Journal of quantum computing

On Factorization of N-Qubit Pure States and Complete Entanglement Analysis of 3-Qubit Pure States Containing Exactly Two Terms and Three Terms

Dhananjay P. Mehendale, Madhav R. Modak

Published Jan 1, 2023• 1 citation

Abstract

A multi-qubit pure quantum state is called separable when it can be factored as the tensor product of 1-qubit pure quantum states. Factorizing a general multi-qubit pure quantum state into the tensor product of its factors (pure states containing a smaller number of qubits) can be a challenging task, especially for highly entangled states. A new criterion based on the proportionality of the rows of certain associated matrices for the existence of certain factorization and a factorization algorithm that follows from this criterion for systematically extracting all the factors is developed in this paper. 3-qubit pure states play a crucial role in quantum computing and quantum information processing. For various applications, the well-known 3-qubit GHZ state which contains two nonzero terms, and the 3-qubit W state which contains three nonzero terms, have been studied extensively. Using the new factorization algorithm developed here we perform a complete analysis vis-à-vis entanglement of 3-qubit states that contain exactly two nonzero terms and exactly three nonzero terms.

DOI: 10.32604/jqc.2023.043370

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