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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 [[Ternary numeral system|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 (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]]. | |||
These are used to describe the qutrit as a [[Superposition principle|superposition]] in the form of a linear combination of the three states: | |||
:<math>|\psi\rangle = \alpha |0\rangle + \beta |1\rangle + \gamma |2\rangle</math>, | |||
where the coefficients are [[probability amplitude]]s, such that the sum of their squares is unity: | |||
: <math>| \alpha |^2 + | \beta |^2 + | \gamma |^2 = 1 \,</math> | |||
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>. | |||
A string of ''n'' qutrits represents 3<sup>''n''</sup> 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.<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> | |||
==See also== | |||
*[[Mutually unbiased bases]] | |||
*[[Quantum computing]] | |||
==References== | |||
{{reflist}} | |||
==External links== | |||
*[http://www.physorg.com/news123244300.html Physicists Demonstrate Qubit-Qutrit Entanglement] by Lisa Zyga at [[Physorg.com]], February 26, 2008 . Accessed March 2008 | |||
{{quantum computing}} | |||
[[Category:Units of information]] | |||
[[Category:Quantum information science]] | |||
Revision as of 09:32, 28 February 2013
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.
Representation
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
References
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External links
- Physicists Demonstrate Qubit-Qutrit Entanglement by Lisa Zyga at Physorg.com, February 26, 2008 . Accessed March 2008
- ↑ 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)
- ↑ 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)