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We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This…
Using the path integral representation of the density matrix propagator of quantum Brownian motion, we derive its asymptotic form for times greater than the localization time, $ (\hbar / \gamma k T )^{\half}$, where $\gamma$ is the…
Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur…
We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show…
We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a…
The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentions of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it…
Operator entanglement of two-qubit joint unitary operations is revisited. Schmidt number is an important attribute of a two-qubit unitary operation, and may have connection with the entanglement measure of the unitary operator. We found the…
Bipartite entanglement entropies, calculated from the reduced density matrix of a subsystem, provide a description of the resources available within a system for performing quantum information processing. However, these quantities are not…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a…
The paper presents an analysis of entangling and nonlocal operations in a quantum nondemolition (QND) interaction between multimode light with orbital angular momentum and an atomic ensemble. A protocol consists of two QND operations with…
In this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials. We obtain analogues of classical results…
The understanding of symmetry operations has brought enormous advancements in physics, ranging from elementary particle to condensed matter systems. In quantum mechanics, symmetry operations are described by either unitary or antiunitary…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
Motivated by importance of operator spaces contained in the set of all scalar multiples of isometries ($MI$-spaces) in a separable Hilbert space for $C^*$-algebras and E-semigroups we exhibit more properties of such spaces. For example, if…
Linear oscillators contribute to most branches of contemporary quantum science. They have already successfully served as quantum sensors and memories, found applications in quantum communication, and hold promise for cluster-state-based…
We compare the multipartite entangling and disentangling powers of unitary operators by assessing their ability to generate or eliminate genuine multipartite entanglement. Our findings reveal that while diagonal unitary operators can…
A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of…