Accessible precisions for estimating two conjugate parameters using Gaussian probes

Abstract

We analyse the precision limits for 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 are 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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• Estimation of Gaussian random displacement using non-Gaussian states
• Verifying the security of a continuous variable quantum communication protocol via quantum metrology
• Classes of Gaussian States for Squeezing Estimation
• Optimal estimation of conjugate shifts in position and momentum by classically correlated probes and measurements
• Multiparameter estimation with two qubit probes in noisy channels