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Register a new userIncorporating Heisenbergs Uncertainty Principle into Quantum Multiparameter Estimation
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The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenbergs uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible, they cannot be jointly performed. We find a correspondence relationship between the inaccuracy of a measurement for estimating the unknown parameter with the measurement error in the context of measurement uncertainty relations. Taking this correspondence relationship as a bridge, we incorporate Heisenbergs uncertainty principle into quantum multiparameter estimation by giving a tradeoff relation between the measurement inaccuracies for estimating different parameters. For pure quantum states, this tradeoff relation is tight, so it can reveal the true quantum limits on individual estimation errors in such cases. We apply our approach to derive the tradeoff between attainable errors of estimating the real and imaginary parts of a complex signal encoded in coherent states and obtain the joint measurements attaining the tradeoff relation. We also show that our approach can be readily used to derive the tradeoff between the errors of jointly estimating the phase shift and phase diffusion without explicitly parameterizing quantum measurements.
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Toy models for quantum evolution in the presence of closed timelike curves (CTCs) have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require non-trivial interactions between the future and past which lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the CTC, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenbergs uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave-packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time-dilation suggests that OTCs provide a novel alternative to existing proposals for the behaviour of quantum systems under gravity.
Atom interferometry tests of universality of free fall based on the differential measurement of two different atomic species provide a useful complement to those based on macroscopic masses. However, when striving for the highest possible sensitivities, gravity gradients pose a serious challenge. Indeed, the relative initial position and velocity for the two species need to be controlled with extremely high accuracy, which can be rather demanding in practice and whose verification may require rather long integration times. Furthermore, in highly sensitive configurations gravity gradients lead to a drastic loss of contrast. These difficulties can be mitigated by employing wave packets with narrower position and momentum widths, but this is ultimately limited by Heisenbergs uncertainty principle. We present a novel scheme that simultaneously overcomes the loss of contrast and the initial co-location problem. In doing so, it circumvents the fundamental limitations due to Heisenbergs uncertainty principle and eases the experimental realization by relaxing the requirements on initial co-location by several orders of magnitude.
Simultaneous quantum estimation of multiple parameters has recently become essential in quantum metrology. Although the ultimate sensitivity of a multiparameter quantum estimation in noiseless environments can beat the standard quantum limit that every classical sensor is bounded by, it is unclear whether the quantum sensor has an advantage over the classical one under realistic noise. In this work, we present a framework of the simultaneous estimation of multiple parameters with quantum sensors in a certain noisy environment. Our multiple parameters to be estimated are three components of an external magnetic field, and we consider the noise that causes only dephasing. We show that there is an optimal sensing time in the noisy environment and the sensitivity can beat the standard quantum limit when the noisy environment is non-Markovian.
The statistical significance that characterizes a discrepancy between a measurement and theoretical prediction is usually calculated assuming that the statistical and systematic uncertainties are known. Many types of systematic uncertainties are, however, estimated on the basis of approximate procedures and thus the values of the assigned errors are themselves uncertain. Here the impact of the uncertainty {it on the assigned uncertainty} is investigated in the context of the muon $g-2$ anomaly. The significance of the observed discrepancy between the Standard Model prediction of the muons anomalous magnetic moment and measured values are shown to decrease substantially if the relative uncertainty in the uncertainty assigned to the Standard Model prediction exceeds around 30%. The reduction in sensitivity increases for higher significance, so that establishing a $5sigma$ effect will require not only small uncertainties but the uncertainties themselves must be estimated accurately to correspond to one standard deviation.
It was suggested in Ref. [Phys. Rev. Lett. 114, 170802] that optical networks with relatively inexpensive overhead---single photon Fock states, passive optical elements, and single photon detection---can show significant improvements over classical strategies for single-parameter estimation, when the number of modes in the network is small (n < 7). A similar case was made in Ref. [Phys. Rev. Lett. 111, 070403] for multi-parameter estimation, where measurement is instead made using photon-number resolving detectors. In this paper, we analytically compute the quantum Cramer-Rao bound to show these networks can have a constant-factor quantum advantage in multi-parameter estimation for even large number of modes. Additionally, we provide a simplified measurement scheme using only single-photon (on-off) detectors that is capable of approximately obtaining this sensitivity for a small number of modes.
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