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...gebra|unital]] [[C*-algebra]], the closure of the [[convex hull]] of the [[unitary element]]s is the closed [[unit ball]].<ref name="Doran Belfi"> ...ast=Russo |first=B. |author2=H. A. Dye |year=1966|title=A Note on Unitary Operators in C*-Algebras |journal=Duke Mathematical Journal |volume=33 |pages=413–416 ...

...s://hal.science/hal-01163568/ |title=Helffer-Sjöstrand formula for Unitary Operators |date=June 2015 |publisher=[[HAL (open archive)]] |year=2015 |ref=hal-01163 ....1007/978-3-642-61497-2 |title=The Analysis of Linear Partial Differential Operators I |date=1983 |publisher=[[Springer Nature]] |series=Classics in Mathematics ...

...the symmetry group leads to groups including both unitary and antiunitary operators. == Corepresentations of unitary/antiunitary groups == ...

...rina|last2=Habermann|first2=Lutz |title = Introduction to Symplectic Dirac Operators| publisher=[[Springer-Verlag]] | year=2006|isbn=978-3-540-33420-0}} page 37 ...rm U}({\mathbf W})\,</math> denotes the [[group (mathematics)|group]] of [[unitary operator]]s acting on a [[Hilbert space]] <math>{\mathbf W}.\,</math> ...

...e (symmetric) [[Lie algebra representation|representations]] of [[Special unitary group#The group SU(2)|su(2)]] in [[Fock space]]. ...annihilation operators in quantum field theories|creation and annihilation operators]] ...

...first3=Joseph | last4=Livine | first4=Etera | title=Exact and approximate unitary 2-designs and their application to fidelity estimation | journal=Physical R ...uantum computing since ideal operations are usually represented by unitary operators. ...

...1 \subset \mathbb{C}</math>, generated by two [[unitary operator|unitary]] operators <math>U, V</math> defined as<blockquote><math>\begin{align} ...fined (up to isomorphism) as the [[universal C*-algebra]] generated by two unitary elements ''U'' and ''V'' satisfying the relation ''VU''&nbsp;=&nbsp;e<sup>2 ...

...en metric''' is a metric on the determinant [[line bundle]] of a family of operators. It was introduced by [[Daniel Quillen]]<ref name="quillen">{{citation|mr=0 |title=Determinants of Cauchy-Riemann operators over a Riemann surface |doi=10.1007/BF01086022 ...

...D_2 </math> are diagonal matrices that make <math> D_1 C(x,y) D_2 </math> unitary (in a real field or a field of a finite characteristic, or orthogonal in th ...aracteristic 2 to a digraph's arcs that make its weighted adjacency matrix unitary and having a non-zero Hamiltonian cycle polynomial then the digraph is Hami ...

...P...01..117B |doi-access=free}}</ref> Since the contribution by irrelevant operators at low energies is small, the low energy theory appears to have this symmet ...is matrix is at first glance. However, it is easy to demonstrate that by a unitary transformation, this matrix is equivalent to:<br><br><math> ...

...but mathematically, this is a more general correspondence between positive operators and the complete positive superoperators.{{cn|date=August 2019}} Let's consider the unitary case first, where the '''Choi state is pure'''. Suppose we have two Choi st ...

...which in general may be [[quantum entanglement|entangled]]) and undergoing unitary evolution given by <math>U_t \,</math>. Then the reduced dynamics of the s where the <math>F_i \,</math> are operators on the [[Hilbert space]] of the system alone, and no reference is made to t ...

An analogous notion can be defined for operators acting on a composite Hilbert space with a tensor product structure. Consid ...relative'' to the proper subgroup <math>U(K)\times U(M)</math> of the full unitary group <math>U(KM)</math>. ...

...the [[electric field strength]], then become [[operator (physics)|quantum operators]]. ...antities are typically expressed in terms of the creation and annihilation operators. In this example, the electric field strength is given by: ...

...] density matrix that is [[Invariant (mathematics)|invariant]] under all [[unitary operator]]s of the form <math>U \otimes U</math>. That is, it is a bipartit for all unitary operators ''U'' acting on ''d''-dimensional Hilbert space. These states were first de ...

...and clarify what is happening physically. One such technique is to apply a unitary transformation to the Hamiltonian. Doing so can result in a simplified vers ...e expressed in terms of a time-dependent Hamiltonian <math>H(t)</math> and unitary operator <math>U(t)</math>. Under this change, the Hamiltonian transforms a ...

...h that at least one of them is invariant, in law, under conjugation by any unitary (resp. orthogonal) matrix and such that the [[empirical spectral measures]] ...nvariant, in law, under multiplication on the left and on the right by any unitary (resp. orthogonal) matrix and such that the [[empirical singular values dis ...

...–Wolff transformation''' is a [[Unitary transformation (quantum mechanics)|unitary transformation]] used to determine an effective (often low-energy) Hamilton ...he standard form of the Schrieffer–Wolff transformation. Note that all the operators on the right-hand side are now expressed in a new basis "dressed" by the in ...

...=Jeongwan |date=2017-07-24 |title=Quantum Entanglement Growth under Random Unitary Dynamics |url=https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.0310 ...ach step, the unitary operator is represented by a tensor product of local unitary gates <math>u_{\tau, x}</math> where the <math>x</math> index specifies the ...

...cs|braiding statistics]]) naturally fit together into the structure of a [[unitary modular tensor category]].<ref name=":0" /><ref name=":1" /><ref name="k319 There is a general dictionary between the categorical structures of a [[unitary modular tensor category]] and the physical operations one can perform with ...