On supporting affine functionals for Entanglement of Formation
A mathematical trap in quantum entanglement that breaks a widely-held assumption
A basic assumption about quantum entanglement has been wrong. Many physicists have assumed that for any quantum state, you can find a mathematical tool (called a supporting affine functional) that perfectly characterizes its entanglement. This paper shows that assumption fails—even in the simplest possible case of two basic quantum particles—when those particles are in certain kinds of states.
Entanglement of Formation is a central concept in quantum information theory, used in everything from quantum computing to quantum cryptography. If the mathematical framework physicists have been using doesn't actually work as promised, then calculations and proofs relying on that framework may be unreliable. This paper forces researchers to be more careful about when they can safely use these mathematical shortcuts and identifies which quantum states need special handling.