
Qutrit

A qutrit (or quantum trit) is a unit of quantum information that is realized by a quantum system described by a superposition of three mutually orthogonal quantum states.
The qutrit is analogous to the classical radix-3 trit, just as the qubit, a quantum system described by a superposition of two orthogonal states, is analogous to the classical radix-2 bit.
There is ongoing for developing quantum computers using qutrits and qubits with multiple states.
Representation.
A qutrit has three orthonormal basis states or vectors, often denoted formula_1, formula_2, and formula_3 in Dirac or bra–ket notation.
These are used to describe the qutrit as a superposition state vector in the form of a linear combination of the three orthonormal basis states:
where the coefficients are complex probability amplitudes, such that the sum of their squares is unity (normalization):
The qubit's orthonormal basis states formula_6 span the two-dimensional complex Hilbert space formula_7, corresponding to spin-up and spin-down of a spin-1/2 particle. Qutrits require a Hilbert space of higher dimension, namely the three-dimensional formula_8 spanned by the qutrit's basis formula_9, which can be realized by a three-level quantum system. However, not all three-level quantum systems are qutrits.
A string of "n" qutrits represents 3"n" different states simultaneously, i.e., a superposition state vector in 3"n"-dimensional complex Hilbert space.
Qutrits have several peculiar features when used for storing quantum information. For example, they are more robust to decoherence under certain environmental interactions. In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an entanglement with a qubit.