Sign in

Jan Kochanowski

@janfkoch.bsky.social
342 followers 219 following 44 posts

PhD student in math. physics & quantum info @IPParis. Formerly TUM&LMU, UniofCam 🇪🇺🏳️‍🌈 kochanowski.notion.site

PostsRepliesMedia
Jan Kochanowski @janfkoch.bsky.social · 07/10/2026
Along the way we also extend Pisier’s seminal formula to many indices and practically all of the tools and result of [Devetak, Junge, King, Ruskai, 2006] I would to thank Thomas Hahn, Aby Philips for discussions about entanglement certification and my supervisors for their continued support 🧑‍🏫🙏👨‍🔬👨‍🔬👨‍🏫
000
Jan Kochanowski @janfkoch.bsky.social · 07/10/2026
Earlier this year (arxiv.org/abs/2604.14055) we put that construction on a matrix-analytic foundations which allowed us to extend it to compatible positive indices. With today’s work we in some sense combine both approaches to give a general theory for any number of compatible indices.
arxiv.org
Two-Indexed Schatten Quasi-Norms with Applications to Quantum Information Theory
We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces, naturally extending the norms defined by Pisier's theory of operator-valued Schat...
110
Jan Kochanowski @janfkoch.bsky.social · 07/10/2026
Their quantum extension, however, is very non-trivial due to non-commutativity. Pisier made the first progress in ‘98 by defining his seminal operator-valued norms and they found direct application to quantum information and in particular entropy additivity statements, but many more.
110
Jan Kochanowski @janfkoch.bsky.social · 07/10/2026
📑 For some more context: In classical info theory, so called ‘mixed’ \ell_p norms have been useful tools to work with Rényi-entropic quantities, which are particularly well suited for near term resource-limited tasks. These are, simple to define, multi-indexed norms, quasi-, or anti-norms.
100
Jan Kochanowski @janfkoch.bsky.social · 07/10/2026
Among generalizing and deriving general tools to handle multiplicativity statements of quantum channels between such spaces I prove additivitiy of cb minimal and the maximal conditional Rényi output entropies of any order and derive a chain rule suited to DI entanglement certification. 🛠️🧾
100
Jan Kochanowski @janfkoch.bsky.social · 07/10/2026
In short these extend classical information theory’s ‘mixed \ell_p norms’ and allow succinct description of Rényi entropic quantities, including external output (conditional) entropies. This also extends Pisier’s norms and our previous work on two-indexed quasi-norms.
100
Jan Kochanowski @janfkoch.bsky.social · 07/10/2026
What a day for quantum information… Yet I am very proud to announce my first single author paper and in some sense a culmination of my work the last two years. It’s on a genuine theory of multi-indexed Schatten spaces: scirate.com/arxiv/2610.0... 🔗📄 What does this mean and what is it useful for?
scirate.com
1111
Reposted by Jan Kochanowski
QIP @qipconference.bsky.social · 13/07/2026
We're pleased to announce the key dates for QIP 2027, as follows (refer to the website qipconference.org/2027/ for up-to-date information). We look forward to your participation!
02210
Jan Kochanowski @janfkoch.bsky.social · 06/05/2026
Neuecast
100
Reposted by Jan Kochanowski
arxiv quant-ph @arxiv-quant-ph.bsky.social · 21/04/2026
\'Alvaro Y\'ang\"uez, Noam Avidan, Jan Kochanowski, Thomas A. Hahn Accessible Quantum Correlations Under Complexity Constraints arxiv.org/abs/2604.15540
022
Jan Kochanowski @janfkoch.bsky.social · 16/04/2026
I would like to thank my supervisors Omar Fawzi and Cambyse Rouzé for the very exiting collaboration. I learned a lot, some of which you can find in scirate.com/arxiv/2604.1... Lastly, here the meme @dulwichquantum.bsky.social
030
Jan Kochanowski @janfkoch.bsky.social · 16/04/2026
These results build on us, as main result, extending Pisier’s two-indexed Schatten norms to the quasi-norm regime q,p<1. Manifestly this allows for a general notion of completely bounded quasi-norm for linear maps between quasi-normed spaces, relevant for example for Rényi entropies with p<1.
110
Jan Kochanowski @janfkoch.bsky.social · 16/04/2026
Complete reverse hypercontractivity is a notion of open system dynamics which is related to their mixing times. In contrast to the prev. considered reverse hypercontractivity we prove it is tensorizes, i.e. if two channels are completely reverse hypercontractive, then so is their tensor product.
110
Jan Kochanowski @janfkoch.bsky.social · 16/04/2026
Interestingly maximal output entropies are additive, in contrast to the famously non additive minimal ones. There this is resolved by completely bounding, which had previously not been possible in the regime p<1 for lack of notion of completely bounded quasi-norm (- the special case of [Li, Xu 2026]
110
Jan Kochanowski @janfkoch.bsky.social · 16/04/2026
We prove additivity of maximum output- and additivity of the completely bounded minimum output Rényi entropy for any p>1/2. The latter was recently independently proven in (arxiv.org/abs/2603.16722). We also prove tensorization of natural notion of complete reverse hypercontractivity.
arxiv.org
110
Jan Kochanowski @janfkoch.bsky.social · 16/04/2026
I am very happy to announce a new work scirate.com/arxiv/2604.1... in which we extend seminal mathematical tools to the quasi-normed regime. With these we prove new additivity of output entropies results and a tenderizing notion of complete reverse hypercontractivity 🤫 there is a meme at the end
scirate.com
Two-Indexed Schatten Quasi-Norms with Applications to Quantum Information Theory
We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces, naturally extending the norms defined by Pisier's theory of operator-valued Schat...
140
Jan Kochanowski @janfkoch.bsky.social · 10/11/2025
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.
arxiv.org
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...
040
Jan Kochanowski @janfkoch.bsky.social · 26/09/2025
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
scirate.com
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...
040
Jan Kochanowski @janfkoch.bsky.social · 26/09/2025
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.
040
Jan Kochanowski @janfkoch.bsky.social · 26/09/2025
⚛️ 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.
160
Jan Kochanowski @janfkoch.bsky.social · 26/09/2025
🔎 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.
120
Jan Kochanowski @janfkoch.bsky.social · 26/09/2025
✨ 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
110
Jan Kochanowski @janfkoch.bsky.social · 26/09/2025
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. 💻
110
Jan Kochanowski @janfkoch.bsky.social · 26/09/2025
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.
scirate.com
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...
2120
Jan Kochanowski @janfkoch.bsky.social · 14/07/2025
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...)
sites.google.com
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...
010
Jan Kochanowski @janfkoch.bsky.social · 14/07/2025
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).
120
Jan Kochanowski @janfkoch.bsky.social · 14/07/2025
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.
scirate.com
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...
150
Jan Kochanowski @janfkoch.bsky.social · 03/07/2025
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.
010
Jan Kochanowski @janfkoch.bsky.social · 03/07/2025
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.
link.springer.com
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...
191
Reposted by Jan Kochanowski
Quantiki @quantiki.bsky.social · 12/04/2025
PhD position in Quantum Information Theory at Inria/Télécom Paris www.quantiki.org/position/phd...
quantiki.org
PhD position in Quantum Information Theory at Inria/Telecom Paris | Quantiki
122
Reposted by Jan Kochanowski
Quantiki @quantiki.bsky.social · 12/04/2025
Postdoc position in Quantum Information Theory at Télécom Paris, Institut Polytechnique de Paris @ipparis.bsky.social www.quantiki.org/position/pos...
quantiki.org
Postdoc position in Quantum Information Theory at Télécom Paris, Institut Polytechnique de Paris | Quantiki
111
Jan Kochanowski @janfkoch.bsky.social · 05/02/2025
Here’s its SciRate entry: scirate.com/arxiv/2502.0... ツ
scirate.com
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...
000
Jan Kochanowski @janfkoch.bsky.social · 04/02/2025
This was a really enjoyable joint work with Omar Fawzi, Cambyse Rouzé, and Thomas van Himbeeck. arxiv.org/abs/2502.01611
000
Jan Kochanowski @janfkoch.bsky.social · 04/02/2025
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
100
Jan Kochanowski @janfkoch.bsky.social · 04/02/2025
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.
100
Jan Kochanowski @janfkoch.bsky.social · 04/02/2025
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]
110
Jan Kochanowski @janfkoch.bsky.social · 04/02/2025
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
arxiv.org
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...
200
Reposted by Jan Kochanowski
Andreas Wallraff @andreasateth.bsky.social · 19/01/2025
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:...
0387
Jan Kochanowski @janfkoch.bsky.social · 13/01/2025
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.
ja.tum.de
Wordshop
010
Jan Kochanowski @janfkoch.bsky.social · 05/12/2024
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.
010
Jan Kochanowski @janfkoch.bsky.social · 05/12/2024
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.
110
Jan Kochanowski @janfkoch.bsky.social · 03/12/2024
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
000
Jan Kochanowski @janfkoch.bsky.social · 03/12/2024
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?
110
Jan Kochanowski @janfkoch.bsky.social · 03/12/2024
For a more technical yet succinct 🧵 see Angelas X x.com/angelacapelc...
x.com
x.com
000
Jan Kochanowski @janfkoch.bsky.social · 03/12/2024
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...
000
Jan Kochanowski @janfkoch.bsky.social · 03/12/2024
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?
210
Jan Kochanowski @janfkoch.bsky.social · 03/12/2024
We can show that for 'marginal commuting' systems at unif. high temperature this holds, but the general question is still open... I'll be giving a talk about this in about 2 weeks for a workshop @unituebingen.bsky.social
100
Jan Kochanowski @janfkoch.bsky.social · 03/12/2024
Examples of such systems include all local quantum CSS codes on D dimensional lattices at uniformly high temperatures. To be honest this work is effectively mixing time bounds of the Davies evolution in disguise.
110
Jan Kochanowski @janfkoch.bsky.social · 03/12/2024
I'm very happy to announce our latest paper on Gibbs state preparation out now: arxiv.org/abs/2412.01732 Tl;dr: Commuting q.Gibbs states satisfying a certain conditional mutual information decay ("the MCMI") property can be prepared efficiently up to small errors in normalized Wasserstein distance.
arxiv.org
Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics
We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension. We prove that any such Gibbs state which satisfi...
150
Reposted by Jan Kochanowski
Dulwich Quantum Computing @dulwichquantum.bsky.social · 21/11/2024
By popular demand, here is a starter pack of all quantum PhD students on BlueSky that we could find. go.bsky.app/AUTn1di
104719