Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem

Details Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem

2004-10-14

arxiv.org/abs/quant-ph/0410117v2

Phys. Rev. A 72, 012309 (2005)

Physics

Quantum Physics

18 pages, 16 figures; typos fixed, some minor corrections, figures of the circuits were changed

Scientific paper

10.1103/PhysRevA.72.012309

We analyze and further develop a new method to represent the quantum state of a system of $n$ qubits in a phase space grid of $N\times N$ points (where $N=2^n$). The method, which was recently proposed by Wootters and co--workers (Gibbons {\it et al.}, quant-ph/0401155), is based on the use of the elements of the finite field $GF(2^n)$ to label the phase space axes. We present a self--contained overview of the method, we give new insights on some of its features and we apply it to investigate problems which are of interest for quantum information theory: We analyze the phase space representation of stabilizer states and quantum error correction codes and present a phase space solution to the so--called ``mean king problem''.

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