Quantum Anti-Cloning.pdf

a r X i v : q u a n t - p h / 0 0 0 1 1 0 5 v 2 2 5 F e b 2 0 0 0 quant-ph/0001105 Quantum Anti-Cloning David D. Song1 and Lucien Hardy2 Centre for Quantum Computation Clarendon Laboratory, University of Oxford Parks Road, Oxford OX1 3PU, U.K. Abstract We derive the transformation for the optimal universal quantum anti-cloner which produces two anti-parallel outputs for a single input state. The fidelity is shown to be 2/3 which is same as the measurement fidelity. We consider a probabilistic quantum anti-cloner and show quantum states can be anti-cloned exactly with non- zero probability and its efficiency is higher than the efficiency of distinguishing between the two states. 1 E-mail: d.song@qubit.org 2 E-mail: l.hardy@qubit.org 1 Introduction Possessing superposition and entanglement properties, quantum information has revealed many interesting features which classical information has no counterpart. Unlike classical information, quantum information cannot be duplicated, i.e. unknown quantum state cannot be copied exactly [1]. However a universal quantum (approximate) cloner has been introduced [2, 3] which takes an unknown quantum state and generates multiple copies, with fidelity 5/6 in case of two copies as outputs regardless of an input. Another feature of quantum information has been discovered recently [4] where it was shown that more quantum information can be gained from two anti-parallel spins than from two parallel ones, i.e. one can measure the spin direction |n〉 with better fidelity when two qubits are in anti-parallel, |n,?n〉, than in parallel, |n,n〉. In this paper, we consider a universal quantum anti-cloner which takes an unknown quantum state just as in quantum cloner but its output as one with the same copy while the second one with opposite spin direction to the input state. For the Bloch vector, an input n, quantum anti-cloner would have the input as 1 2 (1+ n ·σ), then it generates two outputs, 1 2 (1 + ηn · σ) and 1 2 (1 ? ηn · σ), wher