A few decades ago, quantum optics stood out as a new domain of physics by exhibiting states of light with no classical equivalent. The first investigations concerned single photons, squeezed states, twin beams and EPR states, that involve only one or two modes of the electromagnetic field. The study of the properties of quantum light then evolved in the direction of more and more complex and rich situations, involving many modes, either spatial, temporal, frequency, or polarization modes. Actually, each mode of the electromagnetic field can be considered as an individual quantum degree of freedom. It is then possible, using the techniques of nonlinear optics, to couple different modes, and thus to build in a controlled way a quantum network in which the nodes are optical modes, and that is endowed with a strong multipartite entanglement. In addition, such networks can be easily reconfigurable and subject only to weak decoherence. They open indeed many promising perspectives for optical communications and computation. Because of the linearity of Maxwell equations a linear superposition of two modes is another mode. This means that a “modal superposition principle” exists hand in hand with the regular quantum state superposition principle. The purpose of the present review is to show the interest of considering these two aspects of multimode quantum light in a global way. Indeed using different sets of modes allows to consider the same quantum state under different perspectives: a given state can be entangled in one basis, factorized in another. We will show that there exist some properties that are invariant over a change in the choice of the basis of modes. We will also present the way to find the minimal set of modes that are needed to describe a given multimode quantum state. We will then show how to produce, characterize, tailor and use multimode quantum light, consider the effect of loss and of amplification on such light and the modal aspects of the two-photon coincidences. Switching to applications to quantum technologies, we will show in this review that it is possible to find not only quantum states that are likely to improve parameter estimation, but also the optimal modes in which these states “live”. We will finally present how to use such quantum modal networks for measurement-based quantum computation.

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量子光学中的模式和状态

几十年前，量子光学通过展示没有经典等效物的光态而脱颖而出，成为物理学的一个新领域。最初的研究涉及单光子，压缩状态，双光束和EPR状态，它们仅涉及一种或两种电磁场模式。然后，对量子光特性的研究朝着越来越复杂和丰富的情况发展，涉及许多模式，包括空间，时间，频率或偏振模式。实际上，电磁场的每种模式都可以视为一个单独的量子自由度。然后可以使用非线性光学技术耦合不同的模式，从而以可控的方式构建一个量子网络，其中的节点是光学模式，并具有强大的多部分纠缠。另外，这样的网络可以容易地重新配置并且仅经受弱的去相干性。它们确实为光通信和计算打开了许多有希望的前景。由于麦克斯韦方程的线性，两种模式的线性叠加是另一种模式。这意味着“模态叠加原理”与规则的量子态叠加原理并存。本综述的目的是显示出以全局方式考虑多模量子光的这两个方面的兴趣。实际上，使用不同的模式集可以在不同的角度考虑相同的量子状态：给定状态可以在一个基础上纠缠，而在另一个基础上分解。我们将显示存在一些属性，这些属性对于模式基础的选择发生变化。我们还将提供找到描述给定多模量子态所需的最小模集的方法。然后，我们将展示如何产生，表征，定制和使用多模量子光，考虑损耗和放大对此类光的影响以及双光子巧合的模态方面。切换到量子技术的应用程序时，我们将在这篇综述中表明，不仅可以找到可能改善参数估计的量子状态，而且可以找到这些状态“存在”的最佳模式。我们最终将介绍如何使用这种量子模态网络进行基于测量的量子计算。考虑损耗和放大对此类光的影响以及双光子重合的模态方面。切换到量子技术的应用程序时，我们将在这篇综述中表明，不仅可以找到可能改善参数估计的量子状态，而且可以找到这些状态“存在”的最佳模式。我们最终将介绍如何使用此类量子模态网络进行基于测量的量子计算。考虑损耗和放大对此类光的影响以及双光子重合的模态方面。切换到量子技术的应用程序时，我们将在这篇综述中表明，不仅可以找到可能改善参数估计的量子态，而且可以找到使这些态“存活”的最佳模式。我们最终将介绍如何使用这种量子模态网络进行基于测量的量子计算。