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Analysis of 1 and 2 Particle Quantum Systems using Geometric Algebra

Rachel Parker·Chris Doran
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Abstract

When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this entanglement can be described using the Schmidt decomposition. This selects a preferred orthonormal basis for expressing the wavefunction and gives a measure of the degree of entanglement present in the system. The extension of this to the more general case of n subsystems is not yet known. We present a review of this process using the standard representation and apply this method to the geometric algebra representation. This latter form has the advantage of suggesting a generalisation to n subsystems.

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Rachel Parker, Chris Doran. 2001-06-11. Analysis of 1 and 2 Particle Quantum Systems using Geometric Algebra. https://arxiv.org/abs/quant-ph/0106055

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