On the probability amplitude of quantum entanglement and the Pauli matrices
F.J. Duarte, T S Taylor, J. C. Slaten · Optical and Quantum Electronics · 2020
Abstract The probability amplitudes for quantum entanglement, also known as Bell sates, are utilized to arrive explicitly at the identity matrix I and the $$\sigma_{x}$$ σx , $$\sigma_{y}$$ σy , and $$\sigma_{z}$$ σz Pauli matrices, via a straight-forward $$2 \times 2$$ 2×2 matrix representation that utilizes the vector direct product. It is also indicated that this approach is completely equivalent to the utilization of the Kronecker product $$\otimes$$ ⊗ to multiply the relevant ket vectors. Furthermore, it is shown that the polarization rotation matrix R, operating on the various versions of the probability amplitude for quantum entanglement, yields four identities elegantly interconnecting these probability amplitudes.