Author Archives: Mateus Araújo

Hilbert’s Hotel and Gödel’s Freezer

A friend of mine, Flavien Hirsch, invented a fascinating paradox in probability, called Hilbert’s Hotel and Gödel’s Freezer. Technically speaking it is the same thing as the Sleeping Beauty problem, which I’ve written about here, but I find it much … Continue reading

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Beautiful angles with beautiful cosines

I’ve recently proved a theorem that is probably well-known to anyone that studied number theory. I didn’t know it before, though, and it was a lot of fun, so I decided to write it up here in case there are … Continue reading

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Implementing impossible functions via tomography

A long time ago I had a conversation with Daniel Nagaj about the following problem: given access to an unknown unitary gate $U$, is it possible to build the gate control-$U$ out of it? Nagaj argued that it was impossible, … Continue reading

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Explicitly local quantum mechanics

I’ve just attended a nice online talk by Charles Bédard about his somewhat recent paper, where he studies the explicitly local model of quantum mechanics developed by Deutsch and Hayden, with a twist by Raymond-Robichaud. I think it’s a neat … Continue reading

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Why QBism is completely empty

A good friend of mine, Jacques Pienaar, has recently converted to QBism, as often happens to people that spend too much time around Chris Fuchs. Saddened by these news, I’ve decided to write a blog post explaining why QBism doesn’t … Continue reading

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Mistakes, mistakes, mitsakes

When I write someone to tell them there’s a mistake in their paper, I usually get one of these five reactions, ordered from best to worst: “It’s not a mistake.” (and they’re right) “Indeed, that’s wrong, I’ll correct it.” “It’s … Continue reading

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The two-envelope paradox

A colleague of mine, Simon Morelli, told me about a fascinating puzzle, the two-envelope paradox: you can take one of two envelopes with money inside them, promised to contain one $x$ and the other $2x$ for some $x > 0$. … Continue reading

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The problem with being your own father

is not really a moral one. In the typical time travel story you were abandoned as a child, so after you travel back in time you don’t even know who is supposed to be your mother. Now what can you … Continue reading

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Meaningful Bell inequalities part 2: examples

Here I’ll show examples of the meaningful Bell inequalities I talked about in the previous post, where they are rephrased as nonlocal games and the gap between the local bound and the Tsirelson bound is made as large as possible. … Continue reading

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Meaningful Bell inequalities

Since I’ve started learning about Bell inequalities, it always bothered me that they are usually present as just some linear combinations of conditional probabilities, without any physical interpretation besides the fundamental fact that the maximal value this linear combination can … Continue reading

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