Related papers: Information-theoretic lower bounds for quantum sor…
The method for analyzing algorithmic runtime complexity using decision trees is discussed using the sorting algorithm. This method is then extended to optimal algorithms which may find all cliques of size q in network N, or simply the first…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…
If two parties share an unknown quantum state, one can ask how much quantum communication is needed for party A to send her share to party B. Recently, it was found that the number of qubits which should be sent is given by the conditional…
The set equality problem is to decide whether two sets $A$ and $B$ are equal or disjoint, under the promise that one of these is the case. Some other problems, like the Graph Isomorphism problem, is solvable by reduction to the set quality…
We introduce new methods and tools to study and characterise classical and quantum correlations emerging from prepare-and-measure experiments with informationally restricted communication. We consider the most general kind of…
We study the partially ordered set of equivalence classes of quantum measurements endowed with the post-processing partial order. The post-processing order is fundamental as it enables to compare measurements by their intrinsic noise and it…
A simple method to enhance the quality of communication is to send a carrier with its copies. Classical information theory says that information behaves quantitatively under copying. In other words, if a carrier is more informatic than…
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
We discuss the quantum search algorithm using complex queries that has recently been published by Grover (quant-ph/9706005). We recall the algorithm adding some details showing which complex query has to be evaluated. Based on this version…
Transmission of classical information using quantum objects such as polarized photons is studied. The classical (Shannon) channel capacity and its relation to quantum (von Neumann) channel capacity is investigated for various receiver…
In this work we introduce, both for classical communication complexity and query complexity, a modification of the 'partition bound' introduced by Jain and Klauck [2010]. We call it the 'public-coin partition bound'. We show that (the…
Quite often in database search, we only need to extract portion of the information about the satisfying item. Recently Radhakrishnan & Grover [RG] considered this problem in the following form: the database of $N$ items was divided into $K$…
The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a…
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
The quantum search algorithm of Chen and Diao, which finds with certainty a single target item in an unsorted database, is modified so as to be capable of searching for an arbitrary specified number of target items. If the number of…
We consider quantum search algorithms that have access to a noisy oracle that, for every oracle call, with probability $p>0$ completely depolarizes the query registers, while otherwise working properly. Previous results had not ruled out…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
Partially ordered models of time occur naturally in applications where agents or processes cannot perfectly communicate with each other, and can be traced back to the seminal work of Lamport. In this paper we consider the problem of…