Related papers: Algebraic Structure of the Minimum Error Discrimin…
In the changepoint problem, we determine when the distribution observed has changed to another one. We expand this problem to the quantum case where copies of an unknown pure state are being distributed. We study the fundamental case, which…
It is a well-known fact that the optimal POVM for quantum state tomography is the symmetric, informationally complete, positive operator valued measure (SIC-POVM). We investigate the same problem only in the case when there are some a…
The problem of unambiguously distinguishing among nonorthogonal but linearly independent quantum states can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which can then be distinguished without…
Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These…
A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction…
In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is…
Quantum state discrimination involves identifying a given state out of a set of possible states. When the states are mutually orthogonal, perfect state discrimination is always possible using a global measurement. In the case of…
We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure.…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…
The optimal measurement that discriminates nonorthogonal quantum states with fixed rates of inconclusive outcomes (FRIO) can be decomposed into an assisted separation of the inputs, yielding conclusive and inconclusive outputs, followed by…
In this paper, approximate Linear Minimum Variance (LMV) filters for continuous-discrete state space models are introduced. The filters are obtained by means of a recursive approximation to the predictions for the first two moments of the…
We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles…
We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert…
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
Symmetries in an open quantum system lead to degenerated Liouvillian that physically implies the existence of multiple steady states. In such cases, obtaining the initial condition independent stead states is highly nontrivial since any…
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control con- straints and cost are all described by polynomials, and more generally for OCPs with smooth…
Strategies to optimally discriminate between quantum states are critical in quantum technologies. We present an experimental demonstration of minimum error discrimination between entangled states, encoded in the polarization of pairs of…