High-dimensional quantum encoding via photon-subtracted squeezed states

We introduce a high-dimensional quantum encoding based on coherent mode-dependent single-photon subtraction from multimode squeezed states. This encoding can be seen as a generalization to the case of nonzero squeezing of the standard single-photon multirail encoding. The advantage is that the presence of squeezing enables the use of common tools in continuous-variable quantum processing, which in turn allows us to show that arbitrary d-level quantum states can be generated and detected by simply tuning the classical fields that gate the photon-subtraction scheme. Therefore, the scheme is suitable for mapping arbitrary classical data in quantum mechanical form. Regardless of the dimension of the data-set alphabet, the mapping is conditioned on the subtraction of a single photon only, making it nearly unconditional. We prove that this encoding can be used to calculate vector distances, a pivotal primitive in various quantum machine-learning algorithms.