Related papers: Measuring relational information between quantum s…
A novel method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently Vallone and Dequal…
Traditionally, quantum state correlation can be obtained with calculations on a state density matrix already known. Here, we propose a model with which correlations of unknown quantum states can be obtained. There are no needs of classical…
We investigate the total variance of a quantum state with respect to a complete set of mutually complementary measurements and its relation to the Brukner-Zeilinger invariant information. By summing the variances over any complete set of…
We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting…
We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of…
State of a $d$-dimensional quantum system can only be inferred by performing an informationally complete measurement with $m\geqslant d^2$ outcomes. However, an experimentally accessible measurement can be informationally incomplete. Here…
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…
Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement setup that reveals this property with…
Suppose we have $N$ quantum systems in unknown states $\lvert\psi_i \rangle $, but know the value of some pairwise overlaps $\left| \langle \psi_k \lvert \psi_l \rangle \right|^2$. What can we say about the values of the unknown overlaps?…
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these…
Quantum states and the modes of the optical field they occupy are intrinsically connected. Here, we show that one can trade the knowledge of a quantum state to gain information about the underlying mode structure and, vice versa, the…
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the…
We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces.…
We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
For a general multipartite quantum state, we formulate a locally checkable condition, under which the expectation values of certain nonlocal observables are completely determined by the expectation values of some local observables. The…
Quantum universal invariants of general N-beam Gaussian fields are investigated from the point of view of fields' intensity moments. A method that uniquely links these invariants, including the global and marginal fields' purities, to…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
We introduce novel schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in [Phys. Rev. Lett. 98, 220503 (2007), quant-ph/0609149]. Our method makes use of…
The present Thesis covers the subject of the characterization of entangled states by recourse to entropic measures, as well as the description of entanglement related to several issues in quantum mechanics, such as the speed of a quantum…