TY - JOUR
T1 - Accessible precisions for estimating two conjugate parameters using Gaussian probes
AU - Assad, Syed M.
AU - Li, Jiamin
AU - Liu, Yuhong
AU - Zhao, Ningbo
AU - Zhao, Wen
AU - Lam, Ping Koy
AU - Ou, Z. Y.
AU - Li, Xiaoying
PY - 2020/5
Y1 - 2020/5
N2 - We analyze the precision limits for a simultaneous estimation of a pair of conjugate parameters in a displacement channel using Gaussian probes. Having a set of squeezed states as an initial resource, we compute the Holevo Cramér-Rao bound to investigate the best achievable estimation precisions if only passive linear operations are allowed to be performed on the resource prior to probing the channel. The analysis reveals the optimal measurement scheme and allows us to quantify the best precision for one parameter when the precision of the second conjugate parameter is fixed. To estimate the conjugate parameter pair with equal precision, our analysis shows that the optimal probe is obtained by combining two squeezed states with orthogonal squeezing quadratures on a 50:50 beam splitter. If different importance is attached to each parameter, then the optimal mixing ratio is no longer 50:50. Instead, it follows a simple function of the available squeezing and the relative importance between the two parameters.
AB - We analyze the precision limits for a simultaneous estimation of a pair of conjugate parameters in a displacement channel using Gaussian probes. Having a set of squeezed states as an initial resource, we compute the Holevo Cramér-Rao bound to investigate the best achievable estimation precisions if only passive linear operations are allowed to be performed on the resource prior to probing the channel. The analysis reveals the optimal measurement scheme and allows us to quantify the best precision for one parameter when the precision of the second conjugate parameter is fixed. To estimate the conjugate parameter pair with equal precision, our analysis shows that the optimal probe is obtained by combining two squeezed states with orthogonal squeezing quadratures on a 50:50 beam splitter. If different importance is attached to each parameter, then the optimal mixing ratio is no longer 50:50. Instead, it follows a simple function of the available squeezing and the relative importance between the two parameters.
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U2 - 10.1103/PhysRevResearch.2.023182
DO - 10.1103/PhysRevResearch.2.023182
M3 - RGC 21 - Publication in refereed journal
VL - 2
JO - Physical Review Research
JF - Physical Review Research
SN - 2643-1564
IS - 2
M1 - 023182
ER -