Research
Theorem of the Day
One theorem from quantum mechanics, quantum computing, or quantum information theory: its statement, a complete proof, and a new result we derive from it.
Today’s theorem
- The no-cloning theorem
No physical process can copy two distinct, non-orthogonal pure states. We prove it, then derive the exact fidelity tradeoff for approximately cloning two known states from N copies to M.
How each entry works
Each entry states a theorem from quantum mechanics, quantum computing, or quantum information theory precisely, with its assumptions, and gives a complete proof. It then derives a new result from the same idea and proves it in full. A worked numerical check follows.
A new result is our own contribution and has not been peer reviewed. Each entry says which parts are already known, cites the closest prior work, and invites corrections.