Related papers: A mathematical proof for a ground-state identifica…
We study a set of truncated matrices, given by Smith~\cite{Smith2005}, in connection to an identification criterion for the ground state in our proposed quantum adiabatic algorithm for Hilbert's tenth problem. We identify the origin of the…
We review the proposal of a quantum algorithm for Hilbert's tenth problem and provide further arguments towards the proof that: (i) the algorithm terminates after a finite time for any input of Diophantine equation; (ii) the final ground…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
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…
A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalisation quickly becomes impossible when increasing the system size, variational…
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…
We show a geometric formulation for minimum-error discrimination of qubit states, that can be applied to arbitrary sets of qubit states given with arbitrary a priori probabilities. In particular, when qubit states are given with equal…
We consider the problem of optimally identifying the state of a probe qudit, prepared with given prior probability in a pure state belonging to a finite set of possible states which together span a D-dimensional subspace of the…
We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results.
We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to…
We give a lower bound on the probability of error in quantum state discrimination. The bound is a weighted sum of the pairwise fidelities of the states to be distinguished.
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…
We provide quantitative bounds on the characterisation of multiparticle separable states by states that have locally symmetric extensions. The bounds are derived from two-particle bounds and relate to recent studies on quantum versions of…
We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
We present a simple and stable numerical method to approximate the ground state of a quantum many-body system by multiple determinant states. This method searches these determinant states one by one according to the matching pursuit…
There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their…