Jan Kochanowski

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

Happy to see that two of my works were accepted to QIP next year!

"Complexity of mixed Schatten norms of quantum maps“: arxiv.org/abs/2507.08358

"Computational aspects of the trace norm contraction coefficient“: arxiv.org/abs/2507.16737

Thank you to my coauthors! Looking forward to the talks.

Computational Relative Entropy Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained w...

Should also mention concurrent and complementary work tat came out today (scirate.com/arxiv/2509.2...) by @jjmeyer.bsky.social et al.
He also wrote a nice thread ⛓️ about relative entropies und why computational constraints we both consider matter. Check it out

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.

⚛️ 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.

🔎 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.

✨ 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

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 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...

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.

beyondiid13 - Programme and list of talks 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...

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...)

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).

Complexity of mixed Schatten norms of quantum maps 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...

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.

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 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...

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.

PhD position in Quantum Information Theory at Inria/Télécom Paris

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

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

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

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...

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

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

arxiv.org/abs/2502.01611

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

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.

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 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...

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

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:...

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.

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.

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.

We show that for so called ‚marginal commuting Hamiltonians‘ at unif. high temperature the MCMI is exponentially decaying.
However, the case for Gibbs states of general Hamiltonians is still open!

Will be giving a talk ablut this in about 2 weeks in a workshop @unituebingen.bsky.social

To go beyond the 1D or the nearest neighbor setting we introduce the Matrix valued quantum Conditional Mutual Information (MCMI) to the Davies mixing setting. Interestingly the MCMI has been studied before, among others in arXiv:1910.09425v2.

However, the question stands: When does it decay?

For a more technical yet succinct 🧵 see Angelas X

x.com/angelacapelc...

And lastly, this was me recently presenting a poster at @ IP-Paris about this work. It took up a lot of my first year of PhD and was in the works for a very long time...

It's also out in SciRate now, so fell free to check it out there. I want to sincerely thank my co-authors, Ángela Capel, Paul Gondolf, and my supervisor Cambyse Rouzé.

And @dulwichquantum.bsky.social for the inspiration to the memes. Not sure if they are good though?