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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.


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]

See also[edit]


  1. ^ A. Melikidze, V. V. Dobrovitski, H. A. De Raedt, M. I. Katsnelson, and B. N. Harmon, Parity effects in spin decoherence, Phys. Rev. B 70, 014435 (2004) (link)
  2. ^ B. P. Lanyon,1 T. J. Weinhold, N. K. Langford, J. L. O'Brien, K. J. Resch, A. Gilchrist, and A. G. White, Manipulating Biphotonic Qutrits, Phys. Rev. Lett. 100, 060504 (2008) (link)

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