Related papers: Continuous majorization in quantum phase space for…

We explore the role of majorization theory in quantum phase space. To this purpose, we restrict ourselves to quantum states with positive Wigner functions and show that the continuous version of majorization theory provides an elegant and…

Majorization theory is a powerful mathematical tool to compare the disorder in distributions, with wide-ranging applications in many fields including mathematics, physics, information theory, and economics. While majorization theory…

We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is…

The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…

We develop a resource theory for continuous-variable systems grounded on operations routinely available within current quantum technologies. In particular, the set of free operations is convex and includes quadratic transformations and…

The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…

Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…

We analyze and further develop a new method to represent the quantum state of a system of $n$ qubits in a phase space grid of $N\times N$ points (where $N=2^n$). The method, which was recently proposed by Wootters and co--workers (Gibbons…

I show that a nonnegative Wigner function that represents a mixture of Fock states is majorized by the Wigner function of the vacuum state. As a consequence, the integration of any concave function over the Wigner phase space has a lower…

We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We…

Continuous-variable systems realized in quantum optics play a major role in quantum information processing, and it is also one of the promising candidates for a scalable quantum computer. We introduce a resource theory for…

We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…

In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…

The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…

We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a…

This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe…

Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…

We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms considered in the canonical decomposition. Our result relies on the fact that states which are mixed by…

According to a classical result due to Hudson, the Wigner function of a pure, continuous variable quantum state is non-negative if and only if the state is Gaussian. We have proven an analogous statement for finite-dimensional quantum…

Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…