The four-qubit GHZ state is | GHZ _4 = 1 2 (|0000 + |1111 ).
PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Open quantum systems, decoherence and error correction · Open quantum systems, decoherence and error correction
Quantum Information and Technology, Ch The stabilizer formalism
Problem
The four-qubit GHZ state is ∣GHZ4⟩=21(∣0000⟩+∣1111⟩).
((a)) Write four independent generators, each a product of Pauli operators, that stabilize ∣GHZ4⟩.
((b)) Check that they pairwise commute and are independent.
((c)) State the dimension of the space they fix, and hence confirm that ∣GHZ4⟩ is the unique state they stabilize.