Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of the Physical Society Section A

The Density Matrix and the Foundations of the Statistical Theory

Norman Henry March

Published Nov 1, 1957• 7 citations
Publisher
DOI
10.1088/0370-1298/70/11/109

Related papers

Composite Systems, Interaction, and Measurement

Bas C. van Fraassen

The three main issues in the foundations of quantum theory are measurement, non‐locality, and identical particles (quantum statistics). All of these pertain to the relations between different parts of a composite system. Hence this chapter covers tensor products, reduction of the density matrix (reduced states), and certain aspects of Hugh Everett's relative state formalism. This is then utilized in an extended discussion of measurement as a quantum‐mechanical process.

Oxford University Press eBooks•Sep 26, 1991•0 citations

Theory of Density Matrices

K. Husimi, Yoshihiro Kitano, Toshiyuki Nishiyama

Fortschritte der Physik•Jan 1, 1958•27 citations

Asymptotic equivalence of quantum state tomography and noisy matrix completion

Yazhen Wang

Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientific studies. This paper investigates the statistical relationship between trace regression in matrix completion and quantum state tomography in quantum physics and quantum information science. As quantum state tomography and trace regression share the common goal of recovering an unknown matrix, it is nature to put them in the Le Cam paradigm for statistical comparison. Regarding the two types of matrix inference problems as two statistical experiments, we establish their asymptotic equivalence in terms of deficiency distance. The equivalence study motivates us to introduce a new trace regression model. The asymptotic equivalence provides a sound statistical foundation for applying matrix completion methods to quantum state tomography. We investigate the asymptotic equivalence for sparse density matrices and low rank density matrices and demonstrate that sparsity and low rank are not necessarily helpful for achieving the asymptotic equivalence of quantum state tomography and trace regression. In particular, we show that popular Pauli measurements are bad for establishing the asymptotic equivalence for sparse density matrices and low rank density matrices.

arXiv:1311.4976•The Annals of Statistics•Oct 1, 2013•22 citations

Density Matrix Theory and Applications

Karl Blum

Springer eBooks•Jan 1, 1981•1,121 citations

Density Matrix Theory and Applications

Karl Blum

Springer eBooks•Jan 1, 1996•685 citations

Asymptotic Equivalence of Quantum State Tomography and Trace Regression

Yazhen Wang

Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientiflc studies. This paper investigates the statistical relationship between trace regression in matrix completion and quantum state tomography in quantum physics and quantum information science. As quantum state tomography and trace regression share the common goal of recovering an unknown matrix, it is nature to put them in the Le Cam paradigm for statistical comparison. Regarding the two types of matrix inference problems as two statistical experiments, we establish their asymptotic equivalence in terms of deflciency distance. The equivalence study motivates us to introduce a new trace regression model. The asymptotic equivalence provides sound statistical foundation for applying matrix completion techniques to quantum state tomography. We investigate the asymptotic equivalence for sparse density matrices and low rank density matrices and demonstrate that sparsity and low rank are not necessarily helpful for achieving the asymptotic equivalence of quantum state tomography and trace regression. In particular we show that popular Pauli measurements are bad for establishing the asymptotic equivalence for sparse density matrices and low rank density matrices.

•Jan 1, 2012•4 citations
Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientific studies. This paper investigates the statistical relationship between trace regression in matrix completion and quantum state tomography in quantum physics and quantum information science. As quantum state tomography and trace regression share the common goal of recovering an unknown matrix, it is nature to put them in the Le Cam paradigm for statistical comparison. Regarding the two types of matrix inference problems as two statistical experiments, we establish their asymptotic equivalence in terms of deficiency distance. The equivalence study motivates us to introduce a new trace regression model. The asymptotic equivalence provides a sound statistical foundation for applying matrix completion methods to quantum state tomography. We investigate the asymptotic equivalence for sparse density matrices and low rank density matrices and demonstrate that sparsity and low rank are not necessarily helpful for achieving the asymptotic equivalence of quantum state tomography and trace regression. In particular, we show that popular Pauli measurements are bad for establishing the asymptotic equivalence for sparse density matrices and low rank density matrices.
Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientiflc studies. This paper investigates the statistical relationship between trace regression in matrix completion and quantum state tomography in quantum physics and quantum information science. As quantum state tomography and trace regression share the common goal of recovering an unknown matrix, it is nature to put them in the Le Cam paradigm for statistical comparison. Regarding the two types of matrix inference problems as two statistical experiments, we establish their asymptotic equivalence in terms of deflciency distance. The equivalence study motivates us to introduce a new trace regression model. The asymptotic equivalence provides sound statistical foundation for applying matrix completion techniques to quantum state tomography. We investigate the asymptotic equivalence for sparse density matrices and low rank density matrices and demonstrate that sparsity and low rank are not necessarily helpful for achieving the asymptotic equivalence of quantum state tomography and trace regression. In particular we show that popular Pauli measurements are bad for establishing the asymptotic equivalence for sparse density matrices and low rank density matrices.