Qutrit

A qutrit is a unit of quantum information that exists as a superposition of three orthogonal quantum 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. In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an entanglement with a qubit.

See also

• Mutually unbiased bases
• Quantum computing
• Ternary computing

External links

• Physicists Demonstrate Qubit-Qutrit Entanglement by Lisa Zyga at Physorg.com, February 26, 2008 . Accessed March 2008
• qudit—Wiktionary.