Paul Knott

Coined quantum walks on percolation graphs

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line), we introduce a simple notion of quantum tunnelling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero as the percolation probability decreases towards the critical point. This provides an example of fractional scaling in quantum-walk dynamics.

Evidence for the conjecture that sampling generalized cat states with linear optics is hard

Peter P. Rohde, ∗ Keith R. Motes, Paul Knott, 3 William Munro, and Jonathan P. Dowling 5 Centre for Engineered Quantum Systems, Department of Physics & Astronomy, Macquarie University, Sydney NSW 2113, Australia School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan Hearne Institute for Theoretical Physics and Department of Physics & Astronomy, Louisiana State University, Baton Rouge, LA 70803 Computational Science Research Center, Beijing 100084, China (Dated: May 22, 2014)

Local versus global strategies in multiparameter estimation

We consider the problem of estimating multiple phases using a multi-mode interferometer. In this setting we show that while global strategies that estimate all the phases simultaneously can lead to high precision gains, the same enhancements can be obtained with local strategies where each phase is estimated individually. A key resource for the enhancement is shown to be a large particle-number variance in the probe state, and for states where the total particle number is not fixed, this can be obtained for mode-separable states and the phases can be read out with local measurements. This has important practical implications because local strategies are generally preferred to global ones for their robustness to local estimation failure, flexibility in the distribution of resources, and comparatively easier state preparation. We obtain our results by analyzing two different schemes: the first uses a set of interferometers, which can be used as a model for a network of quantum sensors, and the second looks at measuring a number of phases relative to a reference, which is concerned primarily with quantum imaging.

Proposed Robust Entanglement-Based Magnetic Field Sensor Beyond the Standard Quantum Limit.

Recently, there have been significant developments in entanglement-based quantum metrology. However, entanglement is fragile against experimental imperfections, and quantum sensing to beat the standard quantum limit in scaling has not yet been achieved in realistic systems. Here, we show that it is possible to overcome such restrictions so that one can sense a magnetic field with an accuracy beyond the standard quantum limit even under the effect of decoherence, by using a realistic entangled state that can be easily created even with current technology. Our scheme could pave the way for the realizations of practical entanglement-based magnetic field sensors.

Multiparameter estimation in networked quantum sensors

We introduce a general model for a network of quantum sensors, and we use this model to consider the following question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.

Attaining subclassical metrology in lossy systems with entangled coherent states

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.

Practical quantum metrology with large precision gains in the low photon number regime

Quantum metrology exploits quantum correlations to make precise measurements with limited particle numbers. By utilizing inter- and intra- mode correlations in an optical interferometer, we find a state that combines entanglement and squeezing to give a 7-fold 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 3-fold 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.

Effect of multimode entanglement on lossy optical quantum metrology

P.A. Knott, 2, ∗ T.J. Proctor, Kae Nemoto, J.A. Dunningham, and W.J. Munro 3 School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom (Dated: April 15, 2015)

Detecting measurement-induced relative-position localization

The theory of decoherence explains how classicality emerges from an underlying quantum reality. An additional interpretation to this has been proposed in which scattering events induce the localization of relative observables (Rau et al 2003 Science 301 1081). An interesting consequence of this process is that it involves the build-up of certain robust entanglements between the observables being localized. To date the weakness of this interpretation has been the lack of a clear experimental signature that allows it to be tested. Here we provide a simple experimentally accessible scheme that enables just that. We also discuss a Bayesian technique that could, in principle, allow experiments to confirm the localization to any desired degree of accuracy and we present precision requirements that are achievable with current experiments. Finally, we extend the scheme from its initial one dimensional proof of principle to the more real world scenario of three dimensional localization.

A search algorithm for quantum state engineering and metrology

In this paper we present a search algorithm that finds useful optical quantum states which can be created with current technology. We apply the algorithm to the field of quantum metrology with the goal of finding states that can measure a phase shift to a high precision. Our algorithm efficiently produces a number of novel solutions: we find experimentally-ready schemes to produce states that show significant improvements over the state-of-the-art, and can measure with a precision that beats the shot noise limit by over a factor of 4. Furthermore, these states demonstrate a robustness to moderate/high photon losses, and we present a conceptually simple measurement scheme that saturates the Cramer-Rao bound.