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We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…

Operator Algebras · Mathematics 2022-11-17 Mark Girard , Seung-Hyeok Kye , Erling Størmer

The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…

Quantum Physics · Physics 2007-05-23 V. I. Man'ko , G. Marmo , E. C. G. Sudarshan , F. Zaccaria

Entanglement are the non-local correlations permitted by quantum theory, believed to play a fundamental role in a quantum computer. We have investigated these correlations in a number of theoretical models for condensed matter systems. Such…

Quantum Physics · Physics 2007-05-23 Stein Olav Skrøvseth

We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive.…

Quantum Physics · Physics 2009-11-13 Dariusz Chruscinski , Andrzej Kossakowski

Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the…

Quantum Physics · Physics 2023-06-08 Sophia Ohnemus , Heinz-Peter Breuer , Andreas Ketterer

In this work we extend the quantum channel detection method developed in [Phys. Rev. A 88, 042335 (2013)] and [Phys. Script. T153, 014044 (2013)] in order to detect other interesting convex sets of quantum channels. First we work out a…

Quantum Physics · Physics 2013-12-18 C. Macchiavello , M. Rossi

In this article, we present a novel approach to investigating entanglement in the context of quantum computing. Our methodology involves analyzing reduced density matrices at different stages of a quantum algorithm's execution and…

Quantum Physics · Physics 2024-03-14 Ruge Lin

Is entanglement an exclusive feature of quantum systems, or is it common to all non-classical theories? And if this is the case, how strong is quantum mechanical entanglement as compared to that exhibited by other theories? The first part…

Quantum Physics · Physics 2018-03-09 Ludovico Lami

In this paper we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems. We first obtain an explicit formula for the moments of a random quantum state to which the reduction criterion has…

Mathematical Physics · Physics 2014-12-02 Maria Anastasia Jivulescu , Nicolae Lupa , Ion Nechita

This article introduces PnCP, a MATLAB toolbox for constructing positive maps which are not completely positive. We survey optimization and sum of squares relaxation techniques to find the most numerically efficient methods for this…

Optimization and Control · Mathematics 2020-01-07 Abhishek Bhardwaj

We introduce a 3-parameter class of maps acting on a bipartite system that are a natural generalisation of the depolarizing channel (and include it as a special case). Then, we find the exact regions of the parameter space that…

Quantum Physics · Physics 2017-06-02 Ludovico Lami , Marcus Huber

We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…

High Energy Physics - Theory · Physics 2011-12-09 Frank Ferrari , Semyon Klevtsov , Steve Zelditch

The most general quantum object that can be shared between two distant parties is a bipartite channel, as it is the basic element to construct all quantum circuits. In general, bipartite channels can produce entangled states, and can be…

Quantum Physics · Physics 2021-06-29 Gilad Gour , Carlo Maria Scandolo

We provide a generalization of the reduction and Robertson positive maps in matrix algebras. They give rise to a new class of optimal entanglement witnesses. Their structural physical approximation is analyzed. As a byproduct we provide a…

Quantum Physics · Physics 2015-01-27 Dariusz Chruściński , Justyna Pytel

Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of…

Quantum Physics · Physics 2009-11-13 J. K. Korbicz , M. L. Almeida , J. Bae , M. Lewenstein , A. Acin

Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme's validity via the probability that…

For the certification and benchmarking of medium-size quantum devices efficient methods to characterize entanglement are needed. In this context, it has been shown that locally randomized measurements on a multiparticle quantum system can…

Quantum Physics · Physics 2021-08-10 Xiao-Dong Yu , Satoya Imai , Otfried Gühne

Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…

Probability · Mathematics 2025-10-02 Afonso S. Bandeira

This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of…

Strongly Correlated Electrons · Physics 2016-08-11 Nicolas Laflorencie

We demonstrate experimentally the possibility of efficiently detecting properties of quantum channels and quantum gates. The optimal detection scheme is first achieved for non entanglement breaking channels of the depolarizing form and is…