Fully autocompensating high-dimensional quantum cryptography by quantum degenerate four-wave mixing

Bell-State-Exchange-Parity-Based Protocol for Efficient Autocompensation of Quantum Key Distribution Encoded in Polarization or Spatial Modes

“…For the case of polarization modes, if the perturbation on the first trip is P (a SU(2) matrix), then when the pulses return, it becomes P R = ZP T Z, where T denotes the transpose and Z is the third Pauli matrix. Note that off-diagonal elements change sign, apart from being interchanged [15,21], as the axis of propagation is modified when back-propagating, that is,…”

“…If the perturbation for the spatial modes on the first trip is P (a SU(2) matrix), then when the pulses return, it becomes P R = P T , where T denotes the transpose. Therefore, for spatial modes, we have that [15,21]…”

“…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.…”

Active and Quantum Integrated Photonic Elements by Ion Exchange in Glass

“…In this device, we propose to use a rare-earth-doped glass, as discussed in Section 3, for generating four weak laser signals obtained by pumping beams, that is, to use a hybrid glass. On the other hand, the passive part of the above device can in turn be used as an integrated quantum projector, of a high interest in quantum devices, particularly and once again, in quantum cryptography [215,216]. Moreover, another device for measuring Bell states is also described, which is of a great importance in MDI (measurement device independent) protocol [217], which is based on the use of two-photon states unlike the BB84 protocol that uses a single photon.…”

“…Next, it is worth describing the quantum mechanical treatment of the basic passive integrated optical elements of our integrated circuits, that is, the directional couplers 2 × 2 and phase shifters. We must stress that these 2 × 2 integrated optical elements (couplers and phase shifters) are enough to generate unitary transformations of dimension N, that is, SU(N) transformations, by concatening properly such optical elements [216]. Let us start by considering a two-dimensional quantum problem (N = 2), that is, the single photon quantum states are 1-qubits, namely, |L s = c o1 |1 1 + c o2 |1 2 , with 1 and 2 denoting two single mode channel waveguides.…”