TY - GEN
T1 - Zero, pole and fragility of quantum systems
AU - Yanagisawa, Masahiro
PY - 2007
Y1 - 2007
N2 - New fundamental limits on design and control of linear quantum systems are presented. A main difference between quantum and classical systems comes from the fact that quantum signals are represented by operator-valued vectors. The transfer function representation is useful to describe a system in the quantum setting for the same reason as it is useful classically. It is shown that the noncommutative property of quantum signals can be characterized by a specific relation between zeros and poles of a quantum transfer function. Then, two quantum mechanical tradeoffs follows from the transfer function constraint. One is a well known tradeoff, Heisenberg's uncertainty relation, and the other is a tradeoff between the ability of noise reduction and sensitivity to modeling error. While these tradeoffs hold at each frequency, quantum systems have another constraint between different frequencies based on Bode integral as classical systems usually do. In the quantum case, however, this constraint is also dependent on quantum mechanical parameters.
AB - New fundamental limits on design and control of linear quantum systems are presented. A main difference between quantum and classical systems comes from the fact that quantum signals are represented by operator-valued vectors. The transfer function representation is useful to describe a system in the quantum setting for the same reason as it is useful classically. It is shown that the noncommutative property of quantum signals can be characterized by a specific relation between zeros and poles of a quantum transfer function. Then, two quantum mechanical tradeoffs follows from the transfer function constraint. One is a well known tradeoff, Heisenberg's uncertainty relation, and the other is a tradeoff between the ability of noise reduction and sensitivity to modeling error. While these tradeoffs hold at each frequency, quantum systems have another constraint between different frequencies based on Bode integral as classical systems usually do. In the quantum case, however, this constraint is also dependent on quantum mechanical parameters.
UR - http://www.scopus.com/inward/record.url?scp=62749135484&partnerID=8YFLogxK
U2 - 10.1109/CDC.2007.4434567
DO - 10.1109/CDC.2007.4434567
M3 - Conference contribution
SN - 1424414989
SN - 9781424414987
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1216
EP - 1220
BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 46th IEEE Conference on Decision and Control 2007, CDC
Y2 - 12 December 2007 through 14 December 2007
ER -