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 Einstein-Podolsky-Rosen states, which 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 of the spatial, temporal, frequency, or polarization type. 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 build in a controlled way a quantum network [H. Jeff Kimble, Nature (London) 453, 1023 (2008)] 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 are subject only to weak decoherence. They indeed open 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 this 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 one to consider the same quantum state under different perspectives: a given state can be entangled in one basis and factorized in another. It is shown that there exist some properties that are invariant over a change in the choice of the basis of modes. The method of finding the minimal set of modes that are needed to describe a given multimode quantum state is also presented. It is then shown how to produce, characterize, tailor, and use multimode quantum light while also considering the effect of loss and amplification on such light and the modal aspects of the two-photon coincidences. Switching to applications to quantum technologies, this review shows 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.” Finally, details on how to use such quantum modal networks for measurement-based quantum computation are presented.

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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，压缩态，双光束和爱因斯坦-波多尔斯基-罗森态，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，涉及到空间，时间，频率或极化类型的许多模式。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量子网络[H。杰夫·金布尔，《自然》（伦敦） 453，1023（2008）]，其中节点是光学模式，并具有强的多部分纠缠。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。实际上，它们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。这篇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。确实，使用不同的模式集可以使一个人在不同的角度下考虑相同的量子态：给定状态可以在一个基础上纠缠而在另一个基础上分解。结果表明，存在一些属性，这些属性对于模式基础的选择变化是不变的。还介绍了找到描述给定多模量子态所需的最小模集的方法。然后显示了如何产生，表征，定制和使用多模量子光，同时还考虑了损耗和放大对此类光的影响以及双光子巧合的模态方面。转向量子技术的应用程序后，这篇综述表明，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。最后，详细介绍了如何使用这种量子模态网络进行基于测量的量子计算。