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 fac...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.展开更多
文摘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.
