arXiv subjects

Pieter Kok

Publications and source records attributed to Pieter Kok.

At least 37 records · Page 2Linked to original sources

arXiv2021

A quantitative comparison of amplitude versus intensity interferometry for astronomy

Astronomical imaging can be broadly classified into two types. The first type is amplitude interferometry, which includes conventional optical telescopes and Very Large Baseline Interferometry (VLBI). The second type is intensity interferometry, which relies on Hanbury Brown and Twiss-type measurements. At optical frequencies, where direct phase measurements are impossible, amplitude interferometry has an effective numerical aperture that is limited by the distance from which photons can coherently interfere. Intensity interferometry, on the other hand, correlates only photon fluxes and can thus support much larger numerical apertures, but suffers from a reduced signal due to the low average photon number per mode in thermal light. It has hitherto not been clear which method is superior under realistic conditions. Here, we give a comparative analysis of the performance of amplitude and intensity interferometry, and we relate this to the fundamental resolution limit that can be achieved in any physical measurement. Using the benchmark problem of determining the separation between two distant thermal point sources, e.g., two adjacent stars, we give a short tutorial on optimal estimation theory and apply it to stellar interferometry. We find that for very small angular separations the large baseline achievable in intensity interferometry can more than compensate for the reduced signal strength. We also explore options for practical implementations of Very Large Baseline Intensity Interferometry (VLBII).

astro-ph.IM↗

arXiv2021

Fault tolerant quantum data locking

Quantum data locking is a quantum communication primitive that allows the use of a short secret key to encrypt a much longer message. It guarantees information-theoretical security against an adversary with limited quantum memory. Here we present a quantum data locking protocol that employs pseudo-random circuits consisting of Clifford gates only, which are much easier to implement fault tolerantly than universal gates. We show that information can be encrypted into $n$-qubit code words using order $n - H_\mathrm{min}(\mathsf{X})$ secret bits, where $H_\mathrm{min}(\mathsf{X})$ is the min-entropy of the plain text, and a min-entropy smaller than $n$ accounts for information leakage to the adversary. As an application, we discuss an efficient method for encrypting the output of a quantum computer.

quant-ph↗

arXiv2021

Photonic quantum data locking

Quantum data locking is a quantum phenomenon that allows us to encrypt a long message with a small secret key with information-theoretic security. This is in sharp contrast with classical information theory where, according to Shannon, the secret key needs to be at least as long as the message. Here we explore photonic architectures for quantum data locking, where information is encoded in multi-photon states and processed using multi-mode linear optics and photo-detection, with the goal of extending an initial secret key into a longer one. % The secret key consumption depends on the number of modes and photons employed. In the no-collision limit, where the likelihood of photon bunching is suppressed, the key consumption is shown to be logarithmic in the dimensions of the system. Our protocol can be viewed as an application of the physics of Boson Sampling to quantum cryptography. Experimental realisations are challenging but feasible with state-of-the-art technology, as techniques recently used to demonstrate Boson Sampling can be adapted to our scheme (e.g., Phys. Rev. Lett. 123, 250503, 2019).

quant-ph↗

arXiv2021

The quantum limit to incoherent imaging is achieved by linear interferometry

We solve the general problem of determining, through imaging, the three-dimensional positions of $N$ weak incoherent point-like emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a linear interferometer feeds into an array of photo-detectors is always optimal for this estimation problem, in the sense that it saturates the quantum Cramér-Rao bound. We provide a method for the explicit construction of the optimal interferometer. Further explicit results for the quantum Fisher information and the optimal interferometer design that attains it are obtained for the case of one and two incoherent emitters in the paraxial regime. This work provides insights into the phenomenon of super-resolution through incoherent imaging that has attracted much attention recently. Our results will find a wide range of applications over a broad spectrum of frequencies, from fluorescence microscopy to stellar interferometry.

quant-ph↗

arXiv2021

Tight bounds on the simultaneous estimation of incompatible parameters

The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables has greatly diminished the applicability of estimation theory in many practical implementations. The Holevo Cramer-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multi-parameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimisation over multiple variables. In this work, we develop an analytic approach to solving the HCRB for two parameters. Our analysis reveals the role of the HCRB and its interplay with alternative bounds in estimation theory. For more parameters, we generate a lower bound to the HCRB. Our work greatly reduces the complexity of determining the HCRB to solving a set of linear equations that even numerically permits a quadratic speedup over previous state-of-the-art approaches. We apply our results to compare the performance of different probe states in magnetic field sensing, and characterise the performance of state tomography on the codespace of noisy bosonic error-correcting codes. The sensitivity of state tomography on noisy binomial codestates can be improved by tuning two coding parameters that relate to the number of correctable phase and amplitude damping errors. Our work provides fundamental insights and makes significant progress towards the estimation of multiple incompatible observables.

quant-ph↗

arXiv2021

Quantum Conference Key Agreement with Photon Loss

Conference key agreement (CKA) is an information processing task where more than two parties want to share a common secret key. Here, we present a loss-resilient protocol for CKA, based on redundant encoding and error correction. Our protocol provides a speed-up in transmission rate over the existing lossy CKA protocol. However, encoding and error correction come with extra cost. We show that, using photon sources with creation probability p > 0.3, our protocol's secret key rate can overcome the existing protocol's. Hence, high probability entangled photon sources are required for realistic implementation of our loss-resilient protocol.

quant-ph↗

arXiv2020

Quantum-limited estimation of range and velocity

The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity (through Doppler frequency shifts) of a target are inversely related to each other, and dictated by the bandwidth of the signal. Here we use the theoretical toolbox of multi-parameter quantum metrology to determine the ultimate precision of the simultaneous estimation of range and velocity. We consider the case of a single target as well as a pair of closely separated targets. In the latter case, we focus on the relative position and velocity. We show that the trade-off between the estimation precision of position and velocity is relaxed for entangled probe states, and is completely lifted in the limit of infinite entanglement. In the regime where the two targets are close to each other, the relative position and velocity can be estimated nearly optimally and jointly, even without entanglement, using the measurements determined by the symmetric logarithmic derivatives.

quant-ph↗

arXiv2020

Ancilla-assisted schemes are beneficial for Gaussian state phase estimation

We study interferometry with Gaussian states and show that an ancilla-assisted scheme outperforms coherent state interferometry for all levels of loss. We also compare the ancilla-assisted scheme to other interferometric schemes involving squeezing, and show that it is the most advantage in the high-loss, high photon-number regime. In fact, in the presence of high loss, it out-performs many other strategies proposed to date. We find the optimal measurement observable for each scheme discussed. We also find that with the appropriate measurement, the achievable precision of the proposal by Caves [Phys. Rev. D 23, 1693 (1981)] can be improved upon, and is less vulnerable to losses than previously thought.

quant-ph↗

arXiv2019

A Geometric Perspective on Quantum Parameter Estimation

Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this review, we collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. We give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. We address the question how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.

quant-ph↗

arXiv2019

Generating maximal entanglement between spectrally distinct solid-state emitters

We show how to create maximal entanglement between spectrally distinct solid-state emitters embedded in a waveguide interferometer. By revealing the rich underlying structure of multi-photon scattering in emitters, we show that a two-photon input state can generate deterministic maximal entanglement even for emitters with significantly different transition energies and line-widths. The optimal frequency of the input is determined by two competing processes: which-path erasure and interaction strength. We find that smaller spectral overlap can be overcome with higher photon numbers, and quasi-monochromatic photons are optimal for entanglement generation. Our work provides a new methodology for solid-state entanglement generation, where the requirement for perfectly matched emitters can be relaxed in favour of optical state optimisation.

quant-ph↗

arXiv2018

Statistical analysis of quantum entangled network generation

We develop techniques to analyse the statistics of completion times of non-deterministic elements in quantum entanglement generation, and how they affect the overall performance as measured by the secret key rate. By considering such processes as Markov chains, we show how to obtain exact expressions for the probability distributions over the number of errors that a network acquires, as well as the distribution of entanglement establishment times. We show how results from complex analysis can be used to analyse Markov matrices to extract information with a lower computational complexity than previous methods. We apply these techniques to the Innsbruck quantum repeater protocol, and find that consideration of the effect of statistical fluctuations tightens bounds on the secret key rate by 3 orders of magnitude. We also use the theory of order statistics to derive tighter bounds on the minimum quantum memory lifetimes that are required in order to communicate securely.

quant-ph↗

arXiv2018

Analysis of quantum information processors using quantum metrology

Physical implementations of quantum information processing devices are generally not unique, and we are faced with the problem of choosing the best implementation. Here, we consider the sensitivity of quantum devices to variations in their different components. To measure this, we adopt a quantum metrological approach, and find that the sensitivity of a device to variations in a component has a particularly simple general form. We use the concept of cost functions to establish a general practical criterion to decide between two different physical implementations of the same quantum device consisting of a variety of components. We give two practical examples of sensitivities of quantum devices to variations in beam splitter transmitivities: the KLM and Reverse nonlinear sign gates for linear optical quantum computing with photonic qubits, and the enhanced optical Bell detectors by Grice and Ewert & van Loock. We briefly compare the sensitivity to the diamond distance and find that the latter is less suited for studying the behaviour of components embedded within the larger quantum device.

quant-ph↗

arXiv2018

Analytic Few Photon Scattering in Waveguide QED

We develop an approach to light-matter coupling in waveguide QED based upon scattering amplitudes evaluated via Dyson series. For optical states containing more than single photons, terms in this series become increasingly complex and we provide a diagrammatic recipe for their evaluation, which is capable of yielding analytic results. Our method fully specifies a combined emitter-optical state that permits investigation of light-matter entanglement generation protocols. We use our expressions to study two-photon scattering from a $Λ$-system and find that the pole structure of the transition amplitude is dramatically altered as the two ground states are tuned from degeneracy.

quant-ph↗

arXiv2018

Quantum Fisher information for general spatial deformations of quantum emitters

We present a framework for the detection and estimation of deformations applied to a grid of sources. Our formalism uses the Hamiltonian formulation of the quantum Fisher information matrix (\textsc{qfim}) as the figure of merit to quantify the amount of information we have on the deformation matrix. Quantum metrology for grid deformations provides an ideal testbed to examine multi-parameter estimations for arbitrarily parameterised channel evolutions with generally non-commuting Hermitian generators. We generalise the local generator of translations for deformation parameters to multi-parameter estimations and use it to explore how well different deformations can be detected and corrected for. This approach holds for any deformation. We explore the application of our theory to the set of affine geometry maps. Both the configuration of the grid and the properties of the sources help to maximise the sensitivity of the \textsc{qfim} to changes in the deformation parameters. For the non-multiplicative Hamiltonian parameterisations resulting from grid rotations about any chosen axis, oscillatory dependence of the \textsc{qfi} surfaces for a specific interplay between mutual source separation distances and grid configurations.

quant-ph↗

arXiv2018

Burning the Trojan Horse: Defending against Side-Channel Attacks in QKD

The discrete-variable QKD protocols based on BB84 are known to be secure against an eavesdropper, Eve, intercepting the flying qubits and performing any quantum operation on them. However, these protocols may still be vulnerable to side-channel attacks. We investigate the Trojan-Horse side-channel attack where Eve sends her own state into Alice's apparatus and measures the reflected state to estimate the key. We prove that the separable coherent state is optimal for Eve amongst the class of multi-mode Gaussian attack states. We describe how Alice may defend against this by adding thermal noise to the system and give an analytic expression of the resulting secret key rate. We also provide a bound on the secret key rate in the case where Eve may use any separable state, and describe an active defense system based on optical modulators.

quant-ph↗

arXiv2017

Optimal Quantum Metrology of Distant Black Bodies

Measurements of an object's temperature are important in many disciplines, from astronomy to engineering, as are estimates of an object's spatial configuration. We present the quantum optimal estimator for the temperature of a distant body based on the black body radiation received in the far-field. We also show how to perform separable quantum optimal estimates of the spatial configuration of a distant object, i.e. imaging. In doing so we necessarily deal with multi-parameter quantum estimation of incompatible observables, a problem that is poorly understood. We compare our optimal observables to the two mode analogue of lensed imaging and find that the latter is far from optimal, even when compared to measurements which are separable. To prove the optimality of the estimators we show that they minimise the cost function weighted by the quantum Fisher information---this is equivalent to maximising the average fidelity between the actual state and the estimated one.

quant-ph↗

arXiv2017

Practical repeaters for ultra-long distance quantum communication

Quantum communication is at the forefront of quantum technology, enabling the development of absolutely secure encryption, distributed quantum computing, teleportation and more. Whilst quantum communication has been experimentally demonstrated at distances on the order of hundreds of kilometers, the establishment of high-fidelity pairs shared over larger distances remains a formidable technical challenge due to attenuation. However, this may be overcome with the use of quantum repeaters. Here we propose a method to construct a robust quantum repeater network using only existing technology. Our protocol is able to perform all parts of the procedure in a way that is highly tolerant to photon loss and imperfections in detectors, and it achieves secure bit rates on the order of kilohertz over intercontinental distances.

quant-ph↗

arXiv2017

Quantum metrology of spatial deformation using arrays of classical and quantum light emitters

We introduce spatial deformations to an array of light sources and study how the estimation precision of the interspacing distance, d, changes with the sources of light used. The quantum Fisher information (QFI) is used as the figure of merit in this work to quantify the amount of information we have on the estimation parameter. We derive the generator of translations, G, in d due to an arbitrary homogeneous deformation applied to the array. We show how the variance of the generator can be used to easily consider how different deformations and light sources can effect the estimation precision. The single parameter estimation problem is applied to the array and we report on the optimal state that maximises the QFI for d. Contrary to what may have been expected, the higher average mode occupancies of the classical states performs better in estimating d when compared with single photon emitters (SPEs). The optimal entangled state is constructed from the eigenvectors of the generator and found to outperform all these states. We also find the existence of multiple optimal estimators for the measurement of d. Our results find applications in evaluating stresses and strains, fracture prevention in materials expressing great sensitivities to deformations, and selecting frequency distinguished quantum sources from an array of reference sources.

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