Chemistry - Qutrit

A qutrit is a unit of quantum information. Just as the qubit is analogous to the classical bit, the qutrit is analogous to the classical trit. A qutrit is 3-level, or ternary system which has 3 basis states, often denoted $|0\rangle$ , $|1\rangle$ and $|2\rangle$ . Unlike the trit, and like its cousin the qubit, a qutrit can exist in superpositions of the three basis states. Consequently, a string of $n$ qutrits is able to represent $3 n$ different states simultaneously.

Since basis states in quantum systems must be orthogonal to be reliably distinguished, the qutrit's basis states must also be orthogonal. Qubits acheive this by utilizing Hilbert space $H 2$ , corresponding to spin-up and spin-down. Qutrits require a Hilbert space of higher dimension, namely $H 3$ .

As with qubits, a qutrit can be expressed as a linear combination of the basis states, given as

$|\psi\rangle = \alpha |0\rangle + \beta |1\rangle + \gamma |2\rangle$ .