A new two Bloch sphere visualization scheme for entangled two-qubit systems

The use of the Bloch sphere to represent single-qubit states and their transformations is both widespread and conventional given that it provides a geometrical framework with a one-to-one mapping between points in a 3D space and the state space of the system. Generalizing this approach to n-qubit systems, however, is intrinsically difficult given that the number of required parameters scales exponentially, and representing aspects such as purity and entanglement in a system is particularly challenging. Developing a visual framework that addresses this issue is relevant from a pedagogical point of view given the continued interest in teaching quantum information concepts to a broader audience. This motivation has led to the development of multiple approaches to visualize two-qubit systems. In this talk we will present a new framework for visualizing two-qubit systems using two Bloch spheres that is based on projective measurements and a color mapping scheme. This approach can represent both pure and mixed states, as well as relevant systems such as Bell’s and Werner states. In particular, the scheme allows to visually represent the correlations between the qubits on multiple bases, and the application of unitary operations to the involved qubits.