Qutrit
Encyclopedia
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
.
states, or vector
s, often denoted
, 
, and 
in Dirac or bra-ket notation
.
These are used to describe the qutrit as a superposition
in form of a linear combination of the three states:
,
where the coefficients are probability amplitude
s, 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. In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an entanglement
with a qubit
.
Quantum information
In quantum mechanics, quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a two-level quantum system...
that can exist in three possible states.
The qutrit is analogous to the classical trit
Ternary numeral system
Ternary is the base- numeral system. Analogous to a bit, a ternary digit is a trit . One trit contains \log_2 3 bits of information...
, just as the qubit
Qubit
In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....
, a quantum particle of two possible states, is analogous to the classical bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
.
Representation
A qutrit has three orthogonal basisBasis (linear algebra)
In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a "coordinate system"...
states, or vector
Vector space
A vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied by numbers, called scalars in this context. Scalars are often taken to be real numbers, but one may also consider vector spaces with scalar multiplication by complex...
s, often denoted
, , and in Dirac or bra-ket notationBra-ket notation
Bra-ket notation is a standard notation for describing quantum states in the theory of quantum mechanics composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics...
.
These are used to describe the qutrit as a superposition
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...
in form of a linear combination of the three states:
,where the coefficients are probability amplitude
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number whose modulus squared represents a probability or probability density.For example, if the probability amplitude of a quantum state is \alpha, the probability of measuring that state is |\alpha|^2...
s, such that the sum of their squares is unity:
The qutrit's basis states are orthogonal. Qubits achieve this by utilizing Hilbert space
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
, 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. In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an entanglement
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...
with a qubit
Qubit
In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....
.
External links
- Physicists Demonstrate Qubit-Qutrit Entanglement by Lisa Zyga at Physorg.comPhysOrg.comPhysOrg is a popular science, research and technology news website specializing in the hard science subjects of physics, space and earth science, biology, chemistry, electronics, nanotechnology and technology in general. It is known for timely updates of scientific breakthroughs and press releases...
, February 26, 2008 . Accessed March 2008