TITLE

Tsirelson's problem and asymptotically commuting unitary matrices

AUTHOR(S)
Ozawa, Narutaka
PUB. DATE
March 2013
SOURCE
Journal of Mathematical Physics;Mar2013, Vol. 54 Issue 3, p032202
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, we consider quantum correlations of bipartite systems having a slight interaction, and reinterpret Tsirelson's problem (and hence Kirchberg's and Connes's conjectures) in terms of finite-dimensional asymptotically commuting positive operator valued measures. We also consider the systems of asymptotically commuting unitary matrices and formulate the Stronger Kirchberg Conjecture.
ACCESSION #
86446986

 

Related Articles

  • The geometric measure of multipartite entanglement and the singular values of a hypermatrix. Hilling, Joseph J.; Sudbery, Anthony // Journal of Mathematical Physics;Jul2010, Vol. 51 Issue 7, p072102 

    It is shown that the geometric measure of entanglement of a pure multipartite state satisfies a polynomial equation, generalizing the singular-value equation of the matrix of coefficients of a bipartite state. The equation is solved for a class of three-qubit states.

  • Quantum correlation exists in any non-product state. Yu Guo; Shengjun Wu // Scientific Reports;12/5/2014, p1 

    Simultaneous existence of correlation in complementary bases is a fundamental feature of quantum correlation, and we show that this characteristic is present in any non-product bipartite state. We propose a measure via mutually unbiased bases to study this feature of quantum correlation, and...

  • An easy measure of quantum correlation. Cao, Hui; Wu, Zhao-Qin; Hu, Li-Yun; Xu, Xue-Xiang; Huang, Jie-Hui // Quantum Information Processing;Nov2015, Vol. 14 Issue 11, p4103 

    To measure the quantum correlation of a bipartite state, a test matrix is constructed through the commutations among the blocks of its density matrix, which turns out to be a zero matrix for a classical state with zero quantum correlation, and a nonzero one for a quantum state with positive...

  • Some properties of the reformulated Zagreb indices. Bo Zhou; Trinajstić, Nenad // Journal of Mathematical Chemistry;Oct2010, Vol. 48 Issue 3, p714 

    Miličević, Nikolić and Trinajstić (Mol Divers 8:393–399, 2004) proposed the reformed Zagreb indices in 2004. Now we give some properties for the reformed Zagreb indices.

  • How quantum is a quantum ensemble? Shunlong Luo; Nan Li; Wei Sun // Quantum Information Processing;Dec2010, Vol. 9 Issue 6, p711 

    In the Hilbert space operator formalism of quantum mechanics, a single quantum state, which is represented by a density operator, can be regarded as classical in the sense that it can always be diagonalized. However, a quantum ensemble, which is represented by a family of quantum states together...

  • Global versus local quantum correlations in the Grover search algorithm. Batle, J.; Ooi, C.; Farouk, Ahmed; Alkhambashi, M.; Abdalla, S. // Quantum Information Processing;Feb2016, Vol. 15 Issue 2, p833 

    Quantum correlations are thought to be the reason why certain quantum algorithms overcome their classical counterparts. Since the nature of this resource is still not fully understood, we shall investigate how entanglement and nonlocality among register qubits vary as the Grover search algorithm...

  • How the Taxonomy of Products Drives the Economic Development of Countries. Zaccaria, Andrea; Cristelli, Matthieu; Tacchella, Andrea; Pietronero, Luciano // PLoS ONE;Dec2014, Vol. 9 Issue 12, p1 

    We introduce an algorithm able to reconstruct the relevant network structure on which the time evolution of country-product bipartite networks takes place. The significant links are obtained by selecting the largest values of the projected matrix. We first perform a number of tests of this...

  • Computable Cross-norm Criterion for Separability. Rudolph, Oliver // Letters in Mathematical Physics;Oct2004, Vol. 70 Issue 1, p57 

    We describe a computable analytical criterion for separability of bipartite mixed states in arbitrary dimension. The criterion stipulates that a certain norm on the state space (the computable cross-norm) is bounded by 1 for separable states. The criterion is shown to be independent of the...

  • Indecomposable Positive Maps and a New Family of Inseparable PPT States. Simon, Sudhavathani; Rajagopalan, S. P.; Simon, R. // AIP Conference Proceedings;2006, Vol. 864 Issue 1, p67 

    We present a new class of entangled bipartite states. These remain positive under partial transposition, and hence live outside the jurisdiction of the Peres-Horodecki separability criterion. Their inseparability is demonstrated using Choi-type indecomposable positive maps. It is shown that...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics