Related papers: Generalized quantum state discrimination problems
We consider the general measurement scenario in which the ensemble average of an operator is determined via suitable data-processing of the outcomes of a quantum measurement described by a POVM. We determine the optimal processing that…
Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of…
This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given collection of…
We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a…
We describe algorithms, and experimental strategies, for the Pareto optimal control problem of simultaneously driving an arbitrary number of quantum observable expectation values to their respective extrema. Conventional quantum optimal…
The problem of designing optimal quantization rules for sequential detectors is investigated. First, it is shown that this task can be solved within the general framework of active sequential detection. Using this approach, the optimal…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and…
Quantum state tomography is an indispensable but costly part of many quantum experiments. Typically, it requires measurements to be carried in a number of different settings on a fixed experimental setup. The collected data is often…
Satellite mission planning for Earth observation satellites is a combinatorial optimization problem that consists of selecting the optimal subset of imaging requests, subject to constraints, to be fulfilled during an orbit pass of a…
We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of mixed quantum states. Using this…
We investigate variational problems in quantum thermodynamics at positive temperature, in which admissible states are constrained by prescribed outcomes of a finite set of measurements. We solve a problem raised by the recent work [Liu,…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum…
Given a finite set of linearly independent quantum states, an observer who examines a single quantum system may sometimes identify its state with certainty. However, unless these quantum states are orthogonal, there is a finite probability…
The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent…
We show that quantum state discrimination sits neatly in the framework of Bayesian experimental design. In this setting, the two main branches of quantum state discrimination (minimal error and maximal confidence) simply correspond to two…
The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…
A programmable quantum processor is a fundamental model of quantum computation. In this model, any quantum channel can be approximated by applying a fixed universal quantum operation onto an input state and a quantum `program' state, whose…
In this paper, we consider the generalized measurement where one particular quantum signal is unambiguously extracted from a set of non-commutative quantum signals and the other signals are filtered out. Simple expressions for the maximum…