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Register a new userMultiparameter quantum metrology with postselection measurements
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We analyze simultaneous quantum estimations of multiple parameters with postselection measurements in terms of a tradeoff relation. The system, or a sensor, is characterized by a set of parameters, interacts with a measurement apparatus (MA), and then is postselected onto a set of orthonormal final states. Measurements of the MA yield an estimation of the parameters. We first derive classical and quantum Cramer-Rao lower bounds and then discuss their archivable condition and the tradeoffs in the postselection measurements in general, including the case when a sensor is in mixed state. Its whole information can, in principle, be obtained via the MA which is not possible without postselection. We, then, apply the framework to simultaneous measurements of phase and its fluctuation as an example.
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Interacting quantum systems are attracting increasing interest for developing precise metrology. In particular, the realisation that quantum-correlated states and the dynamics of interacting systems can lead to entirely new and unexpected phenomena have initiated an intense research effort to explore interaction-based metrology both theoretically and experimentally. However, the current framework of interaction-based metrology mainly focuses on single-parameter estimations, a demonstration of multiparameter metrology using interactions as a resource was heretofore lacking. Here we demonstrate an interaction-based multiparameter metrology with strongly interacting nuclear spins. We show that the interacting spins become intrinsically sensitive to all components of a multidimensional field when their interactions are significantly larger than their Larmor frequencies. Using liquid-state molecules containing strongly interacting nuclear spins, we demonstrate the proof-of-principle estimation of all three components of an unknown magnetic field and inertial rotation. In contrast to existing approaches, the present interaction-based multiparameter sensing does not require external reference fields and opens a path to develop an entirely new class of multiparameter quantum sensors.
The impact of measurement imperfections on quantum metrology protocols has been largely ignored, even though these are inherent to any sensing platform in which the detection process exhibits noise that neither can be eradicated, nor translated onto the sensing stage and interpreted as decoherence. In this work, we approach this issue in a systematic manner. Focussing firstly on pure states, we demonstrate how the form of the quantum Fisher information must be modified to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving $N$ probes with local measurements undergoing readout noise, the optimal sensitivity dramatically changes its behaviour depending whether global or local control operations are allowed to counterbalance measurement imperfections. In the former case, we prove that the ideal sensitivity (e.g. the Heisenberg scaling) can always be recovered in the asymptotic $N$ limit, while in the latter the readout noise fundamentally constrains the quantum enhancement of sensitivity to a constant factor. We illustrate our findings with an example of an NV-centre measured via the repetitive readout procedure, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.
In multiparameter quantum metrology, the weighted-arithmetic-mean error of estimation is often used as a scalar cost function to be minimized during design optimization. However, other types of mean error can reveal different facets of permissible error combination. By introducing the weighted $f$-mean of estimation error and quantum Fisher information, we derive various quantum Cramer-Rao bounds on mean error in a very general form and also give their refin
We investigate the utility of parity detection to achieve Heisenberg-limited phase estimation for optical interferometry. We consider the parity detection with several input states that have been shown to exhibit sub shot-noise interferometry with their respective detection schemes. We show that with parity detection, all these states achieve the sub-shot noise limited phase estimate. Thus making the parity detection a unified detection strategy for quantum optical metrology. We also consider quantum states that are a combination of a NOON states and a dual-Fock state, which gives a great deal of freedom in the preparation of the input state, and is found to surpass the shot-noise limit.
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We give optimal (up to constant factors) quantum algorithms with postselection for the Majority function, slightly improving upon an earlier algorithm of Aaronson. Finally we show how Newmans classic theorem about low-degree rational approximation of the absolute-value function follows from these algorithms.
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