Fusion of w states using optical quantum gates

In this work, after talking about historical developments leading to ideas of information processing based on quantum dynamics, we will be constructing basic mathematical expressions for qubits and quantum gates, the Toffoli gate and the cNOT gate. To do this, we will mention the superposition of polarization states of photons and their state matrices defining our quantum system since these matrices purely depend on the qubits. Later, we will mention one of the basic theorems in quantum information processing, the no-cloning theorem that states that no operation can be defined cloning some quantum state to steal information. We will also point out the fact that quantum systems must be isolated from environment by showing an example. In the later section, we will talk about the reversibility property of quantum information processing by examining quantum Toffoli and cNOT gates. By showing famous examples, the Deutsch algorithm and the Grover search algorithm, we will adress the fact that quantum information processing can be more advantageous than classical algorithms. Lastly, we will focus on the construction of the optical networks to fuse photonic W states, that is the main subject of this work. For this purpose, we will examine the previous works that use optical setups, and then propose two methods fusing two W states. The first proposal consists of two cascaded Toffoli gates and the basic fusion gate whereas the second proposal consists of a Toffoli and a cNOT gates together with the basic fusion gate. We will use some theoretical and experimental results to show that our setups are more realizable with current photonics technology. We will also talk about why creating large-scale W states is important by pointing out their unique superpositions.