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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.


A qutrit has three orthogonal basis states, or vectors, often denoted , , and 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:


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

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

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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