The notion that the electromagnetic field is quantized is usually inferred from observations such as the photoelectric effect and the black-body spectrum. However accounts of the quantization of this field are usually mathematically motivated and begin by introducing a vector potential, followed by the imposition of a gauge that allows the manipulation of the solutions of Maxwell's equations into a form that is amenable for the machinery of canonical quantization. By contrast, here we quantize the electromagnetic field in a less mathematically and more physically motivated way. Starting from a direct description of what one sees in experiments, we show that the usual expressions of the electric and magnetic field observables follow from Heisenberg's equation of motion. In our treatment, there is no need to invoke the vector potential in a specific gauge and we avoid the commonly used notion of a fictitious cavity that applies boundary conditions to the field.

We propose a repeat-until-success protocol to improve the performance of probabilistic quantum repeaters. Quantum repeaters rely on passive static linear optics elements and photodetectors to perform Bell-state measurements (BSMs). Conventionally, the success rate of these BSMs cannot exceed 50%, which is an impediment for entanglement swapping between distant quantum memories. Every time that a BSM fails, entanglement needs to be re-distributed between the corresponding memories in the repeater link. The key ingredient in our scheme is a repeatable BSM. Although it too relies only on linear optics and photo-detection, it ideally allows us to repeat every BSM until it succeeds. This, in principle, can turn a probabilistic quantum repeater into a deterministic one. Under realistic conditions, where our measurement devices are lossy, our repeatable BSMs may also fail. However, we show that by using additional threshold detectors, we can improve the entanglement generation rate between one and two orders of magnitude as compared to the probabilistic repeater systems that rely on conventional BSMs. This improvement is sufficient to make the performance of probabilistic quantum repeaters comparable with some of existing proposals for deterministic quantum repeaters.Comment: 11 pages, 8 figure

Abstract. Hidden Markov Models are widely used in classical computer science to model stochastic processes with a wide range of applications. This paper concerns the quantum analogues of these machines -socalled Hidden Quantum Markov Models (HQMMs). Using the properties of Quantum Physics, HQMMs are able to generate more complex random output sequences than their classical counterparts, even when using the same number of internal states. They are therefore expected to find applications as quantum simulators of stochastic processes. Here, we emphasise that open quantum systems with instantaneous feedback are examples of HQMMs, thereby identifying a novel application of quantum feedback control.

Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same notion of photons as in linear optics scattering theory and consider a continuum of travelling-wave cavity photon modes. Our model predicts the same stationary state photon emission rates for the different sides of a laser-driven optical cavity as classical theories. Moreover, it predicts the same time evolution of the total cavity photon number as the standard standing-wave description in experiments with resonant and near-resonant laser driving. The proposed resonator Hamiltonian can be used, for example, to analyse coherent cavity-fiber networks [E. Kyoseva et al., New J. Phys. 14, 023023 (2012)].

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