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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.
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We present a method of directly obtaining the parity of a Gaussian state of light without recourse to photon-number counting. The scheme uses only a simple balanced homodyne technique, and intensity correlation. Thus interferometric schemes utilizing coherent or squeezed light, and parity detection may be practically implemented for an arbitrary photon flux. Specifically we investigate a two-mode, squeezed-light, Mach-Zehnder interferometer and show how the parity of the output state may be obtained. We also show that the detection may be described independent of the parity operator, and that this parity-by-proxy measurement has the same signal as traditional parity.
It has been proposed and demonstrated that path-entangled Fock states (PEFSs) are robust against photon loss over NOON states [S. D. Huver emph{et al.}, Phys. Rev. A textbf{78}, 063828 (2008)]. However, the demonstration was based on a measurement scheme which was yet to be implemented in experiments. In this work, we quantitatively illustrate the advantage of PEFSs over NOON states in the presence of photon losses by analytically calculating the quantum Fisher information. To realize such an advantage in practice, we then investigate the achievable sensitivities by employing three types of feasible measurements: parity, photon-number-resolving, and homodyne measurements. We here apply a double-port measurement strategy where the photons at each output port of the interferometer are simultaneously detected with the aforementioned types of measurements.
In this paper, we review the use of parity as a detection observable in quantum metrology as well as introduce some original findings with regards to measurement resolution in Ramsey spectroscopy and quantum non-demolition (QND) measures of atomic parity. Parity was first introduced in the context of Ramsey spectroscopy as an alternative to atomic state detection. It was latter adapted for use in quantum optical interferometry where it has been shown to be the optimal detection observable saturating the quantum Cram{e}r-Rao bound for path symmetric states. We include a brief review of the basics of phase estimation and the connection between parity-based detection and the quantum Fisher information as it applies to quantum optical interferometry. We also discuss the efforts made in experimental methods of measuring photon-number parity and close the paper with a discussion on the use of parity leading to enhanced measurement resolution in multi-atom spectroscopy. We show how this may be of use in the construction of high-precision multi-atom atomic clocks.
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.
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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