Related papers: Commutator methods for unitary operators
We prove a uniform vector-valued Wiener-Wintner Theorem for a class of operators that includes compositions of ergodic Koopman operators with contractive multiplication operators. Our results are new even in the case of complex-valued…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication…
The commutator between operators at different space and time has been a diagnostic for locality of unitary evolution. Most existing results are either for specific tractable (random) Hamiltonians(Out-of-Time-Order-Correlators calculations),…
In this paper, under the monotonicity of pairs of operators, we propose some Generalized Proximal Point Algorithms to solve non-monotone inclusions using warped resolvents and transformed resolvents. The weak, strong, and linear convergence…
We numerically approximate the Tomita-Takesaki modular operator for local subalgebras of the 1+1-dimensional massive Majorana field. Our method works at the one-particle level with a discretisation of time-0 data in position space. The…
The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
We provide a generalization of the idea of unitary designs to cover finite averaging over much more general operations on quantum states. Namely, we construct finite averaging sets for averaging quantum states over arbitrary reductive Lie…
We consider families of random non-unitary contraction operators defined as deformations of CMV matrices which appear naturally in the study of random quantum walks on trees or lattices. We establish several deterministic and almost sure…
A mechanism is described to symmetrize the ultraspherical spectral method for self-adjoint problems. The resulting discretizations are symmetric and banded. An algorithm is presented for an adaptive spectral decomposition of self-adjoint…
The Wigner-von Neumann method, which was previously used for perturbing continuous Schr\"{o}dinger operators, is here applied to their discrete counterparts. In particular, we consider perturbations of arbitrary $T$-periodic Jacobi…
We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital…
The variational quantum eigensolver has been proposed as a low-depth quantum circuit that can be employed to examine strongly correlated systems on today's noisy intermediate-scale quantum computers. We examine details associated with the…
For the tensor of coherences parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at infinitesimal level. The main advantage of this formalism (clearly reminiscent of the…
In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition…
In this paper we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator…
The optimal sufficient conditions for the $L^p$-to-$L^q$ compactness of commutators of singular integral operators of both Calder\'on-Zygmund and of rough type are shown in the different exponent ranges $``q>p"$, $``q=p"$ and $``q<p"$ to…
In this paper we determine a sufficient condition for the quasinilpotency of a commutator of compact operators via block-tridiagonal matrix form associated with a compact operator. We also prove that every compact operator is unitarily…
We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory. In particular we relate the data on boundary operators to short-distance (near-boundary) divergences of bulk…