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| A '''qutrit''' is a unit of [[quantum information]] that can exist in three possible states.
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| The qutrit is analogous to the classical [[Ternary numeral system|trit]], just as the [[qubit]], a quantum particle of two possible states, is analogous to the classical [[bit]].
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| ==Representation==
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| A qutrit has three orthogonal [[Basis (linear algebra)|basis]] states, or [[vector space|vector]]s, often denoted <math>|0\rangle</math>, <math>|1\rangle</math>, and <math>|2\rangle</math> in Dirac or [[bra-ket notation]].
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| These are used to describe the qutrit as a [[Superposition principle|superposition]] in the form of a linear combination of the three states:
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| :<math>|\psi\rangle = \alpha |0\rangle + \beta |1\rangle + \gamma |2\rangle</math>,
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| where the coefficients are [[probability amplitude]]s, such that the sum of their squares is unity:
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| : <math>| \alpha |^2 + | \beta |^2 + | \gamma |^2 = 1 \,</math>
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| The qutrit's basis states are orthogonal. Qubits achieve this by utilizing [[Hilbert space]] <math>H_2</math>, corresponding to spin-up and spin-down. Qutrits require a Hilbert space of higher dimension, namely <math>H_3</math>.
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| A string of ''n'' qutrits represents 3<sup>''n''</sup> different states simultaneously.
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| Qutrits have several peculiar features when used for storing quantum information. For example, they are more robust to [[decoherence]] under certain environmental interactions.<ref>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) ([http://link.aps.org/doi/10.1103/PhysRevB.70.014435 link])</ref> In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an [[quantum entanglement|entanglement]] with a [[qubit]].<ref>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) ([http://link.aps.org/abstract/PRL/v100/e060504 link])</ref>
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| ==See also==
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| *[[Mutually unbiased bases]]
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| *[[Quantum computing]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[http://www.physorg.com/news123244300.html Physicists Demonstrate Qubit-Qutrit Entanglement] by Lisa Zyga at [[Physorg.com]], February 26, 2008 . Accessed March 2008
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| {{quantum computing}}
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| [[Category:Units of information]]
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| [[Category:Quantum information science]]
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