Universal Manipulation of a Single Qubit

Details Universal Manipulation of a Single Qubit Universal Manipulation of a Single Qubit

2000-08-02

arxiv.org/abs/quant-ph/0008011v1

Phys. Rev. A 63, 032304 (2001)

Physics

Quantum Physics

6 pages, 1 figure

Scientific paper

10.1103/PhysRevA.63.032304

We find the optimal universal way of manipulating a single qubit, |psi(theta,phi)>, such that (theta,phi)->(theta-k,phi-l). Such optimal transformations fall into two classes. For 0 =< k =< pi/2 the optimal map is the identity and the fidelity varies monotonically from 1 (for k=0) to 1/2 (for k=pi/2). For pi/2 =< k =< pi the optimal map is the universal-NOT gate and the fidelity varies monotonically from 1/2 (for k=pi/2) to 2/3 (for k=pi). The fidelity 2/3 is equal to the fidelity of measurement. It is therefore rather surprising that for some values of k the fidelity is lower than 2/3.

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