Qutrit

A qutrit is a unit of quantum information that can exist in three possible states.

The qutrit is analogous to the classical trit, just as the qubit, a quantum particle of two possible states, is analogous to the classical bit.

Representation

A qutrit has three orthogonal basis states, or vectors, often denoted $|0\rangle$, $|1\rangle$, and $|2\rangle$ in Dirac or bra–ket notation. These are used to describe the qutrit as a superposition in the form of a linear combination of the three states:

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

where the coefficients are probability amplitudes, such that the sum of their squares is unity:

$| \alpha |^2 + | \beta |^2 + | \gamma |^2 = 1 \,$

The qutrit's basis states are orthogonal. Qubits achieve this by utilizing Hilbert space $H_2$, corresponding to spin-up and spin-down. Qutrits require a Hilbert space of higher dimension, namely $H_3$.

A string of n qutrits represents 3n different states simultaneously.

Qutrits have several peculiar features when used for storing quantum information. For example, they are more robust to decoherence under certain environmental interactions.[1] In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an entanglement with a qubit.[2]