Consider the Hamiltonian H=Z⊗3 acting on 3 qubits.

Question

What is the ground energy of the system? (I.e. the lowest eigenvalue of H?)
What is the dimension of the ground energy subspace? (I.e. multiplicity of that eigenvalue?)
Which of the following correctly describes the ground energy states of this system?

|000⟩ is the only ground energy state.
|111⟩ is the only ground energy state.
|000⟩,|111⟩ and their linear combinations
|001⟩,|010⟩,|100⟩ and their linear combinations
|000⟩,|001⟩,|010⟩,|100⟩ and their linear combinations
|000⟩,|011⟩,|110⟩,|101⟩ and their linear combinations
|001⟩,|010⟩,|100⟩,|111⟩ and their linear combinations

Answer 1

000> is the only ground energy state, I think... don't know others

Answer 2

last option

Answer 3

sure last option?justify

Answer 4

last option worked for me