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Universally Valid Error-Disturbance Relations in Continuous Measurements

Nishizawa, Atsushi and Chen, Yanbei (2015) Universally Valid Error-Disturbance Relations in Continuous Measurements. . (Submitted)

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In quantum physics, measurement error and disturbance were first naively thought to be simply constrained by the Heisenberg uncertainty relation. Later, more rigorous analysis showed that the error and disturbance satisfy more subtle inequalities. Several versions of universally valid error-disturbance relations (EDR) have already been obtained and experimentally verified in the regimes where naive applications of the Heisenberg uncertainty relation failed. However, these EDRs were formulated for discrete measurements. In this paper, we consider continuous measurement processes and obtain new EDR inequalities in the Fourier space: in terms of the power spectra of the system and probe variables. By applying our EDRs to a linear optomechanical system, we confirm that a tradeoff relation between error and disturbance leads to the existence of an optimal strength of the disturbance in a joint measurement. Interestingly, even with this optimal case, the inequality of the new EDR is not saturated because of doublely existing standard quantum limits in the inequality.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Nishizawa, Atsushi0000-0003-3562-0990
Chen, Yanbei0000-0002-9730-9463
Additional Information:The authors would like to thanks to Yiqiu Ma and Huan Yang for valuable discussions. A.N. is supported by JSPS Postdoctoral Fellowships for Research Abroad. Y.C. is supported by NSF grant PHY-1404569 and CAREER Grant PHY-0956189.
Funding AgencyGrant Number
Japan Society for the Promotion of Science (JSPS)UNSPECIFIED
Classification Code:PACS numbers: 03.65.Ta, 42.50.-p, 42.50.Lc
Record Number:CaltechAUTHORS:20160718-094444675
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69088
Deposited By: Tony Diaz
Deposited On:27 Jul 2016 16:39
Last Modified:09 Mar 2020 13:18

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