Question 14
A crazy physicist discovers particles called imons. Some pairs are entangled, and an imon may be entangled with many others. He can perform either operation:
(1) Destroy an imon entangled with an odd number of other imons.
(2) Double the entire family: create a copy $I'$ of each imon $I$. Copies $I',J'$ are entangled exactly when $I,J$ are entangled; each $I'$ is also entangled with $I$. No other entanglements occur or disappear.
Prove that a sequence of operations can leave a family in which no two imons are entangled.
(1) Destroy an imon entangled with an odd number of other imons.
(2) Double the entire family: create a copy $I'$ of each imon $I$. Copies $I',J'$ are entangled exactly when $I,J$ are entangled; each $I'$ is also entangled with $I$. No other entanglements occur or disappear.
Prove that a sequence of operations can leave a family in which no two imons are entangled.