# Qutrit

A **qutrit** (or **quantum trit**) is a unit of quantum information that is realized by a quantum system described by a superposition of three mutually orthogonal quantum states.^{[1]}

The qutrit is analogous to the classical base-3 trit, just as the qubit, a quantum system described by a superposition of two orthogonal states, is analogous to the classical base-2 bit.

## Representation

A qutrit has three orthonormal basis states or vectors, often denoted , , and in Dirac or bra–ket notation. These are used to describe the qutrit as a superposition state vector in the form of a linear combination of the three orthonormal basis states:

- ,

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

The qubit's orthonormal basis states
span the two-dimensional complex Hilbert space
, corresponding to spin-up and spin-down of a spin-1/2 particle. Qutrits require a Hilbert space of higher dimension, namely the three-dimensional
spanned by the qutrit's basis
,^{[2]} which can be realized by a three-level quantum system. Note, however, that not all three-level quantum systems are qutrits.^{[3]}

A string of *n* qutrits represents 3^{n} different states simultaneously, i.e., a superposition state vector in 3^{n}-dimensional complex Hilbert space.^{[4]}

Qutrits have several peculiar features when used for storing quantum information. For example, they are more robust to decoherence under certain environmental interactions.^{[5]} In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an entanglement with a qubit.^{[6]}

## See also

## References

- ↑ Nisbet-Jones, Peter B. R.; Dilley, Jerome; Holleczek, Annemarie; Barter, Oliver; Kuhn, Axel (2013). "Photonic qubits, qutrits and ququads accurately prepared and delivered on demand".
*New Journal of Physics*.**15**(5): 053007. doi:10.1088/1367-2630/15/5/053007. ISSN 1367-2630. - ↑ Byrd, Mark (1998). "Differential geometry on SU(3) with applications to three state systems".
*Journal of Mathematical Physics*.**39**(11): 6125–6136. arXiv:math-ph/9807032. doi:10.1063/1.532618. ISSN 0022-2488. - ↑ "Quantum systems: three-level vs qutrit".
*Physics Stack Exchange*. Retrieved 2018-07-25. - ↑ Caves, Carlton M.; Milburn, Gerard J. (2000). "Qutrit entanglement".
*Optics Communications*.**179**(1–6): 439–446. doi:10.1016/s0030-4018(99)00693-8. ISSN 0030-4018. - ↑ 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)

## External links

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