Xiao-Ming Lu and Mankei Tsang
Published in Quantum Science and Technology.
Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum Cramer-Rao lower error bounds pioneered by Helstrom. Recent work, however, has called into question the tightness of those bounds for highly nonclassical states in the non-asymptotic regime, and better methods are now needed to assess the attainable quantum limits in reality. Here we propose a new class of quantum bounds called quantum Weiss- Weinstein bounds, which include Cramer-Rao-type inequalities as special cases but can also be significantly tighter to the attainable error. We demonstrate the superiority of our bounds through the derivation of a Heisenberg limit and phase-estimation examples.
Xiao-Ming Lu, Sixia Yu, and C.H. Oh
Published in Nature Communications 6, 7282 (2015)
Fragile quantum features such as entanglement are employed to improve the precision of parameter estimation and as a consequence the quantum gain becomes vulnerable to noise. As an established tool to subdue noise, quantum error correction is unfortunately overprotective because the quantum enhancement can still be achieved even if the states are irrecoverably affected, provided that the quantum Fisher information, which sets the ultimate limit to the precision of metrological schemes, is preserved and attained. Here we develop a theory of robust metrological schemes that preserve the quantum Fisher information instead of the quantum states themselves against noise. After deriving a minimal set of testable conditions on this kind of robustness, we construct a family of 2t+1 qubits metrological schemes being immune to t-qubit errors after the signal sensing. In comparison, at least five qubits are required for correcting arbitrary 1-qubit errors in standard quantum error correction.
Xiao-Ming Lu, Sixia Yu, Kazuo Fujikawa, and C. H. Oh
Published in Phys. Rev. A 90, 042113 (2014)
Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report various error-disturbance tradeoff relations by decomposing the measurement errors and disturbance into two different components, namely, operator bias and fuzziness. Our uncertainty relations reveal the tradeoffs between these two components of errors, and imply various conditionally valid error-tradeoff relations for the unbiased and projective measurements. We also design a quantum circuit to measure the two components of the error and disturbance.