no. 4
Théorie spectrale
On the disentanglement of Gaussian quantum states by symplectic rotations
[Sur la désintrication des états quantiques Gaussiens par des rotations symplectiques]
de Gosson, Maurice A.1
1 Universität Wien Fakultät für Mathematik (NuHAG) Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 459-462.

Nous montrons que chaque état quantique Gaussien peut-être rendu séparable (= « désintriqué ») par conjugaison avec un opérateur unitaire associé via le groupe métaplectique à une rotation symplectique. Pour cela nous utilsons la condition de séparabilité de Werner et Wolf sur la matrice de covariance ainsi que la covariance symplectique des opérateurs pseudo-différentiels de Weyl.

We show that every Gaussian mixed quantum state can be disentangled by conjugation with a unitary operator corresponding to a symplectic rotation via the metaplectic representation of the symplectic group. The main tools we use are the Werner–Wolf condition for separability on covariance matrices and the symplectic covariance of Weyl pseudo-differential operators.

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DOI : 10.5802/crmath.57
de Gosson, Maurice A. 1

1 Universität Wien Fakultät für Mathematik (NuHAG) Oskar-Morgenstern-Platz 1, 1090 Wien, Austria 
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de Gosson, Maurice A. On the disentanglement of Gaussian quantum states by symplectic rotations. Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 459-462. doi : 10.5802/crmath.57. http://www.numdam.org/articles/10.5802/crmath.57/

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