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A parametrization of density operators for bipartite quantum systems is proposed. It is based on the particular parametrization of the unitary group found recently by Jarlskog. It is expected that this parametrization will find interesting…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the…
Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
A unitary operator which relates the system of a particle in a linear potential with time-dependent parameters to that of a free particle, has been given. This operator, closely related to the one which is responsible for the existence of…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for…
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…
Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…
Although only two quantum states of a physical system are often used to encode quantum information in the form of qubits, many levels can in principle be used to obtain qudits and increase the information capacity of the system. To take…
In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of…
Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are…
By studying the minimum resources required to perform a unitary transformation, families of metrics and pseudo-metrics on unitary matrices that are closely related to a recently reported quantum speed limit by the author are found.…
Gaussian states -- or, more generally, Gaussian operators -- play an important role in Quantum Optics and Quantum Information Science, both in discussions about conceptual issues and in practical applications. We describe, in a tutorial…
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of diagonalization of these operators…
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…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…