Related papers: Binary search trees for generalized measurement
We analyze the possible results of the most general measurement on two copies of a quantum state. We show that $\mu$ can label a set of outcomes of such measurement if and only if there is a family of completely co--positive (ccP) maps…
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
Each platonic solid defines a single-qubit positive operator valued measure (POVM) by interpreting its vertices as points on the Bloch sphere. We construct simple circuits for implementing this kind of measurements and other simple types of…
Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be…
The notion of Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) arose in physics as a kind of optimal measurement basis for quantum systems. However the question of their existence is equivalent to that of the…
With advances in scientific computing, computer experiments are increasingly used for optimizing complex systems. However, for modern applications, e.g., the optimization of nuclear physics detectors, each experiment run can require…
In this study the determinant of the average quadratic error matrix is used as the measure of state estimation efficiency. This quantity is easily computable in some cases, so it gives us a reasonable tool to find optimal measurement setup…
Traditional tree search algorithms supply a blueprint for modeling problem solving behaviour. A diverse spectrum of problems can be formulated in terms of tree search. Quantum computation, in particular Grover's algorithm, has aroused a…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
We provide a definition of POVM in terms of abstract tensor structure only. It is justified in two distinct manners. i. At this abstract level we are still able to prove Naimark's theorem, hence establishing a bijective correspondence…
High-dimensional systems are an important frontier for photonic quantum correlation experiments. These correlation tests commonly prescribe measurements with many possible outcomes but they are often implemented through many individual…
We study measurements of the unitary generalization of Pauli operators. First, an analytical (constructive) solution to the eigenproblem of these operators is presented. Next, in the case of two subsystems, the Schmidt form of the…
Bipartite entanglement is one of the fundamental quantifiable resources of quantum information theory. We propose a new application of this resource to the theory of quantum measurements. According to Naimark's theorem any rank 1…
We question whether the measurement based quantum computing algorithm is in fact Grover's algorithm or simply a similar oracular search method. The two algorithms share several qualitative features especially in the case of the trivial 4…
We first consider various methods for the indirect implementation of unitary gates. We apply these methods to rederive the universality of 4-qubit measurements based on a scheme much simpler than Nielsen's original construction…
We design an efficient and constructive algorithm to decompose any generalized quantum measurement into a convex combination of extremal measurements. We show that if one allows for a classical post-processing step only extremal rank-1…
For a quantum measurement process described by a quantum instrument $\mathcal{I}$ and a system observable corresponding to a positive-operator valued measure (POVM) $E ,$ $\mathcal{I}$ is said to conserve the information of $E$ if the joint…
It is shown that mean value of any observable with bounded spectrum can be uniquely determined from binary statistics of the measurement performed on {\it single} qubit ancilla coupled to a given system. The observable structure is fully…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…