Related papers: The disentangling power of unitaries
We study the mathematical structure of superoperators describing quantum measurements, including the \emph{entangling measurement}--the generalization of the standard quantum measurement that results in entanglement between the measurable…
Let $u_1,\ldots,u_n$ be unitary operators on a Hilbert space $H$. We study the norm $$\left\|\sum^{i=n}_{i=1} u_i \otimes \bar u_i\right\|\leqno (1)$$ of the operator $\sum u_i \otimes \bar u_i$ acting on the Hilbertian tensor product…
Under certain general conditions, an explicit formula to compute the greatest delta-epsilon function of a continuous function is given. From this formula, a new way to analyze the uniform continuity of a continuous function is given.…
When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This letter shows that entanglement lost in the manipulation can be…
We study the entangling properties of multipartite unitary gates with respect to the measure of entanglement called one-tangle. Putting special emphasis on the case of three parties, we derive an analytical expression for the entangling…
Deterministic classical dynamical systems have an ergodic hierarchy, from ergodic through mixing, to Bernoulli systems that are "as random as a coin-toss". Dual-unitary circuits have been recently introduced as solvable models of many-body…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…
In general case of deformed Heisenberg algebra leading to the minimal length, we present a definition of the $\delta'(x)$ potential as a linear kernel of potential energy operator in momentum representation. We find exactly the energy level…
This paper derives a way to express differentiable complex-valued functions as the sum of powers of $(1-e^{\lambda x})$, where $\lambda\in\mathbb{R}$, with an explicit formula for the remainder. This formulation is then used to associate an…
We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We use the Majorana representation, where these states correspond to points on a sphere. Symmetry of the…
We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric…
Quantum entanglement is a key enabling ingredient in diverse applications. However, the presence of unwanted adversarial entanglement also poses challenges in many applications. In this paper, we explore methods to "break" quantum…
The study of entanglement properties of multi-qubit states that are invariant under permutations of qubits is motivated by potential applications in quantum computing, quantum communication, and quantum metrology. In this work, we…
In this work, the authors provide closed forms and recurrence expressions for computing the $k$th power of the formal power series, some of them in terms of a determinant of some matrices. As a consequence, we obtain the reciprocal of the…
It is proved recently by Benamara-Nikolski that a contraction having finite defects and spectrum not filling in the closed unit disc, is similar to a normal operator if and only if it has the so-called linear resolvent growth property. We…
Like many other physical quantities, the optical force can be expanded using multipole expansion, which has been done in [Nat. Photon. 5, 531], up to electric octupole order. However, in that study, the existence of radiation multipoles…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular,…
Arthur's conjectures predict the existence of some very interesting unitary representations occurring in spaces of automorphic forms. We prove the unitarity of the "Langlands element" (i.e., the one specified by Arthur) of all unipotent…
In this paper, we consider characterisations of the class of unitary matrix integrals $\big\langle (\det U)^q {\rm e}^{s^{1/2} \operatorname{Tr}(U + U^\dagger)} \big\rangle_{U(l)}$ in terms of a first-order matrix linear differential…