Bell-State-Exchange-Parity-Based Protocol for Efficient Autocompensation of Quantum Key Distribution Encoded in Polarization or Spatial Modes  
[PERSON]  
1 Optics Area, Department of Applied Physics and iMATUS, Faculty of Physics/Faculty of Optics and Optometry, University of Santiago de Compostela, 15782 Santiago de Compostela, Galicia, Spain; [EMAIL_ADDRESS] (G.M.C. ); [EMAIL_ADDRESS] (X.P.-B.) [PERSON]  
1 Optics Area, Department of Applied Physics and iMATUS, Faculty of Physics/Faculty of Optics and Optometry, University of Santiago de Compostela, 15782 Santiago de Compostela, Galicia, Spain; [EMAIL_ADDRESS] (G.M.C. ); [EMAIL_ADDRESS] (X.P.-B.) [PERSON]  
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[PERSON]  
1 Optics Area, Department of Applied Physics and iMATUS, Faculty of Physics/Faculty of Optics and Optometry, University of Santiago de Compostela, 15782 Santiago de Compostela, Galicia, Spain; [EMAIL_ADDRESS] (G.M.C. ); [EMAIL_ADDRESS] (X.P.-B.) Footnote 1: [[https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci)]([https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci))  
Footnote 2: [[https://www.mdpi.com/journals/pdf/journals/](https://www.mdpi.com/journals/pdf/journals/)]([https://www.mdpi.com/journals/pdf/journals/](https://www.mdpi.com/journals/pdf/journals/))  
However, as said, the photon states are fragile. When propagating along a fiber, photons can be lost (scattered, absorbed...) and their quantum states perturbed (modal coupling, phase drifting, dispersion,...). In this paper, apart from losses, we will consider that photonic modes can be coupled between themselves and may pick up a relative phase. The relevant aspect here is that these couplings and/or phases are fundamentally unpredictable. Such fiber perturbations noise-pollute the information encoded in photons, leading to errors in the secret key. To handle this practically by using already deployed optical fiber technology, and to achieve what has been termed as \"plug and play QKD\" [12], autocompensation techniques constitute a feasible and simple solution. Different autocompensating systems have been proposed (some of them recently) for polarization perturbations [13], phase perturbations [14], and even general perturbations [15]. This research shows that, via suitable light circulation and application of passive transformations on photonic states, it is possible and practical to cancel optical fiber perturbations of the quantum light states. In this way, QKD protocols can be made robust against both coupling and phase perturbations at a reduced cost. This passive approach towards quantum optical state processing in QKD is not restricted to noise mitigation but also can be applied in other stages of the protocol [16]. A particular challenge is to apply autocompensation to states that are already entangled. As it is well known, there is whole subset of QKD protocols that are entanglement-based, meaning that they employ Bell states from the start and generate keys from the strong quantum correlations captured in such states. Even though production of entangled pairs is not an easy task, entanglement-based QKD has various advantages of its own [17]. Hence, it is desirable to analyze the issue of autocompensation in such protocols, that is, to study the effect of optical fiber perturbations on entangled states and how to remove their undesired effects by autocompensation techniques. In particular, we will be interested in removing perturbations across various fiber implementations by using polarization modes, for instance, in a single-mode optical fiber (SMF), or two collinear modes in FMFs, or two codirectional modes in MCFs, where Bell states (entangled states) will be excited in two optical fibers. To illustrate the problems associated with entanglement-based QKD, we will focus first on a well-known case: the BBM92 protocol with polarization modes [18]. We will show that only phase drift between optical polarization modes of an SMF can be autocompensated.