scholarly journals A non-Markovian Dissipative Maryland Model

2013 ◽  
Vol 20 (03) ◽  
pp. 1340001
Author(s):  
F. Benatti ◽  
F. Carollo
Keyword(s):  
Stochastic Process ◽  
Anderson Localization ◽  
Completely Positive Maps ◽  
Completely Positive ◽  
Quantum Process ◽  
Positive Maps ◽  
Kicked Rotor ◽  
Linear Version ◽  
Discrete Family ◽  
Maryland Model

The so-called Maryland model is a linear version of the quantum kicked rotor; it exhibits Anderson localization in momentum space. By turning the kicks into a Markovian stochastic process, the dynamics becomes a dissipative quantum process described by a discrete family of completely positive maps that allows to explicitly study the relation between divisibility of the maps and the degree of memory of the process.

Complete Positivity

2019 ◽  
pp. 225-264
Author(s):  
Chris Heunen ◽  
Jamie Vicary
Keyword(s):  
Quantum Theory ◽  
Quantum Information ◽  
Linear Structure ◽  
Complete Positivity ◽  
Completely Positive Maps ◽  
Completely Positive ◽  
Quantum Process ◽  
Positive Maps

Completely positive maps give a notion of quantum process that allows the description of probabilistic effects in quantum theory. We show how to describe this categorically in terms of the CP construction and contrast the behaviour of classical and quantum information in this setting. We also study the behaviour of duality and linear structure under the CP construction.

scholarly journals Quantum weakest preconditions

2006 ◽  
Vol 16 (3) ◽  
pp. 429-451 ◽  
Author(s):  
ELLIE D'HONDT ◽  
PRAKASH PANANGADEN
Keyword(s):  
Quantum Computation ◽  
Representation Theorem ◽  
Completely Positive Maps ◽  
Completely Positive ◽  
Weakest Precondition ◽  
Positive Maps ◽  
Weakest Preconditions ◽  
Predicate Transformer ◽  
Usual State ◽  
Stone Type

We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest precondition semantics. Rather than trying to reduce quantum computation to probabilistic programming, we develop a notion that is directly taken from concepts used in quantum computation. The proof that weakest preconditions exist for completely positive maps follows immediately from the Kraus representation theorem. As an example, we give the semantics of Selinger's language in terms of our weakest preconditions. We also cover some specific situations and exhibit an interesting link with stabilisers.

MODULES OVER MONOTONE COMPLETE C*-ALGEBRAS

1992 ◽  
Vol 03 (02) ◽  
pp. 185-204 ◽  
Author(s):  
MASAMICHI HAMANA
Keyword(s):  
Completely Positive Maps ◽  
Completely Positive ◽  
C Algebra ◽  
C Algebras ◽  
Positive Maps

The main result asserts that given two monotone complete C*-algebras A and B, B is faithfully represented as a monotone closed C*-subalgebra of the monotone complete C*-algebra End A(X) consisting of all bounded module endomorphisms of some self-dual Hilbert A-module X if and only if there are sufficiently many normal completely positive maps of B into A. The key to the proof is the fact that each pre-Hilbert A-module can be completed uniquely to a self-dual Hilbert A-module.

Sign in / Sign up

Export Citation Format

Share Document