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Journal Articles Physical Review Letters Year : 2020

Stellar representation of non-Gaussian quantum states

Damian Markham
Frédéric Grosshans


The so-called stellar formalism allows to represent the non-Gaussian properties of single-mode quantum states by the distribution of the zeros of their Husimi Q-function in phase-space. We use this representation in order to derive an infinite hierarchy of single-mode states based on the number of zeros of the Husimi Q-function, the stellar hierarchy. We give an operational characterisation of the states in this hierarchy with the minimal number of single-photon additions needed to engineer them, and derive equivalence classes under Gaussian unitary operations. We study in detail the topological properties of this hierarchy with respect to the trace norm, and discuss implications for non-Gaussian state engineering, and continuous variable quantum computing.

Dates and versions

hal-02316973 , version 1 (15-10-2019)



Ulysse Chabaud, Damian Markham, Frédéric Grosshans. Stellar representation of non-Gaussian quantum states. Physical Review Letters, 2020, ⟨10.1103/PhysRevLett.124.063605⟩. ⟨hal-02316973⟩
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