Quantum disentanglers

Abstract

It is not possible to disentangle a qubit in an unknown state $|ψ>$ from a set of (N-1) ancilla qubits prepared in a specific reference state $|0>$. That is, it is not possible to {\em perfectly} perform the transformation $(|ψ,0...,0\r +|0,ψ,...,0\r +...+ |0,0,...ψ\r) \to |0,...,0>\otimes |ψ>$. The question is then how well we can do? We consider a number of different methods of extracting an unknown state from an entangled state formed from that qubit and a set of ancilla qubits in an known state. Measuring the whole system is, as expected, the least effective method. We present various quantum ``devices'' which disentangle the unknown qubit from the set of ancilla qubits. In particular, we present the optimal universal disentangler which disentangles the unknown qubit with the fidelity which does not depend on the state of the qubit, and a probabilistic disentangler which performs the perfect disentangling transformation, but with a probability less than one.