I explain quantum technology in plain English. Free course at https://xitter.cf/t.co/m5G8nDpcVv. Independent researcher in quantum foundations, with formal proofs in Lean.
London
Joined January 2010
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In 2021 the Dutch nuclear safety regulator told people to stop wearing their "quantum" pendants because they were radioactive. The word quantum sells everything from computers to jewellery and some of it is real. I've written five questions that sort real claims from the rest.
Higuchi and Sudbery showed in 2000 that you can't entangle four quantum coins so that any two on their own look completely random. It works for two, three, five and six.
I've proved it in Lean with a shorter argument by Felix Huber and coauthors.
github.com/zblore/fc-ame-4-2
The invariant subspace problem asks whether every operator on an infinite-dimensional Hilbert space keeps some smaller space to itself. It's open.
For normal operators the answer is yes and I've proved it in Lean. baobingzhang beat me to it in September.
github.com/zblore/fc-isp-nor…
Stanisław Mazur asked whether a space that looks the same in every direction has to measure distance with Pythagoras.
It's open in general but in finite dimensions the answer is yes. I've proved that case in Lean, following a sketch by Sergei Ivanov.
palomar-registry.org/entry.h…
Mark Kac proved in 1947 that a system returns to a region as often as its size says.
It's why a room's air never crowds into one half. In a simple model the wait doubles with each molecule.
I've proved it in Lean after Sébastien Gouëzel did in Isabelle.
palomar-registry.org/entry.h…
Bevins and Bidav found how to entangle twelve five-sided quantum dice so any six look completely random on their own.
I've proved it in Lean by checking all 924 ways to pick the six. Kenta Kitamura beat me to it and I only found his after writing mine.
palomar-registry.org/entry.h…
Can you entangle seven quantum dice so any three alone look completely random? Two-sided dice can't. Dice with three or more sides can.
Six and ten sides stayed open until Shi, Zhang, Zhao and Li settled them this year. My Lean proof checks every case.
palomar-registry.org/entry.h…
In 1782 Euler asked if 36 officers of six ranks and six regiments fit a square with no repeats in a row or column. They don't. Entangled ones do.
Rather and colleagues found the state in 2022. Google DeepMind's Formal Conjectures now links my Lean proof.
github.com/google-deepmind/f…
In 1968 Dixmier asked if you can always reverse a map that keeps the rules of quantum position and momentum. Alpöge's Jacobian counterexample shows you can't from dimension 3 on.
My Lean proof is on Palomar. It credits those who got dimension 3 in July.
palomar-registry.org/entry.h…
Dimensions 1 and 2 are still open, and Dixmier's own question was dimension 1.
I've also registered a related result: the Jacobian conjecture in dimension 2n implies the Poisson conjecture in dimension n. Google DeepMind's Formal Conjectures links it.
palomar-registry.org/entry.h…
My Lean proof of the Lie–Trotter product formula is now registered on Palomar. It holds in any real Banach algebra, with an error bound that scales with the commutator:
‖(e^{A/n} e^{B/n})ⁿ − e^{A+B}‖ ≤ ‖AB − BA‖/(2n) · e^{‖A‖+‖B‖}
palomar-registry.org/entry.h…
The Poisson conjecture is false from dimension 2 on. C. D. Long proved it in August (arXiv:2608.23777). My Lean proof of it is now registered on Palomar and linked from Google DeepMind's Formal Conjectures.
palomar-registry.org/entry.h…
It's chapter 16 of my free course, no sign-up needed explainquantum.com/learn/hyp…
Will quantum computers break today's encryption? Estimates fell from 20 million qubits in 2019 to under a million in 2025. No machine is close yet but the switch to quantum-safe maths has started and your browser may already use it. I've explained it here explainquantum.com/learn/wil…
Read's 1985 counterexample to the invariant subspace problem on ℓ¹ is now formally proved in Lean, following Śliwa's explicit operator. Google DeepMind's Formal Conjectures merged the link this week.
github.com/zblore/fc-read-l1
explainquantum.com
Explaining Quantum, without the dice.
Choose your entry point & enjoy!
#quantum #quantummechanics
My Lean proof of Gleason's theorem is now registered on Palomar, the new registry of machine-checked proofs.
In three or more dimensions, the Born rule is the only consistent way to assign quantum probabilities. Proved against Kim Morrison's statement.
palomar-registry.org/entry.h…
My AME(6,2) proof is now merged into Google DeepMind's Formal Conjectures too.
Six qubits where any three, on their own, look like pure coin flips. The largest case possible for qubits. Known since 2004. Symmetry cuts 720 checks to 4.
github.com/google-deepmind/f…
My AME(5,2) proof is now merged into Google DeepMind's Formal Conjectures.
It shows a five-qubit state exists where any two qubits, on their own, look like pure coin flips. Known since 2004. Mine is the first machine-checked proof, in Lean.
github.com/google-deepmind/f…
