A Note on the Disentanglement of Gaussian Quantum States by Symplectic Rotations

A Few Almost Trivial Notes on the Symplectic Radon Transform and the Tomographic Picture of Quantum Mechanics

We emphasize in these pedagogical notes the that the theory of the Radon transform and its applications is best understood using the theory of the metaplectic group and the quadratic Fourier transforms generating metaplectic operator.. Doing this we hope that these notes will be useful to a larger audience, including researchers in time-frequency analysis.

Notes on the Fidelity of Symplectic Quantum Error-Correcting Codes

Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the correctable errors for general quantum channels. The second observation states that for any coding rate below the quantum capacity, exponential convergence of the fidelity of some codes to unity is possible.

关于量子比特相空间与离散辛结构的注记

Notes on the Qubit Phase Space and Discrete Symplectic Structures

本文从非对易空间视角研究量子比特离散相空间，给出 Moyal 括号的显式微分算子形式，并证明经典 Poisson 括号不满足 Jacobi 恒等式，从而确立 Moyal 括号为唯一相容辛结构，并推广到素数维 Hilbert 空间。