scholarly journals The joint distribution of the marginals of multipartite random quantum states

2019 ◽  
Vol 09 (03) ◽  
pp. 2050010
Author(s):  
Stephane Dartois ◽  
Luca Lionni ◽  
Ion Nechita
Keyword(s):  
Tensor Product ◽  
Joint Distribution ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Product Spaces ◽  
Wishart Matrix ◽  
Matrix Integrals ◽  
The Matrix ◽  
Combinatorial Maps ◽  
Random Quantum States

We study the joint distribution of the set of all marginals of a random Wishart matrix acting on a tensor product Hilbert space. We compute the limiting free mixed cumulants of the marginals, and we show that in the balanced asymptotical regime, the marginals are asymptotically free. We connect the matrix integrals relevant to the study of operators on tensor product spaces with the corresponding classes of combinatorial maps, for which we develop the combinatorial machinery necessary for the asymptotic study. Finally, we present some applications to the theory of random quantum states in quantum information theory.

scholarly journals Approximation with monotone norms in tensor product spaces

1992 ◽  
Vol 68 (2) ◽  
pp. 183-205 ◽  
Author(s):  
W.A Light ◽  
M.v Golitschek ◽  
E.W Cheney
Keyword(s):  
Tensor Product ◽  
Product Spaces

scholarly journals Matrix integrals & finite holography

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Dionysios Anninos ◽  
Beatrix Mühlmann
Keyword(s):  
Critical Exponents ◽  
Continuum Theory ◽  
Point Of View ◽  
Leading Order ◽  
Minimal Models ◽  
Point Evaluation ◽  
Brst Cohomology ◽  
Matrix Integrals ◽  
The Matrix ◽  
The Continuum

Abstract We explore the conjectured duality between a class of large N matrix integrals, known as multicritical matrix integrals (MMI), and the series (2m − 1, 2) of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an S2 topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. From the continuum point of view the corresponding critical exponents are obtained upon computing the partition function in the presence of a given conformal primary. Further to this, we elaborate on a Hilbert space of the continuum theory, and the putative finiteness thereof, on both an S2 and a T2 topology using BRST cohomology considerations. Matrix integrals support this finiteness.

scholarly journals Clustering and enhanced classification using a hybrid quantum autoencoder

2021 ◽  
Author(s):  
Maiyuren Srikumar ◽  
Charles Daniel Hill ◽  
Lloyd Hollenberg
Keyword(s):  
Machine Learning ◽  
Supervised Classification ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Data Sets ◽  
New Paradigm ◽  
Novel Approach ◽  
Representational Space ◽  
Quantum Machine Learning ◽  
Pure States

Abstract Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within quantum states themselves. In this work, we propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space, obtained through the training of a hybrid quantum autoencoder (HQA). Hence, given a set of pure states, this variational QML algorithm learns to identify – and classically represent – their essential distinguishing characteristics, subsequently giving rise to a new paradigm for clustering and semi-supervised classification. The analysis and employment of the HQA model are presented in the context of amplitude encoded states – which in principle can be extended to arbitrary states for the analysis of structure in non-trivial quantum data sets.

Finding Cut-Edges and the Minimum Spanning Tree via Semi-Tensor Product Approach

2018 ◽  
Vol 6 (5) ◽  
pp. 459-472
Author(s):  
Xujiao Fan ◽  
Yong Xu ◽  
Xue Su ◽  
Jinhuan Wang
Keyword(s):  
Tensor Product ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Matrix ◽  
Product Approach ◽  
Matrix Expression ◽  
Necessary And Sufficient ◽  
Logical Functions

Abstract Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for cycles of graph, based on which a new necessary and sufficient condition is established to find all cycles for any graph. Secondly, using the necessary and sufficient condition of cycles, two algorithms are established to find all cut-edges and the minimum spanning tree, respectively. Finally, the study of an illustrative example shows that the results/algorithms presented in this paper are effective.

Johnson pseudo-contractibility of second duals of certain Banach algebras

2019 ◽  
pp. 2150012
Author(s):  
A. Sahami ◽  
E. Ghaderi ◽  
S. M. Kazemi Torbaghan ◽  
B. Olfatian Gillan
Keyword(s):  
Tensor Product ◽  
Matrix Algebra ◽  
Banach Algebras ◽  
Amenable Group ◽  
Semigroup Algebra ◽  
Archimedean Semigroup ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
The Matrix ◽  
Second Dual

In this paper, we study Johnson pseudo-contractibility of second dual of some Banach algebras. We show that the semigroup algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is a finite amenable group, where [Formula: see text] is an archimedean semigroup. We also show that the matrix algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is finite. We study Johnson pseudo-contractibility of certain projective tensor product second duals Banach algebras.

scholarly journals Generating and using truly random quantum states in Mathematica

2012 ◽  
Vol 183 (1) ◽  
pp. 118-124 ◽  
Author(s):  
Jarosław Adam Miszczak
Keyword(s):  
Quantum States ◽  
Random Quantum States

scholarly journals Signatures of Anderson localization and delocalized random quantum states

2018 ◽  
Vol 514 ◽  
pp. 141-149
Author(s):  
Giorgio J. Moro ◽  
Giulia Dall'Osto ◽  
Barbara Fresch
Keyword(s):  
Anderson Localization ◽  
Quantum States ◽  
Random Quantum States
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