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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

I also wanted to add a shout-out to Álvaro, Thomas and Jan who put out a work with similar mindset today: arxiv.org/abs/2509.21308. It turns out that our results mostly complement each other quite nicely, so please have a look there as well!

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...

arxiv.org

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

A big thanks to my coauthors Asad, Jacopo, Lorenzo, Sofiene and Jens.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

This is in stark contrast to how people approached computational information theory to date, where the approaches focused on single-shot statements. These are of course more exact, but also much more complicated to manipulate and build intuition for.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

We believe that our definition has a nice level of abstraction that captures the essence of information theory under computational constraints while at the same time having the look and feel of unbounded information theory.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

I invite you to discover many exciting things in the paper, like computationally measured divergences and a computational Stein's Lemma or a computational Rains bound on efficiently distillable entanglement.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

Another highlight is the fact that we can obtain separations in hypothesis testing, both between bounded and unbounded observers as well as classical-quantum separations. This means there exist classical distributions testable when having access to a quantum computer but not classically.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

We can use the computational relative entropy as a mother quantity. We exemplify this by defining a computational entropy S̲(ρₙ):=−D(ρₙ‖𝕀) and show that it quantifies the best rate at which we can compress a state under complexity restrictions -- just like the entropy in the unbounded setting.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

For example, we obtain a computational version of Pinsker's inequality, which looks exactly like the unbounded relation only that the involved quantities carry underscores, marking them as computational quantities.

The computational version of Pinsker's inequality.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

One of our main contributions is to turn this process of "polynomial regularization" into a rigorous notion. It allows us to reap the benefits of regularizing to obtain simpler expressions that closely resemble their counterparts from unbounded information theory.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

Of course, talking about polynomial scaling only makes sense when there is a scaling parameter. Therefore, all our results pertain to families of quantum states indexed by some parameter n. This is often the number of qubits, but need not be.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

We propose the following remedy: we define the computational relative entropy D̲(ρₙ‖σₙ) as the best error exponent in asymmetric hypothesis testing when restricted to polynomially many copies and polynomial-time tests and take the polynomials to be arbitrarily large.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

But there is a catch! The connection between hypothesis testing and the relative entropy only holds if arbitrary tests can be performed. The optimal tests, however, could be exponentially complex to implement. We also need a large number of copies of the state to get sufficient statistics.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

The fact that the relative entropy and its derived quantities appear so often in information theory is that it quantifies the best achievable error exponent in asymmetric hypothesis testing, a primitive many important information processing tasks can be reduced to.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

The relative entropy D(ρ‖σ) is a fundamental quantity in classical and quantum information theory. It appears in many important theorems and serves as a mother quantity to derive other important measures from -- for example mutual information or entropy.

The definition of the Umegaki relative entropy.

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Johannes Jakob Meyer @jjmeyer.bsky.social · 13d

You think we already have enough entropies and divergence measures? I don't think so!

In our latest work (arxiv.org/abs/2509.20472), we introduce yet another information theoretic measure -- the computational relative entropy.

Let's have a quick rundown👇

The distracted boyfriend meme, with the "girlfriend" being the relative entropy and the distraction being the computational relative entropy.

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Johannes Jakob Meyer @jjmeyer.bsky.social · May 12

arxiv.org/abs/2410.18196

Simulating quantum chaos without chaos

Quantum chaos is a quantum many-body phenomenon that is associated with a number of intricate properties, such as level repulsion in energy spectra or distinct scalings of out-of-time ordered correlat...

arxiv.org

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Johannes Jakob Meyer @jjmeyer.bsky.social · Apr 20

I think the best bit is that they have a guy named "Clifford Mapp" on their team!

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Johannes Jakob Meyer @jjmeyer.bsky.social · Mar 27

Very nice! Michael Wolf also has some very good newer ones: mediatum.ub.tum.de/download/170...

mediatum.ub.tum.de

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Reposted by Johannes Jakob Meyer

qctip2025.bsky.social @qctip2025.bsky.social · Feb 17

Registrations are now open for #QCTiP2025: qctip2025.com/registration....
Don’t wait too long—spots for participants without a talk are first-come, first-served!

Registrations

Registrations Registrations close: 14 March To register please create an account on our ConfTool portal, accessible through the link below (or use the same account you created for submissions of ta…

qctip2025.com

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Johannes Jakob Meyer @jjmeyer.bsky.social · Jan 18

Context please

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Johannes Jakob Meyer @jjmeyer.bsky.social · Jan 14

I guess that particular myth was formulated so that you can debunk it. I never heard anyone claim that error mitigation cannot be used, just that it is no scalable solution for the problem.

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Johannes Jakob Meyer @jjmeyer.bsky.social · Dec 9

We should all recall once in a while that we as a community are in a hamster wheel of our own making. This means we can also just choose to be nicer and more helpful to each other.

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Johannes Jakob Meyer @jjmeyer.bsky.social · Dec 9

That said, one line rejects should not happen. At the end of the day we've all been on the other side and justifiably annoyed by bad reviews.

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Johannes Jakob Meyer @jjmeyer.bsky.social · Dec 9

Therefore, it's more of an answer to the question: "how likely is this to cross the bar relative to the other submissions in your batch?". In that way, "weak reject" doesn't mean the submission is not good science, but just that there is so much other good stuff out there.

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Johannes Jakob Meyer @jjmeyer.bsky.social · Dec 9

Something that is important for context – and that I only realized after seeing the process from the inside – is that the scores are not meant to judge the quality of the submission. The task of the PC is to make a program.

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