计算明亮 "香蕉 "态准概率分布的有效算法

Boulat Nougmanov
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摘要

由负值维格纳函数描述的非高斯量子态对于量子物理学的基础测试和新兴量子信息技术都非常重要。从相干态生成非高斯态的一个可行方法是利用立方(克尔)光学非线性,它能使生成的量子态具有香蕉状的特征。然而,在高度透明的光学材料中,克尔效应很弱(无量纲非线性参数Γ≲10-6)。因此,要产生可观测到的非高斯性,光学模式中必须有大量光子(n≳106)。在这种情况下,直接计算 Wigner 函数的方法计算成本极高。在这项工作中,我们开发了利用克尔非线性计算这些非高斯态的侯西米和维格纳准概率函数的快速算法。该算法可用于光子数和非线性的任何实际值。
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Effective algorithms for calculation of quasi-probability distributions of bright “banana” states
Non-Gaussian quantum states, described by negative-valued Wigner functions, are important for both fundamental tests of quantum physics and for emerging quantum information technologies. One of the promising ways of generating a non-Gaussian state from a coherent one is the use of cubic (Kerr) optical nonlinearity, which produces the characteristic banana-like shape of the resulting quantum states. However, the Kerr effect is weak in highly transparent optical materials (dimensionless nonlinearity parameter Γ≲10−6). Therefore, a big number of the photons in the optical mode (n≳106) is necessary to generate an observable non-Gaussianity. In this case, the direct approach to calculation of the Wigner function becomes extremely computationally expensive. In this work, we develop quick algorithms for computing the Husimi and Wigner quasi-probability functions of these non-Gaussian states by means of the Kerr nonlinearity. This algorithm can be used for any realistic values of the photon numbers and the nonlinearity.
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