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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. Mehendale1,*, Madhav R. Modak2

1 Department of Physics, Sir Parashurambhau College, Pune, 411030, India
2 Department of Mathematics, Sir Parashurambhau College, Pune, 411030, India

* Corresponding Author: Dhananjay P. Mehendale. Email: email

Journal of Quantum Computing 2023, 5, 15-24.


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.


Cite This Article

D. P. Mehendale and M. R. Modak, "On factorization of n-qubit pure states and complete entanglement analysis of 3-qubit pure states containing exactly two terms and three terms," Journal of Quantum Computing, vol. 5, pp. 15–24, 2023.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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