Related papers: Extending Hudson's theorem to mixed quantum states
Quantum non-Gaussian states, which cannot be written as mixtures of Gaussian states, are necessary to achieve a quantum advantage in continuous variable systems. They represent an important benchmark for the realization of an advanced…
A generalization of the Hohenberg-Kohn theorem proves the existence of a density functional for an intrinsic state, symmetry violating, out of which a physical state with good quantum numbers can be projected.
The aim of this work is to estimate a quadratic functional of a unknown Wigner function from noisy tomographic data. The Wigner function can be seen as the representation of the quantum state of a light beam. The estimation of a quadratic…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…
Quantum states of motion are critical components in the second quantum revolution. We investigate the generation and control of non-Gaussian motional states in a tripartite hybrid quantum system consisting of a collection of qubits coupled…
We study the possibility of giving a classical interpretation to quantum projective measurements for a particle described by a pure Gaussian state whose Wigner function is non-negative. We analyze the case of a projective measurement which…
Non-Gaussian quantum states, described by negative valued Wigner functions, are important both for fundamental tests of quantum physics and for emerging quantum information technologies. However, they are vulnerable to dissipation. It is…
We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection. We rank experimental non-Gaussian states according to the recently defined stellar hierarchy…
The measurement based, or one-way, model of quantum computation for continuous variables uses a highly entangled state called a cluster state to accomplish the task of computing. Cluster states that are universal for computation are a…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
A bipartite quantum state is tomographically faithful when it can be used as an input of a quantum operation acting on one of the two quantum systems, such that the joint output state carries a complete information about the operation…
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 investigate different geometries and invariant measures on the space of mixed Gaussian quan- tum states. We show that when the global purity of the state is held fixed, these measures coincide and it is possible, within this constraint,…
We introduce and experimentally explore the concept of quantum non-Gaussian depth of single-photon states with a positive Wigner function. The depth measures the robustness of a single-photon state against optical losses. The directly…
A complete set of mutually unbiased bases in a Hilbert space of dimension $d$ defines a set of $d+1$ orthogonal measurements. Relative to such a set, we define a "MUB-balanced state" to be a pure state for which the list of probabilities of…
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
Full reconstruction of quantum states from measurement samples is often a prohibitively complex task, both in terms of the experimental setup and the scaling of the sample size with the system. This motivates the relatively easier task of…
We present the experimental investigation of the non-Gaussian nature of some mixtures of Fock states by reconstructing their Wigner function and exploiting two recently introduced measures of non-Gaussianity. In particular, we demonstrate…