Polarization-entanglement distribution in fiber-optic channels

Entanglement is a key ingredient in many quantum communication protocols, and robust quantum channels are needed for its fast and reliable distribution over long distances. As quantum communication technology matures, it moves towards utilizing actual fibers, which leads to a growing need for physical models describing decoherence and the other effects that take place in this kind of media. In this work, we analyze how two phenomena that are ever-present in fiber-optic based networks, namely polarization-mode dispersion (PMD) and polarization-dependent loss (PDL), affect the distribution of polarization-entangled photons. The former represents the main source of decoherence in a fiber-optic channel, while the latter is an example of modal filtering. We start by considering the distribution of polarization-entangled photon pairs through optical fibers where PMD acts as a decoherence mechanism. We analyze both the case in which PMD is present in the channel of one photon only, and the case in which the propagation of both photons is affected by PMD. We quantify the entanglement quality of the received two-photon states by means of a well known entanglement metric, known as concurrence, and we analyze how this is impacted by the main system parameters. We also develop a a treatment of this problem in the framework of quantum information theory, where the total correlations between different parts of a system are quantified by making use of the von Neumann entropy and the quantum mutual information. We discuss the concept of nonlocal PMD compensation and quantify its beneficial effect on entanglement in terms of concurence and quantum mutual information restoration. We then move on to analyzing the case in which PMD and PDL are present in the channel of one photon of a polarization-entangled pair. The primary challenge when dealing with these combined effects is to concisely account for numerous elements that in general are distributed along a lengthy optical path. We approach this by starting with an analytical model of a channel with just two lumped elements, one representing PMD and the other representing PDL. Interestingly, we find that, while the order and relative orientation of the two elements produce a wealth of different biphoton states, the amount of entanglement in all those states is exactly the same, a result that we explained also in simple, intuitive terms. Then, we conduct experiments that implement this channel and verify our analytical findings. We turn our attention to the most general fiber polarization channel, comprised of a statistically significant number of arbitrarily oriented elements. We show that, over an ample range of parameters, our two-element analytical model is quite accurate in describing the fiber channel, which makes it an effective tool for gaining insights into channel decoherence. We conclude this part by extending the analysis to the case in which PDL affects the propagation of both photons, in conjunction with PMD in one optical path. Finally, we show how the presence of PMD and PDL alone can lead to the formation of peculiar entangled states that can’t be detected by a conceptually simple and experimentally prevalent class of entanglement witnesses, known as fidelity witnesses. These states, usually referred to as unfaithful states, are exceedingly common among bipartite states, especially for higher dimensional systems. In this work, we show that even among two-qubit states, the simplest of all entangled states, unfaithful states can be created through a suitable application of PMD and PDL to a Bell state. We also show that the faithfulness is not monotonic to entanglement, as measured by the concurrence. Finally, we experimentally verify our predictions and specifically demonstrate a situation where an unfaithful state is brought to faithfulness at the expense of further reducing the entanglement of the state.