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Related papers: A Decomposition of Separable Werner States

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Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as…

Combinatorics · Mathematics 2023-10-04 Kazuo Murota , Akihisa Tamura

In this paper, we present a novel approach to decompose a given piecewise affine (PWA) function into two convex PWA functions. Convex decompositions are useful to speed up or distribute evaluations of PWA functions. Different approaches to…

Systems and Control · Electrical Eng. & Systems 2021-08-10 Nils Schlüter , Moritz Schulze Darup

We first analyze the integrated density of states (IDS) of periodic Schr\"odinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with…

Spectral Theory · Mathematics 2018-09-28 Daniel Lenz , Norbert Peyerimhoff , Olaf Post , Ivan Veselic'

It is known that from entangled states that have positive partial transpose it is not possible to distill maximally entangled states by local operations and classical communication (LOCC). A long-standing open question is whether maximally…

Quantum Physics · Physics 2013-08-27 Lukasz Pankowski , Fernando G. S. L. Brandao , Michal Horodecki , Graeme Smith

We measure complete and continuous Wigner functions of a two-level cesium atom in both a nearly pure state and highly mixed states. We apply the method [T. Tilma et al., Phys. Rev. Lett. 117, 180401 (2016)] of strictly constructing…

Quantum Physics · Physics 2018-01-26 Yali Tian , Zhihui Wang , Pengfei Zhang , Gang Li , Jie Li , Tiancai Zhang

Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…

Analysis of PDEs · Mathematics 2015-05-19 Agissilaos G. Athanassoulis , Norbert J. Mauser , Thierry Paul

As it is well known, every bipartite $2\otimes 2$ density matrix can be obtained from Bell decomposable states via local quantum operations and classical communications (LQCC). Using this fact, the Lewenstein-Sanpera decomposition of an…

Quantum Physics · Physics 2007-05-23 S. J. Akhtarshenas , M. A. Jafarizadeh

By means of a well-grounded mapping scheme linking Schwinger unitary operators and generators of the special unitary group $\mathrm{SU(N)}$, it is possible to establish a self-consistent theoretical framework for finite-dimensional discrete…

Quantum Physics · Physics 2019-08-20 Marcelo A. Marchiolli , Diogenes Galetti

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…

Quantum Physics · Physics 2009-11-07 Pablo Bianucci , Cesar Miquel , Juan Pablo Paz , Marcos Saraceno

Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation…

In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…

Numerical Analysis · Mathematics 2020-02-12 Hendrik Ranocha , Katharina Ostaszewski , Philip Heinisch

A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance $\epsilon$ in its neighborhood. We say that such nearby states are…

Quantum Physics · Physics 2017-01-27 Michel Boyer , Aharon Brodutch , Tal Mor

Wigner function tomography is indispensable for characterizing quantum states, but its commonly used version, balanced homodyne detection, suffers from several weaknesses. First, it requires efficient detection, which is critical for…

Quantum Physics · Physics 2023-08-25 Mahmoud Kalash , Maria V. Chekhova

In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the…

Numerical Analysis · Mathematics 2023-01-18 Zhuo-Ran Chen , Seak-Weng Vong , Ze-Jia Xie

We propose a second version of the van der Waals density functional (vdW-DF2) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient…

Materials Science · Physics 2010-08-17 Kyuho Lee , Éamonn D. Murray , Lingzhu Kong , Bengt I. Lundqvist , David C. Langreth

In this contribution we group the operator basis for d^2 dimensional Hilbert space in a way that enables us to relate bases of entangled states with single particle mutually unbiased state bases (MUB), each in dimensionality d. We utilize…

Quantum Physics · Physics 2015-05-13 A. Kalev , F. C. Khanna , M. Revzen

We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators $\rho_1$ and $\rho_2$ of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two…

Quantum Physics · Physics 2009-11-13 Ulrike Herzog

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in…

Quantum Physics · Physics 2015-05-19 A. J. Bracken , P. Watson

We discuss the possibility of generating and detecting, by a tomographic reconstruction of the Wigner function, a macroscopic superposition of two coherent states. The superposition state is created using a conditioned measurement on the…

Quantum Physics · Physics 2009-11-06 M. Genovese , C. Novero

We present an analytical formula for the asymptotic relative entropy of entanglement for Werner states of arbitrary dimension. We then demonstrate its validity using methods from convex optimization. To our knowledge, this is the first case…

Quantum Physics · Physics 2007-05-23 K. Audenaert , J. Eisert , E. Jane , M. B. Plenio , S. Virmani , B. De Moor