We generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

1 aQian, Kevin1 aEldredge, Zachary1 aGe, Wenchao1 aPagano, Guido1 aMonroe, Christopher1 aPorto, James, V.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1901.0904201538nas a2200157 4500008004100000245007800041210006900119260001500188520103700203100001601240700001701256700002201273700002501295700002301320856003701343 2018 eng d00aDistributed Quantum Metrology and the Entangling Power of Linear Networks0 aDistributed Quantum Metrology and the Entangling Power of Linear c2018/07/253 aWe derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

1 aGe, Wenchao1 aJacobs, Kurt1 aEldredge, Zachary1 aGorshkov, Alexey, V.1 aFoss-Feig, Michael uhttps://arxiv.org/abs/1707.0665501425nas a2200157 4500008004100000245007800041210006900119260001500188520092400203100001601127700001701143700002201160700002501182700002301207856003701230 2018 eng d00aDistributed Quantum Metrology and the Entangling Power of Linear Networks0 aDistributed Quantum Metrology and the Entangling Power of Linear c2018/07/253 aWe derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

1 aGe, Wenchao1 aJacobs, Kurt1 aEldredge, Zachary1 aGorshkov, Alexey, V.1 aFoss-Feig, Michael uhttps://arxiv.org/abs/1707.06655