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.


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 3n different states simultaneously, i.e., a superposition state vector in 3n-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


  1. 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.
  2. 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.
  3. "Quantum systems: three-level vs qutrit". Physics Stack Exchange. Retrieved 2018-07-25.
  4. 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.
  5. 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)
  6. 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)
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.