On transmission efficiency of quantum modulations
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CHAPMAN
INSTITUTE FOR
U N I V E R S I T Y QUANTUM STUDIES
REGULAR PAPER
On transmission efficiency of quantum modulations Kyouhei Ohmura
· Noboru Watanabe
Received: 17 July 2019 / Accepted: 3 December 2019 © Chapman University 2019
Abstract In quantum information theory, it is important to find modulations with low information loss for noisy channels. In this paper, using the quantum dynamical entropy and the quantum dynamical mutual entropy, we investigate the transmission efficiency of two quantum modulators through attenuation channels. Keywords Quantum information theory · Quantum dynamical entropy · Quantum dynamical mutual entropy · Quantum modulated states · Operator algebras
1 Introduction The dynamical entropy, formulated by Kolmogorov to solve mathematical isomorphic problems, is also important in information theory since it gives the average of information amount of information sources [5,9–11]. This entropy has several noncommutative generalizations, and they are used for classifications of operator algebras [2,6–8]. On the other hand, another important measure in information theory is dynamical mutual entropy. The dynamical mutual entropy gives the average of the amount of information transmitted correctly from the input system to the output system. In [14], Ohya and Muraki formulated new noncommutative dynamical entropy and dynamical mutual entropy on C ∗ -algebras using the concept of compound states introduced by Ohya [18]. The dynamical entropies are used not only for mathematical classification of operator algebras but also for model calculations of quantum information theory [3,32]. Incidentally, when considering the transmission of quantum states, it is important to study modulating the initial states into suitable states for the channel. That is, it is important to investigate modulation schemes that efficiently transmit quantum information [21,23,25]. In this paper, using the quantum dynamical entropy and dynamical mutual entropy given by Ohya and Muraki, when the attenuation channel is used as the channel between input system and output system, we investigate which K. Ohmura (B) · N. Watanabe Department of Information Sciences, Tokyo University of Science, Noda City, Chiba 278-8510, Japan e-mail: [email protected]; [email protected] N. Watanabe e-mail: [email protected]
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K. Ohmura, N. Watanabe
modulator, PPM (pulse position modulator) or PWM (pulse width modulator), transmits quantum information more efficiency. The paper is organized as follows: in Sect. 2, we recall the definitions of some quantum channels and the attenuation channel. In Sect. 3, we mention the definitions of basic quantum entropies to define the quantum dynamical mutual entropy, and recall some known facts about the entropies. Section 4 is devoted to describe the definitions of quantum dynamical entropy and quantum dynamical mutual entropy given by Ohya and to state their properties. The main result in this paper is Sect. 5, where we discuss the efficiency of the optical modulations (PPM a
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