# How many minimum Quantum Rats are needed to figure out which bottle contains poison?

For the classical Poison and Rat puzzle, we need at least $$\lceil\log_2({\rm bottles})\rceil$$ rats to figure out the poisoned bottle.

If we have Schrödinger’s quantum rats, can we use fewer rats(qubits) to determine which bottle is poisonous?

No, the lower bound for the number of rats you need is still the same. Let $$N$$ be the number of bottles, so our experiment must return $$\log_2(N)$$ bits of information. For each rat, we know if it lives or dies, so we get a maximum of 1 bit of information from it (even though it's a qubit, you still have to measure it, and that reveals at most 1 bit of information). Hence, you need at least $$\lceil\log_2(N)\rceil$$ rats.