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A qutrit (or quantum trit) is a unit of quantum information that is realized by a 3-level quantum system, that may be in a superposition of three mutually orthogonal quantum states. [1]


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

There is ongoing work to develop quantum computers using qutrits and qubits with multiple states. [2]


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 , [3] which can be realized by a three-level quantum system. However, not all three-level quantum systems are qutrits. [4]

An n-qutrit register can represents 3n different states simultaneously, i.e., a superposition state vector in 3n-dimensional complex Hilbert space. [5]

The quantum logic gates operating on single qutrits are unitary matrices and gates that act on registers of qutrits are unitary matrices (the elements of the unitary groups U(3) and U(3n) respectively). [6]

Qutrits have several peculiar features when used for storing quantum information. For example, they are more robust to decoherence under certain environmental interactions. [7] In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an entanglement with a qubit. [8]

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Quantum computing Study of a model of computation

Quantum computing is the exploitation of collective properties of quantum states, such as superposition and entanglement, to perform computation. The devices that perform quantum computations are known as quantum computers. They are believed to be able to solve certain computational problems, such as integer factorization, substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. Expansion is expected in the next few years as the field shifts toward real-world use in pharmaceutical, data security and other applications.

Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away. While teleportation is commonly portrayed in science fiction as a means to transfer physical objects from one location to the next, quantum teleportation only transfers quantum information. Moreover, the sender may not know the location of the recipient, and does not know which particular quantum state will be transferred.

In quantum computing, a qubit or quantum bit is the basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states simultaneously, a property that is fundamental to quantum mechanics and quantum computing.

Quantum entanglement Correlation between measurements of quantum subsystems, even when spatially separated

Quantum entanglement is a physical phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics lacking in classical mechanics.

In quantum mechanics, wave function collapse occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an "observation". It is the essence of a measurement in quantum mechanics which connects the wave function with classical observables like position and momentum. Collapse is one of two processes by which quantum systems evolve in time; the other is the continuous evolution via the Schrödinger equation. Collapse is a black box for a thermodynamically irreversible interaction with a classical environment. Calculations of quantum decoherence show that when a quantum system interacts with the environment, the superpositions apparently reduce to mixtures of classical alternatives. Significantly, the combined wave function of the system and environment continue to obey the Schrödinger equation. More importantly, this is not enough to explain wave function collapse, as decoherence does not reduce it to a single eigenstate.

Quantum decoherence Loss of quantum coherence

Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave function is used to explain various quantum effects. As long as there exists a definite phase relation between different states, the system is said to be coherent. A definite phase relationship is necessary to perform quantum computing on quantum information encoded in quantum states. Coherence is preserved under the laws of quantum physics.

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In quantum computing, a quantum register is a system comprising multiple qubits. It is the quantum analog of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register.

Greenberger–Horne–Zeilinger state "Highly entangled" quantum state of 3 or more qubits

In physics, in the area of quantum information theory, a Greenberger–Horne–Zeilinger state is a certain type of entangled quantum state that involves at least three subsystems. It was first studied by Daniel Greenberger, Michael Horne and Anton Zeilinger in 1989. Extremely non-classical properties of the state have been observed.

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