 No-communication theorem

A trace-preserving operation on subsystem $B$ cannot change the reduced density matrix of a disjoint subsystem $A$ when its unobserved outcomes are averaged. Local measurements on $A$ therefore cannot reveal which operation was chosen on $B$.

The No-communication theorem is a concept in quantum mechanics that pertains to the behavior of entangled particles. It states that quantum entanglement cannot be used to transmit information or communicate faster than the speed of light, even though the measurement of one entangled particle can instantaneously affect the state of another, distant entangled particle.