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arXiv:1401.3969

Precise Phase Measurements using an Entangled Coherent State

Paul Knott, Jacob Dunningham

Published Jan 16, 2014• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1401.3969

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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 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 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.
We investigate the phase enhancement of quantum states subject to nonlinear phase shifts. The optimal phase estimation of even entangled coherent states (ECSs) is shown to be better than that of NOON states with the same average particle number $\ensuremath{\langle}n\ensuremath{\rangle}$ and nonlinearity exponent kkk. We investigate the creation of an approximate entangled coherent state (AECS) from a photon-subtracted squeezed vacuum with current optical technology methods and show that a pure AECS is even better than an even ECS for large $\ensuremath{\langle}n\ensuremath{\rangle}$. Finally, we examine the simple, but physically relevant, cases of loss in the nonlinear interferometer for a fixed average photon number $\ensuremath{\langle}n\ensuremath{\rangle}$.
Quantum metrology explores quantum features to ameliorate resolution, precision, and sensitivity beyond classical limits when the quantum theory determines the ultimate limit on the accuracy of any measurement. More recently, it is shown that entangled coherent states (ECSs) have the potential to perform robust sub-classical measurements considering only the case of a weak-coupling regime. In this paper, we examine the dynamics of the phase sensitivity for ECSs in the framework of the non-Markovian lossy channels and show how the non-Markovian features and reservoir parameters may be exploited for quantum-enhanced phase estimation. The influences of memory effects and the Ohmic reservoir with Lorentz–Drude regularization are examined under the following conditions: ωc≪ω0, ωc≈ω0, or ωc≫ω0, where ω0 is the field mode frequency of interest and ωc is the cutoff frequency of the Ohmic reservoir. In shape contract with results obtained in the presence of Markovian lossy, we obtain that the memory effects lead to an enhanced phase estimation while the ratio ωc/ω0 provides a way to control and improve the precision during the time evolution. We show that the smallest variance in the phase parameter highly depends on the combination of the ration ωc/ω0 and non-Markovian effects.
Abstract We investigate phase estimation in a lossy interferometer using entangled coherent states, with a particular focus on a scenario where no reference beam is employed. By calculating the quantum Fisher information, we reveal two key results: (1) the metrological equivalence between scenarios with and without a reference beam, established under ideal lossless conditions for the two-phase-shifting configuration, breaks down in the presence of photon loss, and (2) the pronounced inferior performance of ECSs relative to NOON states, observed in the presence of a reference beam, disappears in its absence.
Abstract We propose a quantum-enhanced metrological scheme utilizing unbalanced entangled coherent states (ECSs) generated by passing a coherent state and a coherent state superposition through an unbalanced beam splitter (BS). We identify the optimal phase sensitivity of this scheme by maximizing the quantum Fisher information (QFI) with respect to the BS transmission ratio. Our scheme outperforms the conventional scheme with a balanced BS, particularly in the presence of single-mode photon loss. Notably, our scheme retains quantum advantage in phase sensitivity in the limit of high photon intensity, where the balanced scheme offers no advantage over the classical strategy.