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Superposition of optical coherent states $\left|\pm\alpha\right\rangle$,possessing opposite phases, play an important role as qubits in quantuminformation processing (QIP) tasks and are of fundamental importance in testingquantum mechanics. Passage of such superposition of coherent states (SCS) froma 50:50 beam splitter lead to generation of entangled coherent states.Recently, ququats and qutrits defined in four and three dimensional Hilbertspace respectively, have attracted much attention as they offer advantage insecure quantum communication. However, practical utilization of theseadvantages essentially require physical realization of quantum optical ququatsand qutrits. Here, we define four new multi-photonic states (MPS) with $4n +j$(here, $j =0, 1, 2$ or $3$, and $n = 0, 1, ..., \infty$) numbers of photon andshow how the SCS can be used to encode ququat using these MPS as basis vectorsof a four dimensional Hilbert space. When these MPS fall upon a 50:50 beamsplitter, the resulting states are bipartite four-component entangled coherentstates (BFECS) equivalently representing the entangled ququats. We brieflydiscuss the photon statistical properties of such MPS and BFECS. We show thatthese MPS and BFECS can be synthesized using even coherent states as input toan interferometer. We give a simple linear optical protocol for almost perfectteleportation of a ququat encoded in SCS with the aid of BFECS as quantumchannel. We also describe how these ququats can be used for realization ofhigher dimensional BB84 protocol in order to increase the security of quantumkey distribution. Finally, we discuss the possible advantages of using SCS asququats and BFECS as quantum channel in different QIP tasks.

Ququat as superposition of coherent state and their application in quantum information processing