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We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…
We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained…
In the realm of a quantum cosmological model for dark energy in which we have been able to construct a well-defined Hilbert space, a consistent coherent state representation has been formulated that may describe the quantum state of the…
Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics.…
We present new bell inequalities for arbitrary dimensional bipartite quantum systems. The maximal violation of the inequalities is computed. The Bell inequality is capable of detecting quantum entanglement of both pure and mixed quantum…
As a means to solve optimization problems using quantum computers, the problem is typically recast into a Ising spin model whose ground-state is the solution of the optimization problem. An alternative to the Ising formulation is the…
In this paper we approach the problem of perturbation from symmetry of strongly indefinite elliptic systems in dimension N>=3. We prove the existence of infinitely many solutions under suitable growth coinditions on the nonlinear terms.
We study the application of a generalized form of the level set method used in classical physical contexts to quantum optimal control situations. The set of OCT equations needed to keep the expectation value of an observable constant is…
The measurement problem is to explain why a system which is in a linear combination of states appears, upon measurement, to be in just one of those states. The solution given here is to first show that if one assumes linear, unitary, no…
We have solved the quantum version of the Mattis model with infinite-range interactions. A variational approach gives the exact solution for the infinite-range system, in spite of the non-commutative nature of the quantum spin components;…
We consider the problem of determining the state of an unknown quantum sequence without error. The elements of the given sequence are drawn with equal probability from a known set of linearly independent pure quantum states with the…
We present a generic study of unambiguous discrimination between two mixed quantum states. We derive operational optimality conditions and show that the optimal measurements can be classified according to their rank. In Hilbert space…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…
We establish a connection between optimal quantum cloning and optimal state estimation for d-dimensional quantum systems. In this way we derive an upper limit on the fidelity of state estimation for d-dimensional pure quantum states and,…
We consider the extremal pointset configuration problem of maximizing a kernel-based energy subject to the geometric constraints that the points are contained in a fixed set, the pairwise distances are bounded below, and that every closed…
We provide a simplified characterization of entanglement in physical systems which are symmetric under the action of subgroups of the symmetric group acting on the party labels. Sets of entanglements are inherently equal, lying in the same…
We present a formula that determines the optimal number of qubits per message that allows asymptotically faithful compression of the quantum information carried by an ensemble of mixed states. The set of mixed states determines a…
A necessary and sufficient condition for the maximal entanglement of bipartite nonorthogonal pure states is found. The condition is applied to the maximal entanglement of coherent states. Some new classes of maximally entangled coherent…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
In this paper we present the solution to the problem of optimally discriminating among quantum states, i.e., identifying the states with maximum probability of success when a certain fixed rate of inconclusive answers is allowed. By varying…