aqora

Positive and Completely Positive Maps, Quantum Operations and Generalized Measurement Theory

Chapman & Hall/CRC applied mathematics and nonlinear science seriesAug 3, 20070 citations

On the Quantum Theory of Non-Local Fields

孟大中

Jan 1, 19591 citation

On a dilation of a some class of completely positive maps

Эльсаев Якуб Витальевич

In this article we investigate sesquilinear forms defined on the Cartesian product of Hilbert C^*-module M over C^*-algebra B and taking values in B. The set of all such defined sesquilinear forms is denoted by S_B (M). We consider completely positive maps from locally C^*-algebra A to S_B (M). Moreover we assume that these completely positive maps are covariant with respect to actions of a group symmetry. This allow us to view these maps as generalizations covariant quantum instruments which are very important for the modern quantum mechanic and the quantum field theory. We analyze the dilation problem for these class of maps. In order to solve this problem we construct the minimal Stinespring representation and prove that every two minimal representations are unitarily equivalent.In this article we investigate sesquilinear forms defined on the Cartesian product of Hilbert C^*-module M over C^*-algebra B and taking values in B. The set of all such defined sesquilinear forms is denoted by S_B (M). We consider completely positive maps from locally C^*-algebra A to S_B (M). Moreover we assume that these completely positive maps are covariant with respect to actions of a group symmetry. This allow us to view these maps as generalizations covariant quantum instruments which are very important for the modern quantum mechanic and the quantum field theory. We analyze the dilation problem for these class of maps. In order to solve this problem we construct the minimal Stinespring representation and prove that every two minimal representations are unitarily equivalent.

Tambov University Reports Series Natural and Technical SciencesJan 1, 20190 citations

Local random quantum circuits: Ensemble completely positive maps and swap algebras

Paolo Zanardi A

We define different classes of local random quantum circuits (L-RQC) and show that (a) statistical properties of L-RQC are encoded into an associated family of completely positive maps and (b) average purity dynamics can be described by the action of these maps on operator algebras of permutations (swap algebras). An exactly solvable one-dimensional case is analyzed to illustrate the power of the swap algebra formalism. More in general, we prove short time area-law bounds on average purity for uncorrelated L-RQC and infinite time results for both the uncorrelated and correlated cases.We define different classes of local random quantum circuits (L-RQC) and show that (a) statistical properties of L-RQC are encoded into an associated family of completely positive maps and (b) average purity dynamics can be described by the action of these maps on operator algebras of permutations (swap algebras). An exactly solvable one-dimensional case is analyzed to illustrate the power of the swap algebra formalism. More in general, we prove short time area-law bounds on average purity for uncorrelated L-RQC and infinite time results for both the uncorrelated and correlated cases.

arXiv:1303.2832Journal of Mathematical PhysicsAug 1, 20148 citations

Local operators in massive quantum field theories

A. Koubek

arXiv:hep-th/9508109Springer eBooksJan 4, 20070 citations

Aspects of non-perturbative approximation schemes for local quantum field theory

Richard Cant

Jan 1, 19800 citations

Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory

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