(a) Apply the determinant test to each of the following states, and factorise each…
PHYSICS · Subjective · Fermi University Physics · Quantum Information & Technology · Quantum states, measurement and entanglement · The quantum circuit model and quantum algorithms
Quantum Information and Technology, Ch Qubits, registers and the Bloch sphere
Problem
(a) Apply the determinant test c00c11−c01c10 to each of the following states, and factorise each one that turns out to be a product state: (i) (∣00⟩+i∣01⟩+i∣10⟩−∣11⟩)/2; (ii) (∣00⟩+∣01⟩+∣10⟩)/3; (iii) (3∣00⟩+∣01⟩+3∣10⟩+∣11⟩)/(22). (b) Show, using 4×4 matrices, that CNOT(H⊗I)∣11⟩=∣Ψ−⟩.