Related papers: Generalized quantum state discrimination problems
We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated…
We study the optimization of any quantum process by minimizing the "randomness" in the measurement result at the output of that quantum process. We conceptualize and propose a measure of such randomness and inquire whether an optimization…
In the absence of experimental constraints, optimal measurement schemes for quantum state tomography are well understood. We consider the scenario where the experimenter doesn't have arbitrary freedom to construct their measurement set, and…
Quantum sensors are among the most promising quantum technologies, allowing to attain the ultimate precision limit for parameter estimation. In order to achieve this, it is required to fully control and optimize what constitutes the…
Recently there have been fruitful results on resource theories of quantum measurements. Here we investigate the number of measurement outcomes as a kind of resource. We cast the robustness of the resource as a semi-definite positive…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
Quantum state discrimination is a fundamental information processing task that serves as a building block for numerous applications and provides implications at the foundational level. In this work, we consider minimum error discrimination…
We prove limitations on LOCC and separable measurements in bipartite state discrimination problems using techniques from convex optimization. Specific results that we prove include: an exact formula for the optimal probability of correctly…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
We show that the quantum measurement known as the pretty good measurement can be used to identify an unknown quantum state picked from any set of $n$ mixed states that have pairwise fidelities upper-bounded by a constant below 1, given…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…
Achieving quantum-enhanced performances when measuring unknown quantities requires developing suitable methodologies for practical scenarios, that include noise and the availability of a limited amount of resources. Here, we report on the…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
Optimizing over separable quantum objects is challenging for two key reasons: determining separability is NP-hard, and the dimensionality of the problem grows exponentially with the number of qubits. We address both challenges by…
Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting…
Quantum measurements are the means by which we recover messages encoded into quantum states. They are at the forefront of quantum hypothesis testing, wherein the goal is to perform an optimal measurement for arriving at a correct…
In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…
A theorem of Davies states that for symmetric quantum states there exists a symmetric POVM maximizing the mutual information. To apply this theorem the representation of the symmetry group has to be irreducible. We obtain a similar yet…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…