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Robust quantum metrology

Paul Knott

Published Mar 1, 2015• 2 citations
OpenAlex

Abstract

In optical interferometry path-entangled states such as NOON states have shown to give quantum-enhanced precision measurements, but these states are notoriously fragile to particle losses, which typically collapse the quantum state and destroy the phase information. A class of inherently robust states that show the potential for great improvements over the alternatives are the entangled coherent states (ECSs). We show that these states allow substantial improvements over unentangled `classical' states and highly-entangled NOON states for a wide range of loss values. We then describe a measurement scheme that can be used to measure these states with a precision close to the theoretical bound given by the quantum Fisher information. \nWe then look at the quantum mechanisms that lead to precise measurements. In optical interferometry multi-mode entanglement is often assumed to be the driving force behind quantum enhanced measurements. Recent work has shown this assumption to be false, and here we show that when photon losses occur multi-mode entanglement is actually detrimental to obtaining quantum enhanced measurements. We specifically apply this idea to a superposition of coherent states, demonstrating that these states show a robustness to loss that allows them to significantly outperform their competitors in realistic systems. A practically viable measurement scheme is then presented that allows measurements close to the theoretical bound, even with loss. \nIn this thesis we also consider superpositions of spin coherent states and their application to quantum metrology. Compared to optical states, spin systems have a distinctly different process of decoherence known as non-Markovian dephasing, which has shown to give greatly improved robustness to loss. We see that spin cat states give an enhanced scaling over the shot noise limit, even with dephasing, whilst being realisable with current technology.

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•Nov 1, 2017•0 citations
In optical interferometry path-entangled states such as NOON states have shown to give quantum-enhanced precision measurements, but these states are notoriously fragile to particle losses, which typically collapse the quantum state and destroy the phase information. A class of inherently robust states that show the potential for great improvements over the alternatives are the entangled coherent states (ECSs). We show that these states allow substantial improvements over unentangled `classical' states and highly-entangled NOON states for a wide range of loss values. We then describe a measurement scheme that can be used to measure these states with a precision close to the theoretical bound given by the quantum Fisher information. \nWe then look at the quantum mechanisms that lead to precise measurements. In optical interferometry multi-mode entanglement is often assumed to be the driving force behind quantum enhanced measurements. Recent work has shown this assumption to be false, and here we show that when photon losses occur multi-mode entanglement is actually detrimental to obtaining quantum enhanced measurements. We specifically apply this idea to a superposition of coherent states, demonstrating that these states show a robustness to loss that allows them to significantly outperform their competitors in realistic systems. A practically viable measurement scheme is then presented that allows measurements close to the theoretical bound, even with loss. \nIn this thesis we also consider superpositions of spin coherent states and their application to quantum metrology. Compared to optical states, spin systems have a distinctly different process of decoherence known as non-Markovian dephasing, which has shown to give greatly improved robustness to loss. We see that spin cat states give an enhanced scaling over the shot noise limit, even with dephasing, whilst being realisable with current technology.
Quantum mechanics allows entanglement enhanced measurements to be performed, but loss remains an obstacle in constructing realistic quantum metrology schemes. However, recent work has revealed that entangled coherent states (ECSs) have the potential to perform robust subclassical measurements [J. Joo et al., Phys. Rev. Lett. 107, 083601 (2011)]. Up to now no read-out scheme has been devised that exploits this robust nature of ECSs, but we present here an experimentally accessible method of achieving precision close to the theoretical bound, even with loss. We show substantial improvements over unentangled classical states and highly entangled NOON states for a wide range of loss values, elevating quantum metrology to a realizable technology in the near future.
In optical interferometry multimode entanglement is often assumed to be the driving force behind quantum enhanced measurements. Recent work has shown this assumption to be false: single-mode quantum states perform just as well as their multimode entangled counterparts. We go beyond this to show that when photon losses occur, an inevitability in any realistic system, multimode entanglement is actually detrimental to obtaining quantum enhanced measurements. We specifically apply this idea to a superposition of coherent states, demonstrating that these states show a robustness to loss that allows them to significantly outperform their competitors in realistic systems. A practically viable measurement scheme is then presented that allows measurements close to the theoretical bound, even with loss. These results promote an alternate way of approaching optical quantum metrology using single-mode states that we expect to have great implications for the future.
Quantum entanglement offers the possibility of making measurements beyond the classical limit, however some issues still need to be overcome before it can be applied in realistic lossy systems. Recent work has used the quantum Fisher information (QFI) to show that entangled coherent states (ECSs) may be useful for this purpose as they combine sub-classical phase precision capabilities with robustness (Joo et al., 2011). However, to date no effective scheme for measuring a phase in lossy systems using an ECS has been devised. Here we present a scheme that does just this. We show how one could measure a phase to a precision significantly better than that attainable by both unentangled "classical" states and highly-entangled NOON states over a wide range of different losses. This brings quantum metrology closer to being a realistic and practical technology.
Quantum metrology exploits quantum correlations to make precise measurements with limited particle numbers. By utilizing inter- and intramode correlations in an optical interferometer, we find a state that combines entanglement and squeezing to give a sevenfold enhancement in the quantum Fisher information (QFI)---a metric related to the precision---over the shot-noise limit, for low photon numbers. Motivated by practicality we then look at the squeezed cat state, which has recently been made experimentally, and shows further precision gains over the shot-noise limit and a threefold improvement in the QFI over the optimal Gaussian state. We present a conceptually simple measurement scheme that saturates the QFI, and we demonstrate a robustness to loss for small photon numbers. The squeezed cat state can therefore give a significant precision enhancement in optical quantum metrology in practical and realistic conditions.
Quantum metrology aims to yield higher measurement precisions via quantum techniques such as entanglement. It is of great importance for both fundamental sciences and practical technologies, from testing equivalence principle to designing high-precision atomic clocks. However, due to environment effects, highly entangled states become fragile and the achieved precisions may even be worse than the standard quantum limit (SQL). Here we present a high-precision measurement scheme via spin cat states (a kind of non-Gaussian entangled states in superposition of two quasi-orthogonal spin coherent states) under dissipation. In comparison to maximally entangled states, spin cat states with modest entanglement are more robust against losses and their achievable precisions may still beat the SQL. Even if the detector is imperfect, the achieved precisions of the parity measurement are higher than the ones of the population measurement. Our scheme provides a realizable way to achieve high-precision measurements via dissipative quantum systems of Bose atoms.
Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.