Generalizations of Pauli matrices and Pauli matrices

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Difference between Generalizations of Pauli matrices and Pauli matrices

Generalizations of Pauli matrices vs. Pauli matrices

In mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices which are Hermitian and unitary.

Bloch sphere

In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch.

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Gell-Mann matrices

The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3x3 traceless Hermitian matrices used in the study of the strong interaction in particle physics.

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Hermitian matrix

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.

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Hilbert–Schmidt operator

In mathematics, a Hilbert–Schmidt operator, named for David Hilbert and Erhard Schmidt, is a bounded operator A on a Hilbert space H with finite Hilbert–Schmidt norm where \|\ \| is the norm of H, \ an orthonormal basis of H, and Tr is the trace of a nonnegative self-adjoint operator.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Quantum information

In physics and computer science, quantum information is information that is held in the state of a quantum system.

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Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

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Trace (linear algebra)

In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.

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Unitary matrix

In mathematics, a complex square matrix is unitary if its conjugate transpose is also its inverse—that is, if where is the identity matrix.

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