rotations, reflections, and the Fourier operator. Unitary operators generalize unitary matrices. Unitary operators are usually taken as operating on a Hilbert...

Semi-orthogonal matrix Quantum logic gate Special Unitary group SU(n) Symplectic matrix Unitary group U(n) Unitary operator Li, Chi-Kwong; Poon, Edward (2002). "Additive...

according to the Schrödinger equation is mathematically represented by a unitary operator. This is typically taken as an axiom or basic postulate of quantum...

Examples of normal operators are unitary operators: U ∗ = U − 1 {\displaystyle U^{\ast }=U^{-1}} Hermitian operators (i.e., selfadjoint operators): N ∗ = N {\displaystyle...

shift operator acting on two-sided sequences is a unitary operator on ⁠ ℓ 2 ( Z ) . {\displaystyle \ell _{2}(\mathbb {Z} ).} ⁠ The shift operator acting...

mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every...

decomposition of antiunitary operators contrasts with the spectral decomposition of unitary operators. In particular, a unitary operator on a complex Hilbert...

direction of time. Every antiunitary operator can be written as the product of the time reversal operator and a unitary operator that does not reverse time. For...

one-parameter unitary groups is a basic theorem of functional analysis that establishes a one-to-one correspondence between self-adjoint operators on a Hilbert...

is a unitary operator and Γ is completely non-unitary in the sense that it has no non-zero reducing subspaces on which its restriction is unitary. If U = 0...

performed by classical circuits. Quantum gates are unitary operators, and are described as unitary matrices relative to some orthonormal basis. Usually...

Unitary equivalence may refer to: Unitary equivalence of bounded operators in Hilbert space; see self-adjoint operator Unitary equivalence of a unitary...

are the same space, a unitary transformation is an automorphism of that Hilbert space, and then it is also called a unitary operator. A closely related notion...

functional calculus, the operator U = e − i H t / ℏ {\displaystyle U=e^{-iHt/\hbar }} is a unitary operator. It is the time evolution operator or propagator of...

unique). The unitary operator U is not unique. Rather it is possible to determine a "natural" unitary operator as follows: AP+ is a unitary operator from the...

morphism Unitary operator Unitary transformation Unitary representation Unitarity (physics) E-unitary inverse semigroup Unitary authority Unitary state Unital...

Translation operators are unitary. Translation operators are closely related to the momentum operator; for example, a translation operator that moves by...

f with a subroutine (sometimes called an oracle) in the form of a unitary operator Uω that acts as follows: { U ω | x ⟩ = − | x ⟩ for  x = ω , that is...

t units of time on the state of an isolated system S is given by a unitary operator Ut on the Hilbert space H associated to S. This means that if the system...

wave function. The evolution of the wave function is determined by a unitary operator, and unitarity implies that the wave function at any instant of time...

evolution. In matrix mechanics, this means that the time evolution operator is a unitary operator. In contrast to, for example, the Klein Gordon equation, although...

normal operators are unitary operators: U ∗ = U − 1 {\displaystyle U^{\ast }=U^{-1}} Hermitian operators (i.e., self-adjoint operators): N ∗ = N {\displaystyle...

mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations...

operator. This operator was introduced independently by Richard Feynman and Roy J. Glauber in 1951. The displacement operator is a unitary operator,...

yields a unitary operator U on H ⊗ H {\displaystyle H\otimes H} , the Hilbert space of the combined system. However, no such unitary operator U can clone...

square matrix A and unitary U, it is true that |tr(AU)| ≤ tr((A*A)1⁄2). Furthermore, equality is achieved if U* is the unitary operator in the polar decomposition...

{F}}:L^{2}(\mathbb {R} ^{n})\to L^{2}(\mathbb {R} ^{n})} is a unitary operator. For an operator to be unitary it is sufficient to show that it is bijective and preserves...

corresponding to an eigenvalue of a given unitary operator. Because the eigenvalues of a unitary operator always have unit modulus, they are characterized...

constant-coefficient differential operator is unitarily equivalent to a multiplication operator. Indeed, the unitary operator that implements this equivalence...

true for a more general class of operators. A unitary operator is normal. By the spectral theorem, a bounded operator on a Hilbert space H is normal if...