You can't erase it in the physics sense, but you can erase information in an engineering sense, such that it is irretrievable in practice. NAND gates erase information this way; given an output, there's no way to determine in all cases what the inputs were.

A NAND gate doesn't erase information; you still have the inputs. In Quantum computers it's more a matter of "overwriting" a qubit with a new value.

Every gate that has more inputs than outputs erases information. (NOT gates don't erase information.)

Quantum gates generally have the same number of outputs as inputs, so they don't erase.

Ahh, clarity. Thanks for posting.

In other words, Laundauer's Principle might be rephrased as, "all possible physical realizations of information erasure are (by Conservation of quantum information) actually forms of information transmission in disguise."