Quantum disentanglers
Vladimír Bužek, Mark S. Hillery · Physical Review A · 2000
It is not possible to disentangle a qubit in an unknown state $|\ensuremath{\psi}〉$ from a set of $N\ensuremath{-}1$ ancilla qubits prepared in a specific reference state $|0〉.$ That is, it is not possible to perfectly perform the transformation $(|\ensuremath{\psi},0,\dots{},0〉+|0,\ensuremath{\psi},\dots{},0〉+\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}+|0,0,\dots{},\ensuremath{\psi}〉)\ensuremath{\rightarrow}|0,\dots{},0〉\ensuremath{\bigotimes}|\ensuremath{\psi}〉.$ 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 a 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 a fidelity that 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 1.