scholarly journals On the nonlinearity of quantum dynamical entropy

2019 ◽  
Vol 60 (5) ◽  
pp. 053504
Author(s):  
George Androulakis ◽  
Duncan Wright
Keyword(s):  
Quantum Dynamical ◽  
Dynamical Entropy

Some Aspects of Complexities for Quantum Processes

2009 ◽  
Vol 16 (02n03) ◽  
pp. 293-304 ◽  
Author(s):  
Noboru Watanabe
Keyword(s):  
Communication Systems ◽  
Von Neumann Entropy ◽  
Quantum Processes ◽  
Initial State ◽  
Dynamical Processes ◽  
Mixing Entropy ◽  
Quantum Dynamical ◽  
Dynamical Entropy ◽  
The Mean ◽  
Mutual Entropy

In quantum information theory, Emch, Conne, and Stormer were the first who studied the complexity of quantum dynamical processes. After that, Ohya introduced the [Formula: see text]-mixing entropy for general quantum systems and he defined the mean entropy and the mean mutual entropy for quantum dynamical systems based on the [Formula: see text]-mixing entropy. Conne, Narnhoffer and Thirring introduced the dynamical entropy (CNT entropy) and several researchers discussed this concept. Alicki and Fannes defined a different dynamical entropy — AF entropy. In 1995, Voiculescu proposed the dynamical approximation entropy. Accardi, Ohya and Watanabe defined yet another dynamical entropy (AOW entropy) through a quantum Markov process in 1997. In 1999, Kossakowski, Ohya and Watanabe introduced the dynamical entropy (KOW entropy) with respect to completely positive maps. In this paper, we discuss the complexity of quantum dynamical processes to calculate the dynamical entropy for noisy optical channels.In order to discuss the efficiency of information communication processes, a measure of complexity of initial state itself and a measure of transmitted complexity through communication channels are necessary. Quantum entropies were formulated on the basis of the quantum probability theory. In quantum communication systems, von Neumann entropy and Ohya mutual entropy relate to these measures of complexities, respectively. Recently, several mutual entropy type measures (Lindblad-Nielsen entropy and coherent entropy) were defined making use of entropy exchange with respect to a channel and initial state. In this paper, we show which of the measures is the most suitable one for discussing the efficiency of information transmission for quantum processes.

QUANTUM DYNAMICAL ENTROPY FOR COMPLETELY POSITIVE MAP

1999 ◽  
Vol 02 (02) ◽  
pp. 267-282 ◽  
Author(s):  
A. KOSSAKOWSKI ◽  
M. OHYA ◽  
N. WATANABE
Keyword(s):  
Markov Chain ◽  
Completely Positive Map ◽  
Completely Positive ◽  
Positive Map ◽  
Quantum Markov Chain ◽  
Quantum Dynamical ◽  
Dynamical Entropy

A dynamical entropy for not only shift but also completely positive (CP) map is defined by generalizing the AOW entropy1 defined through quantum Markov chain and AF entropy defined by a finite operational partition. Our dynamical entropy is numerically computed for several models.

Defining quantum dynamical entropy

1994 ◽  
Vol 32 (1) ◽  
pp. 75-82 ◽  
Author(s):  
R. Alicki ◽  
M. Fannes
Keyword(s):  
Quantum Dynamical ◽  
Dynamical Entropy

scholarly journals Quantum dynamical entropy of spin systems

2005 ◽  
Vol 56 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Takayuki Miyadera ◽  
Masanori Ohya
Keyword(s):  
Spin Systems ◽  
Quantum Dynamical ◽  
Dynamical Entropy

A CONTINUITY PROPERTY OF QUANTUM DYNAMICAL ENTROPY

1999 ◽  
Vol 02 (04) ◽  
pp. 511-527 ◽  
Author(s):  
M. FANNES ◽  
P. TUYLS
Keyword(s):  
Quantum System ◽  
Spin Chain ◽  
Coarse Grained ◽  
Continuity Property ◽  
Natural Class ◽  
Quantum Dynamical ◽  
Dynamical Entropy ◽  
Toral Automorphisms

In this paper, we are mainly concerned with the computation of the dynamical entropy for the noncommutative toral automorphisms and the noncommutative shifts on a spin chain. The entropy that we consider is based on coarse-grained models of the system. In contrast to the classical situation, successive observations of a quantum system can generate entropy by themselves. We pay special attention to the delicate problem of delimiting a natural class of models for computing the entropy.

On quantum dynamical entropy for open systems

2016 ◽  
Vol 14 (04) ◽  
pp. 1640005 ◽  
Author(s):  
Noboru Watanabe
Keyword(s):  
System Dynamics ◽  
Numerical Computation ◽  
Open System ◽  
Open Systems ◽  
Quantum Systems ◽  
Quantum Dynamical ◽  
Dynamical Entropy

We review some notions for quantum dynamical entropies. The dynamical entropy of quantum systems is discussed and a numerical computation of the dynamical entropy is carried for the open system dynamics.

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