## PROGRAMME

Scroll down for abstracts

## Tue 14 June 2016, Keighton Auditorium (Nottingham, UK)

09.00-09.20 Registration

09.20-09.30 Welcome

09.30-10.10 Richard Leach (Engineering, Nottingham)

10.10-10.50 Mankei Tsang (National University of Singapore)

10.50-11.20 Coffee/Tea

11.20-12.00 Cosmo Lupo (University of York)

12.00-12.40 Katarzyna Macieszczak (Physics & Astronomy, Nottingham)

12.40-14.30 Lunch & Posters

14.30-15.10 Rong Su (Engineering, Nottingham)

15.10-15.50 Christos Gagatsos (University of Warwick)

15.50-16.20 Coffee/Tea

16.20-17.00 Tommaso Tufarelli (Mathematical Sciences, Nottingham)

19.00 Dinner (for registered participants) at 4550 Miles from Delhi

Maid Marian Way, Nottingham NG1 6HE

09.20-09.30 Welcome

09.30-10.10 Richard Leach (Engineering, Nottingham)

*Beating the fundamental limits of 3D optical**manufacturing metrology*10.10-10.50 Mankei Tsang (National University of Singapore)

*Quantum metrology kills Rayleigh's criterion*10.50-11.20 Coffee/Tea

11.20-12.00 Cosmo Lupo (University of York)

*Ultimate precision limits for quantum sub-Rayleigh imaging*12.00-12.40 Katarzyna Macieszczak (Physics & Astronomy, Nottingham)

*Dynamical phase transitions as a resource for quantum**enhanced metrology*12.40-14.30 Lunch & Posters

14.30-15.10 Rong Su (Engineering, Nottingham)

*The role of light source in coherence scanning interferometry**and optical coherence tomography*15.10-15.50 Christos Gagatsos (University of Warwick)

*Multimode quantum optical metrology*15.50-16.20 Coffee/Tea

16.20-17.00 Tommaso Tufarelli (Mathematical Sciences, Nottingham)

*Probing the diamagnetic term in light-matter interaction*19.00 Dinner (for registered participants) at 4550 Miles from Delhi

Maid Marian Way, Nottingham NG1 6HE

## Abstracts

## Invited Talks

Richard Leach (University of Nottingham)

Optical instruments are now used extensively in manufacturing industry to determine the 3D geometry of objects. Optical instruments offer a range of benefits over mechanical contacting techniques; not least, much higher measurement speeds. However, despite their benefits, optical instruments have a number of fundamental limitations when being used for 3D measurement, many of which cannot be overcome by simply improvements in engineering and technology. These limitations will be discussed in this talk along with limitations in current technology. Approaches will be presented that can partially overcome some of the limitations by using a new approach called "information-rich metrology".

Mankei Tsang (National University of Singapore)

Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of farfield optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially detrimental to the estimation of the separation between the sources, and modern superresolution techniques rely on suppressing the emission of close sources to enhance the localization precision. Using quantum optics, quantum metrology, and statistical analysis, here we show that, even if two close incoherent sources emit simultaneously, measurements with linear optics and photon counting can estimate their separation almost as precisely as conventional methods do for isolated sources, rendering Rayleigh's criterion irrelevant to the problem. Our results demonstrate that superresolution can be achieved not only for fluorophores but also for stars.

Cosmo Lupo (University of York)

We solve the problem of estimating the angular or linear separation between two point-like sources emitting light in an arbitrary state, by using a diffraction-limited linear-optical imaging device in the paraxial approximation. First we show that this problem is formally equivalent to the estimation of the loss parameters of two lossy bosonic channels, i.e., the transmissivities of two beam splitters. Then we determine the sources whose separation can be estimated optimally. We find that entangled sources can be super-resolved at the sub-Rayleigh scale and that the ultimate precision bound scales with the number of collected photons according to the standard quantum limit.

We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. “Heisenberg scaling”). In fact, the QFI is identical to the variance of the dynamical observable that characterizes the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification makes it possible to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realization of these ideas, we describe a theoretical scheme for quantum enhanced estimation of an optical phase shift using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.

We find that for a fixed average energy, and under some assumptions, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We consider the quantum Cramer-Rao bound that provides a lower bound to the covariance matrix via the quantum Fisher information matrix, whose elements we derive to be the covariances of the photon numbers across the modes. We show this for a multimode interferometer, with a rigorously defined reference mode and a phase shift in each of the other modes, using Gaussian inputs and passive elements.

Coherence scanning interferometry (CSI) and optical coherence tomography (OCT) are powerful three-dimensional (3D) imaging techniques relying on the coherence property of the light sources. These two techniques both provides non-contact, high-speed and high-resolution measurements of 3D objects. The former has mainly been used for measurement of surface topography of industrial samples, while the major applications of the latter are in medical area. In this talk the properties of the light sources in CSI and OCT will be discussed, also the effects on optical transfer functions of the instruments.

Should the Dicke model of light-matter interaction include a diamagnetic term? This question has generated intense debate in the literature, and is particularly relevant in the modern contexts of cavity and circuit quantum electrodynamics. We design an appropriate probing strategy to address the issue experimentally. Applying the tools of quantum estimation theory to a general Dicke model, we quantify how much information about the diamagnetic term (or lack thereof) is contained in the ground state of the coupled system. We demonstrate that feasible measurements, such as homodyne detection or photon counting, give access to a significant fraction of such information. These measurements could be performed by suddenly switching off the light-matter coupling, and collecting the radiation that naturally leaks out of the system. We further show that, should the model admit a critical point, both measurements would become asymptotically optimal in its vicinity. We finally discuss binary discrimination strategies between the two most debated hypotheses involving the diamagnetic term.

*Beating**the fundamental limits of 3D optical manufacturing metrology*Optical instruments are now used extensively in manufacturing industry to determine the 3D geometry of objects. Optical instruments offer a range of benefits over mechanical contacting techniques; not least, much higher measurement speeds. However, despite their benefits, optical instruments have a number of fundamental limitations when being used for 3D measurement, many of which cannot be overcome by simply improvements in engineering and technology. These limitations will be discussed in this talk along with limitations in current technology. Approaches will be presented that can partially overcome some of the limitations by using a new approach called "information-rich metrology".

Mankei Tsang (National University of Singapore)

__Quantum metrology kills Rayleigh's criterion__Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of farfield optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially detrimental to the estimation of the separation between the sources, and modern superresolution techniques rely on suppressing the emission of close sources to enhance the localization precision. Using quantum optics, quantum metrology, and statistical analysis, here we show that, even if two close incoherent sources emit simultaneously, measurements with linear optics and photon counting can estimate their separation almost as precisely as conventional methods do for isolated sources, rendering Rayleigh's criterion irrelevant to the problem. Our results demonstrate that superresolution can be achieved not only for fluorophores but also for stars.

Cosmo Lupo (University of York)

__Ultimate precision limits for quantum sub-Rayleigh imaging__We solve the problem of estimating the angular or linear separation between two point-like sources emitting light in an arbitrary state, by using a diffraction-limited linear-optical imaging device in the paraxial approximation. First we show that this problem is formally equivalent to the estimation of the loss parameters of two lossy bosonic channels, i.e., the transmissivities of two beam splitters. Then we determine the sources whose separation can be estimated optimally. We find that entangled sources can be super-resolved at the sub-Rayleigh scale and that the ultimate precision bound scales with the number of collected photons according to the standard quantum limit.

**Katarzyna Macieszczak**(University of Nottingham)__Dynamical phase transitions as a resource for quantum enhanced metrology__We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. “Heisenberg scaling”). In fact, the QFI is identical to the variance of the dynamical observable that characterizes the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification makes it possible to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realization of these ideas, we describe a theoretical scheme for quantum enhanced estimation of an optical phase shift using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.

**Christos Gagatsos**(University of Warwick__Multimode quantum optical metrology__We find that for a fixed average energy, and under some assumptions, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We consider the quantum Cramer-Rao bound that provides a lower bound to the covariance matrix via the quantum Fisher information matrix, whose elements we derive to be the covariances of the photon numbers across the modes. We show this for a multimode interferometer, with a rigorously defined reference mode and a phase shift in each of the other modes, using Gaussian inputs and passive elements.

**Rong Su**(University of Nottingham)__The role of light source in coherence scanning interferometry and optical coherence tomography__Coherence scanning interferometry (CSI) and optical coherence tomography (OCT) are powerful three-dimensional (3D) imaging techniques relying on the coherence property of the light sources. These two techniques both provides non-contact, high-speed and high-resolution measurements of 3D objects. The former has mainly been used for measurement of surface topography of industrial samples, while the major applications of the latter are in medical area. In this talk the properties of the light sources in CSI and OCT will be discussed, also the effects on optical transfer functions of the instruments.

**Tommaso Tufarelli**(University of Nottingham)__Probing the diamagnetic term in light-matter interaction__Should the Dicke model of light-matter interaction include a diamagnetic term? This question has generated intense debate in the literature, and is particularly relevant in the modern contexts of cavity and circuit quantum electrodynamics. We design an appropriate probing strategy to address the issue experimentally. Applying the tools of quantum estimation theory to a general Dicke model, we quantify how much information about the diamagnetic term (or lack thereof) is contained in the ground state of the coupled system. We demonstrate that feasible measurements, such as homodyne detection or photon counting, give access to a significant fraction of such information. These measurements could be performed by suddenly switching off the light-matter coupling, and collecting the radiation that naturally leaks out of the system. We further show that, should the model admit a critical point, both measurements would become asymptotically optimal in its vicinity. We finally discuss binary discrimination strategies between the two most debated hypotheses involving the diamagnetic term.

## Posters

__Anirudh Acharya (University of Nottingham)__

__The construction of physically relevant low dimensional state models, and the design of appropriate measurements are key issues in tackling quantum state tomography for large dimensional systems. We consider the statistical problem of estimating low rank states in the set-up of multiple ions tomography, and investigate how the estimation error behaves with a reduction in the number of measurement settings, compared with the standard ion tomography setup. We present extensive simulation results showing that the error is robust with respect to the choice of states of a given rank, the random selection of settings, and that the number of settings can be significantly reduced with only a negligible increase in error. We present an argument to explain these findings based on a concentration inequality for the Fisher information matrix. In the more general setup of random basis measurements we use this argument to show that for certain rank r states it suffices to measure in O(rlogd) bases to achieve the average Fisher information over all bases.__

Statistically efficient tomography of low rank states with incomplete measurementsStatistically efficient tomography of low rank states with incomplete measurements

Lewis Clark (University of Leeds)

__Quantum-enhanced metrology with single-mode coherent states__In this paper, we use the temporal quantum correlations in the photon statistics of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the phase space volume occupied by the resonator field, thereby increasing the dependence of its final state on the measured phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly-efficient single photon detectors, it should be of practical interest until technologies for the generation of highly-entangled many-photon states become more readily available.

Matthieu Arnhem (Université Libre de Bruxelles)

__Individual and joint measurement strategies: Focus on figures of merit__We compare different cases of individual and joint quantum measurement strategies where different figures of merit are used (fidelity, score function, quantum Fisher information...) and lead to different conclusions. There exist some case where joint measurement have been considered as better than individual measurement in the sense that they optimize one or other figure of merit. On the other hand, some individual measurements schemes can reach Cramer-Rao bounds and therefore be considered optimal. We focus our attention on understanding why different figures of merit that are used give different conclusions in similar measurement schemes.

Matthew Levitt (University of Nottingham)

__Identification of SISO quantum linear systems__Our goal is to investigate system identification for general single input single output (SISO) quantum linear systems. For a given input we would like to understand the following questions: (1) WHICH parameters can be identified? (2) HOW can we reconstruct the system from sufficient input-output data? We consider two parallel approaches: (a) Time-dependent inputs, or (b) Stationary inputs.

Rosanna Nichols (University of Nottingham)

__Practical quantum metrology in noisy environments__The problem of estimating an unknown phase ϕ using two-level probes in the presence of unital phase-covariant noise and using finite resources is investigated. In particular, we introduce a simple model in which the phase imprinting operation on the probes is realized by a unitary transformation with a randomly sampled generator. We find a general form for the optimal phase sensitivity under this type of noise. In a sequential estimation protocol, this is shown to grow quadratically with the number of applications N of the phase-imprinting operation, then attain a maximum at some Nopt, and eventually decay to zero. We express a close approximation of Nopt in terms of accessible geometric properties of the noise and illustrate its usefulness as a practical guideline for the optimization of the estimation protocol. The use of entangled probes in parallel to improve the phase sensitivity is also considered. We find that multi-probe entanglement generally offers no practical advantage over single-probe coherence if the interrogation of the probes at the output is restricted to separable measurements.

Luis A. Correa (University of Nottingham)

__Low-temperature thermometry enhanced by dissipation__The problem of estimating the temperature T of an equilibrium sample is usually tackled by thermally coupling it to a probe. After equilibration, one may estimate T by monitoring some temperature-dependent feature of the sensor via a suitable measurement and data analysis scheme. One often assumes that the back-action on the sample can be neglected, and that the probe ends up in a Gibbs state at the sample temperature. Such simple picture runs into trouble if the sample is too cold, especially when using a quantum thermometer. On the one hand, the seemingly natural assumption that the probe reaches thermal equilibrium at the sample temperature might break down at low T. Even if this was not the case, the ‘thermal sensitivity’ of an equilibrium probe drops quickly as T decreases. Overcoming these fundamental limitations calls for a paradigm shift. Here, we will explore quantum thermometry beyond weak coupling. Specifically, we will be interested in the estimation of the temperature of an equilibrium sample by coupling it strongly to a single-mode quantum thermometer. We will obtain the steady state of the probe exactly and show that its low-temperature thermal sensitivity can be significantly enhanced by increasing the dissipation strength.