Unique factorization theorem for pure quantum states

• Main Author: Dhananjay P Mehendale (Author)
• Format: Book
• Published: Annals of Mathematics and Physics - Peertechz Publications, 2023-09-15.
• Subjects: Research Article
• Online Access: Connect to this object online.

<p>In this paper we establish a unique factorization theorem for pure quantum states expressed in computational basis. We show that there always exists unique factorization for any given N-qubit pure quantum state in terms of the tensor product of non-factorable or ``prime'' pure quantum states. This result is based on a simple criterion: Given N-qubit pure quantum state in computational basis can be factorized as the tensor product of an m-qubit pure quantum state and an n-qubit pure quantum state, where (m + n) = N, if and only if the rank of the certain associated matrix is equal to one. This simple criterion leads to a factorization algorithm which when applied to an N-qubit pure quantum state factorizes that state into the tensor product of non-factorable or ``prime'' pure quantum states. This paper shows that for any given N-qubit pure quantum state the said factorization always ``exists'' and is ``unique''. We demonstrated our work here on a computational basis.</p><p>PACS Number: 03.67.Mn, 03.65.Ca, 03.65.Ud</p>