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Jan Kochanowski @janfkoch.bsky.social · 16d

As a fun aside, I am very happy with the continuity bound and its proof. It contains, I think, a very fun and beautiful, but out of context meaningless formula that I want to leave you with. Made me reflect about beauty in maths. And I'd never thought so many different Ms could have real meaning.

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Jan Kochanowski @janfkoch.bsky.social · 16d

⚛️ Computational Quantum Resources Theory:

We introduce complexity-aware resource measures, prove an asymptotic continuity bound, and demonstrate explicit separations from the information-theoretic regime (e.g., entanglement) implying that computational restrictions do matter in practice.

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Jan Kochanowski @janfkoch.bsky.social · 16d

🔎 Computational Hypothesis Testing:

Even with many copies, the asymmetric hypothesis-testing exponent (Steins exponent) achievable by efficient measurements is upper-bounded by the regularized computational measured relative entropy.

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Jan Kochanowski @janfkoch.bsky.social · 16d

✨ We introduce computational versions of the max-divergence (via some beautiful conical structures in QIT) and measured Rényi divergences. We analyze their behavior under efficient operations and show that they from a cohesive framework (for α→∞ they coincide).
Further we consider two applications

Jan Kochanowski @janfkoch.bsky.social · 16d

In practice, experiments are fundamentally bound to efficiently implementable operations. 🧪

Together with Alvaro Yángüez and Thomas A. Hahn, we formalize quantum state discrimination and resource quantification under these efficiency constraints. 💻

Efficient Quantum Measurements: Computational Max- and Measured Rényi Divergences and Applications

Jan Kochanowski @janfkoch.bsky.social · 16d

Happy to finally share our new preprint: Efficient Quantum Measurements: Computational Max- and Measured Rényi Divergences and Applications.
scirate.com/arxiv/2509.2...

We are tackling the problem that information theoretic quantities may not be very meaningful in practical scalable experiments.

Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfull...

beyondiid13 - Programme and list of talks

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Jan Kochanowski @janfkoch.bsky.social · Jul 14

I’ll be giving a talk about this work at Beyond IID this Thursday, which will be recorded and live streamed should you be interested!
(sites.google.com/view/beyondi...)

Below you will find the schedule and the list of talks. In addition to the technical talks, there will be a public lecture by Hans Maassen on Wednesday evening (16 July, 18:30-19:30), "How Does a Quan...

sites.google.com

Complexity of mixed Schatten norms of quantum maps

Jan Kochanowski @janfkoch.bsky.social · Jul 14

We present a ‚quantum’ extension of mixed matrix norms showing hardness results for among other the tasks of computing the minimal output Rényi entropy of entanglement breaking (EB) channels (1->p) and the optimal one-shot distinguishability of a difference of EB channels (1->1).

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Jan Kochanowski @janfkoch.bsky.social · Jul 14

I’m happy to announce that my new work on „Complexities of mixed Matrix norms“ is out now scirate.com/arxiv/2507.0...

This is joint work with Cambyse Rouzé and Omar Fawzi that’s been quite some time in the making.

We study the complexity of computing the mixed Schatten $\|\Phi\|_{q\to p}$ norms of linear maps $\Phi$ between matrix spaces. When $\Phi$ is completely positive, we show that $\| \Phi \|_{q \to p}$ c...

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Jan Kochanowski @janfkoch.bsky.social · Jul 3

And I am thankful to my coauthors and teachers @angelacapel.bsky.social, @alvalhambra.bsky.social, and Cambyse Rouzé for your guidance and patience along the way, and from whom I learned and continue to learn a lot.

Rapid Thermalization of Dissipative Many-Body Dynamics of Commuting Hamiltonians - Communications in Mathematical Physics

Jan Kochanowski @janfkoch.bsky.social · Jul 3

I am very happy to announce that my first published article „Rapid Thermalization of Dissipative Many-Body Dynamics of Commuting Hamiltonians“ is now published in Communications in Mathematical Physics.

rdcu.be/euy1Y

I feel honored and humbled to have been accepted in such a prestigious journal.

Quantum systems typically reach thermal equilibrium rather quickly when coupled to a thermal environment. The usual way of bounding the speed of this process is by estimating the spectral gap of the d...

link.springer.com

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Reposted by Jan Kochanowski

Quantiki @quantiki.bsky.social · Apr 12

PhD position in Quantum Information Theory at Inria/Télécom Paris

www.quantiki.org/position/phd...

PhD position in Quantum Information Theory at Inria/Telecom Paris | Quantiki

www.quantiki.org

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Reposted by Jan Kochanowski

Quantiki @quantiki.bsky.social · Apr 12

Postdoc position in Quantum Information Theory at Télécom Paris, Institut Polytechnique de Paris @ipparis.bsky.social

www.quantiki.org/position/pos...

Postdoc position in Quantum Information Theory at Télécom Paris, Institut Polytechnique de Paris | Quantiki

www.quantiki.org

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Jan Kochanowski @janfkoch.bsky.social · Feb 5

Here’s its SciRate entry: scirate.com/arxiv/2502.0...
ツ

Additivity and chain rules for quantum entropies via multi-index Schatten norms

The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minim...

Jan Kochanowski @janfkoch.bsky.social · Feb 4

This was a really enjoyable joint work with Omar Fawzi, Cambyse Rouzé, and Thomas van Himbeeck.

arxiv.org/abs/2502.01611

Jan Kochanowski @janfkoch.bsky.social · Feb 4

These norms can be defined for arbitrary many indices. In particular for two they give nice expression for certain entropic quantities, which are why most applications restrict to those.

Importantly we give more tractable formulas for 3+ indexed ones opening the way to many more QI-applications

Jan Kochanowski @janfkoch.bsky.social · Feb 4

Our main technical tool are norms on so called operator values Schatten spaces. We can these ‚multi-index Schatten norms‘.

Even though they have been knows since ~80, their usefulness is QIT was realized in ~06, yet they still seems somewhat niece in the QI community.

Jan Kochanowski @janfkoch.bsky.social · Feb 4

On the applications side do we generalize and give new results that are of interest in quantum cryptography and e.g. for entropy accumulation theorems.

But in particular do we want to highlight the bridge and usefulness of operator space in quantum information theory.
See also [Beigi,Goodarzi 22]

Additivity and chain rules for quantum entropies via multi-index Schatten norms

Jan Kochanowski @janfkoch.bsky.social · Feb 4

I’m very happy to announce our new work on Additivity and chain rules for conditional entropies via ‚multi-indexed Schatten norms‘.

We use tools from operator space theory that in a rather ‚simple‘ way give non-trivial chain rules and additivity statements.

Find it at:
arxiv.org/abs/2502.01611

The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minim...

arxiv.org

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Reposted by Jan Kochanowski

Andreas Wallraff @andreasateth.bsky.social · Jan 19

I added some memory to this quantum feed.
Let's see if this works.
The quantum community out here seems to get more lively with time.
Still slower than X somehow.
Convince your friends to join here.

bsky.app/profile/did:...

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Jan Kochanowski @janfkoch.bsky.social · Jan 13

I‘m not quite sure if I have the right audience here, but in case you speak both German and are in Munich there will be a reading of a short story I wrote about a funny encounter with the fascination behind physics.

Infos: www.ja.tum.de/ja/events/wo...

The event will, however, only be in German.

Wordshop

www.ja.tum.de

Jan Kochanowski @janfkoch.bsky.social · Dec 5

As for non-hypercubic systems, usually if the growth constant or the degree is bounded qualitatively similar results should hold. Ours pretty surely extend.
Otherwise you may need much stronger assumptions to get decay.

Jan Kochanowski @janfkoch.bsky.social · Dec 5

Q.random walks are also a tool to prove efficiency state preparation, but I am not an expert on that. I think you also points to what happens to correlations over time (OTOC) which is interesting to look into. They can prob. also yield rapid mixing if you look at the right (prob. entropic) ones.