The Choi–Jamiolkowski forms of quantum Gaussian channels

2010/04/30 by A. S. Holevo · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Bounded function #Gaussian #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Quantum optics and atomic interactions #math-ph #math.MP #msc:81Qxx #quant-ph

paper · pdf · doi:10.1063/1.3581879

published as J. Math. Phys., 52 (2011), 042202 · Results in Sec. 3,4 are strengthened. Sec. 4 is complemented with treatment of three degenerate cases. Sec. 5 is added where a decomposition of the Gaussian CJ form into product of the four principal types and a necessary and sufficient condition for existence of the bounded CJ operator are given

arxiv created 2011/01/22 · openalex publication_date 2011/04/01 · arxiv updated 2011/11/16 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/22

Abstract

We obtain explicit expressions for the Choi–Jamiolkowski (CJ) forms and operators defining a general bosonic Gaussian channel. The four principal cases are considered in Sec. III; in Sec. IV, we give a decomposition of Gaussian CJ form into product of these four principal types and provide a necessary and sufficient condition for the existence of the bounded CJ operator.

Citations

• Completely positive linear maps on complex matrices
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