Early State Exclusion in 7-Qubit Spin Chains

The existence of infinite families of $N\times N$ Jacobi matrices representing the Hamiltonians of quantum spin chains with and without early state exclusion (ESE) has been shown to exist for any even $N\ge 4$. However, their existence for odd $N\ge 7$ has remained an open problem. In Section 3, we consider a chain of qubits experiencing nearest-neighbor interactions with environmental effects and present infinite families of $7\times 7$ Jacobi matrices with and without ESE.