The Density Operators of Qubit Systems in the Multiparticle Spacetime Algebra

Abstract

We provide a method to write down the density operator for any pure state of multi-qubit systems in the multiparticle spacetime algebra (MSTA) introduced by Doran, Gull, and Lasenby. Using the MSTA formulation, we analyze several aspects of quantum mechanics in a geometrical way including the Bell inequality and the dynamics of two coupled qubits. Lastly, we provide a natural way to construct the local unitary invariants in the MSTA. Using these invariants, we analyze the space of the two-qubit and three-qubit pure states with local and non-local degrees of freedom separated.

42 pages, 8 figures

References in corpus (3)

• A Geometric Algebra Perspective On Quantum Computational Gates And Universality In Quantum Computing
• Bloch sphere model for two-qubit pure states
• Natural Parameterization of Two-Qubit States

Cited by in corpus (1)

• Two-Qubit Bloch Sphere