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We consider the optimal discrimination of bipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition for a measurement to…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
We point out a general framework that encompasses most cases in which quantum effects enable an increase in precision when estimating a parameter (quantum metrology). The typical quantum precision-enhancement is of the order of the square…
In this paper, an optimal control problem governed by a class of p-Laplacian elliptic equations is studied. In particular, as no monotonicity assumption is assumed on the nonlinear term, the state equation may admit several solutions for…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state…
An optimal control problem for the continuity equation is considered. The aim of a controller is to maximize the total mass within a target set at a given type moment. An iterative numerical algorithm for solving this problem is presented.
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…
We study the fully entangled fraction of a quantum state. An upper bound is obtained for arbitrary bipartite system. This upper bound only depends on the Frobenius norm of the state.
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
A setup for discriminating between arbitrary two coherent states of a single light mode with the highest success rate allowed by quantum mechanics is presented. Its application to time-multiplexed quantum key distribution is discussed.
In the functional approach to quantum chromodynamics, the properties of hadronic bound states are accessible via covariant integral equations, e.g. the Bethe-Salpeter equations for mesons. In particular, one has to deal with linear,…
We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}_{k \in \mathbb{N}}$ in $\mathbb{R}^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k\in \mathbb{N}$. We obtain rates of convergence of…
We study maximally multipartite entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite entangled states,…
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…
This paper discusses the energy optimal control problem for the class of quantum systems that possess dynamical symmetry of SU(1,1), which are widely studied in various physical problems in the quantum theory. Based on the maximum principle…
We show that supersymmetry is a simple but powerful tool to exactly solve quantum mechanics problems. Here, the supersymmetric approach is used to analyse a quantum system with periodic P\"oschl-Teller potential, and to find out the exact…
We study a control-constrained optimal control problem governed by a semilinear elliptic equation. The control acts in a bilinear way on the boundary, and can be interpreted as a heat transfer coefficient. A detailed study of the state…