One hundred
statements that
define the theory.
Theorems, identities and physical principles, each with its formula, an explanation and the conditions under which it holds.
Enter the formalism.
Six doorways into quantum theory.
Each opens a full statement page.
Slide 1 of 6: Born rule
From operators
to many-body physics.
The 100 statements are grouped into seven connected topics.
Linear algebra
The mathematical grammar of quantum theory: Hermitian and unitary operators, Pauli matrices, projectors and tensor products.
02 / STATESStates and measurements
Density operators, the Born rule, and the limits on cloning, broadcasting, signalling and state discrimination.
03 / FOUNDATIONSUncertainty and quantum foundations
Uncertainty relations, Bell and Tsirelson bounds, contextuality, Gleason’s theorem and the Zeno effect.
04 / ENTANGLEMENTEntanglement and quantum information
Schmidt decomposition, entropy inequalities, monotones under channels and the structure of entanglement.
05 / DYNAMICSQuantum dynamics and symmetries
Schrödinger and von Neumann evolution, conservation laws, Wigner and Stone theorems, Kramers degeneracy and open systems.
06 / COMPUTINGQuantum computing and algorithms
Gates, Clifford circuits, error correction, teleportation, and the algorithms of Grover and Shor.
07 / MANY-BODYAtomic physics
Quantum statistics, condensates, superfluidity, lattices, dark states and electromagnetically induced transparency.
From the reference
A compact formula is not a claim of unrestricted validity.Dimension, finite size, equilibrium and model assumptions are essential. Read how to use this reference ↗
Four stages of understanding.
Operators, states and measurements: the grammar of the theory.
Uncertainty, Bell nonlocality and the entropy of entanglement.
Dynamics, symmetry, error correction and quantum algorithms.
Quantum statistics, condensates, lattices and light–matter coherence.
Ten results.
A research programme.
Schur’s lemma, no-cloning, strong subadditivity, the Knill–Laflamme condition and more: the results to prove, illustrate and exemplify first.
Open the priority results ↗Why can’t a quantum state be cloned?
Expanded study edition
All 100 statements now include deeper conceptual context, mathematical reading guidance, a worked example or guided exercise, real-world relevance, and self-check questions.