on systems A→B and R ≃ A, then S(𝒩) ≡ min_ρ S(B|R), where ρ is any input on AR.
August 7, 2025 at 10:33 AM
The entropy of a channel 𝒩 measures “how thermalizing” 𝒩 is. It quantifies how entropic 𝒩's output is guaranteed to be, for any input state, and even using a reference system as side information. Specifically: if 𝒩 acts on systems A→B and R ≃ A, then S(𝒩) ≡ min_ρ S(B|R), where ρ is any input on AR.
This maximum entropy principle for channels generalizes Jaynes' famous maximum entropy principle for states.
But what's the entropy of a channel?
Fortunately, we already have an answer thanks to [Devetak et al. quant-ph/0506196], [Wilde and Gour 1808.06980], and [Yuan 1807.05958].
But what's the entropy of a channel?
Fortunately, we already have an answer thanks to [Devetak et al. quant-ph/0506196], [Wilde and Gour 1808.06980], and [Yuan 1807.05958].
August 7, 2025 at 10:33 AM
This maximum entropy principle for channels generalizes Jaynes' famous maximum entropy principle for states.
But what's the entropy of a channel?
Fortunately, we already have an answer thanks to [Devetak et al. quant-ph/0506196], [Wilde and Gour 1808.06980], and [Yuan 1807.05958].
But what's the entropy of a channel?
Fortunately, we already have an answer thanks to [Devetak et al. quant-ph/0506196], [Wilde and Gour 1808.06980], and [Yuan 1807.05958].
Sumeet Khatri and I answer this question in arxiv.org/abs/2508.03993 (short) and arxiv.org/abs/2508.03994 (technical).
We define the *thermal quantum channel* as the channel with maximal entropy that reproduces expectation values of physically accessible quantities.
We define the *thermal quantum channel* as the channel with maximal entropy that reproduces expectation values of physically accessible quantities.
Thermalization with partial information
A many-body system, whether in contact with a large environment or evolving under complex dynamics, can typically be modeled as occupying the thermal state singled out by Jaynes' maximum entropy princ...
arxiv.org
August 7, 2025 at 10:33 AM
Sumeet Khatri and I answer this question in arxiv.org/abs/2508.03993 (short) and arxiv.org/abs/2508.03994 (technical).
We define the *thermal quantum channel* as the channel with maximal entropy that reproduces expectation values of physically accessible quantities.
We define the *thermal quantum channel* as the channel with maximal entropy that reproduces expectation values of physically accessible quantities.
Congratulations, the idea looks beautiful!
April 30, 2025 at 1:38 PM
Congratulations, the idea looks beautiful!
Sounds like a fun project!
March 27, 2025 at 11:53 PM
Sounds like a fun project!
What would you like to parse? Pylatexenc should be able to give you a workable abstract-syntax-tree-like representation of your formula. (You can also transpire a subset of pylatexenc to js, in case it’s useful for your web app.)
March 25, 2025 at 6:34 PM
What would you like to parse? Pylatexenc should be able to give you a workable abstract-syntax-tree-like representation of your formula. (You can also transpire a subset of pylatexenc to js, in case it’s useful for your web app.)
Almost as good as the company! 😀
February 26, 2025 at 6:49 PM
Almost as good as the company! 😀