Superposition of optical coherent states (SCS) [Formula: see text], possessing opposite phases, plays an important role as qubits in quantum information processing tasks like quantum computation, teleportation, key distribution, etc. and are of fundamental importance in testing quantum mechanics. Passage of such SCS from a 50:50 beam splitter leads to generation of entangled coherent states. Recently, ququats and qutrits defined in four- and three-dimensional Hilbert space, respectively, have attracted much attention as they offer advantage in secure quantum communication. However, practical utilization of these advantages essentially requires physical realization of quantum optical ququats and qutrits. Here, we define four new multi-photonic states (MPS) with [Formula: see text] (here, [Formula: see text] or 3 and [Formula: see text]) numbers of photon and show how the SCS can be used to encode ququat using these MPS as basis vectors of a four-dimensional Hilbert space. When these MPS fall upon a 50:50 beam splitter, the resulting states are bipartite four-component entangled coherent states (BFECS) equivalently representing the entangled ququats. We briefly discuss the photon statistical properties of such MPS and BFECS. We show that these MPS and BFECS can be synthesized using even coherent states as input to an interferometer. We give a simple linear optical protocol for almost perfect teleportation of a ququat encoded in SCS with the aid of BFECS as quantum channel. We also describe how these ququats can be used for realization of higher-dimensional BB84 protocol to increase the security of quantum key distribution. Finally, we discuss the possible advantages of using SCS as ququats and BFECS as quantum channel in different quantum information processing tasks.
A high-speed tunable beam splitter for feed-forward photonic quantum information processing