Quantum Inf Process (2017) 16:179
Entanglement-assisted quantum feedback control
· Tomoaki Mikami
Received: 17 August 2016 / Accepted: 27 May 2017 / Published online: 7 June 2017
© The Author(s) 2017. This article is an open access publication
Abstract The main advantage of quantum metrology relies on the effective use of
entanglement, which indeed allows us to achieve strictly better estimation performance
over the standard quantum limit. In this paper, we propose an analogous method uti-
lizing entanglement for the purpose of feedback control. The system considered is a
general linear dynamical quantum system, where the control goal can be systemati-
cally formulated as a linear quadratic Gaussian control problem based on the quantum
Kalman ﬁltering method; in this setting, an entangled input probe ﬁeld is effectively
used to reduce the estimation error and accordingly the control cost function. In par-
ticular, we show that, in the problem of cooling an opto-mechanical oscillator, the
entanglement-assisted feedback control can lower the stationary occupation number
of the oscillator below the limit attainable by the controller with a coherent probe ﬁeld
and furthermore beats the controller with an optimized squeezed probe ﬁeld.
Keywords Quantum metrology · Entanglement · Feedback control · Continuous
measurement · Opto-mechanics · Feedback cooling
Entanglement is a special notion that had been considered as a “spooky” correlation .
However, over recent decades it has gained a positive impression mainly thanks to its
This work was supported in part by JSPS Grant-in-Aid No. 15K06151 and JST PRESTO No.
JPMJPR166A. The authors acknowledge helpful discussions with M. R. Hush, A. R. R. Carvalho, and S.
Department of Applied Physics and Physico-Informatics, Keio University, Hiyoshi 3-14-1,
Kohoku, Yokohama 223-8522, Japan