Tensor Product in Quantum Computing
The state of a single quantum bit can be represented as a unit vector in a two-dimensional vector space C. However, quantum information processing systems in general use multiple qubits. The joint state of such a system can only be described using a new vector space that takes into account the interaction among the qubits. This vector space is generated by using a special operation known as a tensor product.
The tensor product denoted ⊗ combines the smaller vector spaces of the individual qubits and forms a bigger space. The elements of the bigger vector space are identified as tensors. A tensor product is also called a Kronecker product or direct product.