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INRIM National Metrological Research Institute,

Turin, Piedmont, Italy

In the last years the specific properties of quantum states (as entanglement), for long time considered as peculiarities discussed by the restricted community of physicists interested in the foundations of quantum mechanics, became a fundamental resource for the development of new technologies (as quantum communication, computation and imaging), collectively dubbed “quantum technologies”.

In this talk, after a generic introduction, I will introduce in details the new possibilities in imaging and sensing offered by quantum measurements. In particular I will discuss two fields that we have contributed to explore at INRIM: quantum imaging & sensing based on photon correlated states (as ghost and sub shot noise imaging, quantum illumination,…) and new paradigms of quantum measurement as weak and protective measurements.

Complutense University of Madrid,

Spain

In this lecture, I will introduce the Majorana representation, which maps a pure state of a spin S into a constellation of 2S points on the Bloch sphere. For quasiclassical coherent states, this constellation reduces to a single point. The converse case of states that are uniformly distributed over the sphere gives rise to different notions of extremal quantum states. I will explore the properties of these states and show that they are optimal for some metrological tasks.

Leibniz Institute of Photonic Technology,

Jena Germany

Experiments in the past decades have convincingly demonstrated that artificially fabricated macroscopic solid state superconducting systems can be in a superposition of macroscopically distinct quantum states. On one hand, this has important implications for the quantum measurement theory. Indeed, the «textbook» concept of projective measurement, which is frequently described by making use in terms of the «microscopic object» and the «macroscopic measuring device», should be definitely modified. On the other hand, this is providing an implementation of new generation of quantum limited detectors and quantum information processing devices.

Basically, these realizations resulted from the quantum mechanical description of the Josephson junction, the key element of superconducting qubits. Due to the fact, that the phase across a junction and its charge are canonical conjugates, there are two alternative realizations of superconducting qubits termed as the charge and phase qubits. In practical applications, quantum state initialization and manipulations are heavily restricted by the quantum coherence of the qubit itself and of the qubit‐based systems.

In the lecture both – basic ideas and practical realization of superconducting qubits will be discussed. In particular, this lecture covers a description of basic types of superconducting qubits and gives a general description of their use that includes dissipation and decoherence, coupling schemes, experimental realization, and basic measurement techniques. Finally, their use as building blocks for the realization of quantum computation is discussed.

Department of Optics, Palacky University Olomouc,

Olomouc, Czech Republic

There are many problems where optics and quantum theory overlap, one of them being the fundamental limit upon the resolution. The spatial resolution of any imaging device is restricted by diffraction, which causes a sharp point on the object to blur into a finite-sized spot in the image. This intrinsic blurring is encoded in the point-spread function, which hinders to distinguish two neighbourhood points- an effect known as «Rayleigh curse». The same problem can be reconsidered from the perspective of quantum estimation theory, as done by Tsang and coworkers, see [1]. Here the constraints on resolution are more fundamental and correspond to the so called Fisher information and Cram’er-Rao lower bound (CRLB) for parameter estimation.

When only light intensity at the image plane is measured on the basis of all the traditional techniques such as CCD detection, the Fisher information falls to zero as the separation between two sources decreases in accordance with Rayleigh curse. On the other hand, when the Fisher

information is calculated for optimal measurement saturating the quantum Cramer-Rao Lower bound (qCRLB), it remains constant implying that the Rayleigh limit is subsidiary to the problem and super-resolution is in principle achievable see [1, 2]. The optimal measurements, on the contrary to the direct imaging, depends crucially on the number of parameters, which have to be estimated.

Multi-parameter quantum Cramer-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using a linear imaging system were addressed in [3]. For equally bright sources, CRLB is independent of their separation as before. However, for the general case of unequally bright sources, the amount of information one can gain about the separation falls to zero, but we show that there is always a quadratic improvement in an optimal detection in comparison with the intensity measurements. This advantage can be of utmost importance in realistic scenarios, such as observational astronomy. Attainability of the qCRLB and feasibility of the multi-parameter estimation scheme was addressed in [4] . Estimation of 3 parameters requires at least 4 detected channels constructed from the projection into the superposition of the modes spanned by derivatives of the PSF.

Quantum-inspired imaging techniques can be nontrivially extended in several ways, for example to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses demonstrating the resolution up to ten-fold improvement in precision over the intensity detection [5], for axial resolution reaching the limit of quantum Fisher information even for intensity detection [6] or clarifying the role of coherence in estimation problems [7].

**References**

[1] M.Tsang, R.~Nair, and X.-M. Lu, Phys. Rev. X 6, 031033 (2016).

[2] J. Rehacek, M. Paur, B. Stoklasa, Z. Hradil, L.L. Sanchez-Soto, Optimal measurements for resolution beyond the Rayleigh limit, Opt. Letters 42, 231-234 (2017): doi: 10.1364/OL.42.000231.

[3] J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Saanchez-Soto, Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution, Phys. Rev. A 96, 062107 (2017); doi.org/10.1103/PhysRevA.96.062107.

[4] J. Rehacek, Z. Hradil, D. Koutny, J. Grover, A. Krzic, L. L. Sanchez-Soto, Optimal measurements for quantum spatial superresolution Phys. Rev. A 98, 012103 (2018) , DOI: 10.1103/Phys Rev A.98.012103; arXiv:1712.08524

[5] J. M. Donohue, V.Ansari, J.Rehacek, Z.Hradil, B.Stoklasa, M. Paur, L. L. Sanchez-Soto, Ch. Silberhorn, Quantum-limited time-frequency estimation through mode-selective photon measurement, Phys. Rev. Lett. 121, 090501 (2018); arXiv:1805.02491;

[6] Rehacek, J , Paur, M, Stoklasa, B, Koutny, D, Hradil, Z , Sanchez-Soto, LL , Intensity-Based Axial Localization at the Quantum Limit, PRL 123 193601,(2019) DOI: 10.1103/PhysRevLett.123.193601

[7] Hradil, Z , Rehacek, J, Sanchez-Soto, L , Englert, BG, Quantum Fisher information with coherence, Optica 6, 1437-1440 (2019), DOI: 10.1364/OPTICA.6.001437 .

Prokhorov General Physics Institute of the Russian Academy of Sciences,

Moscow, Russia

Subjects to be discussed are: Schmidt theorem, its consequences and applications to biphoton states with either discrete or continuous variables; definitions of the Schmidt parameter K for evaluation of the degree of entanglement; separation of Schmidt modes of arbitrary biphoton polarization states (qutrits); Double-Gaussian modeling of wave functions with continuous variables; comparison with the parameter R defined as the ratio of widths of single-particle and conditional (coincidence) distributions; “migration” or “no migration” of transverse entanglement between near and far zones of biphotons produced in the collinear, frequency-degenerate SPDC.

Deep Quantum Labs, Skolkovo Institute

of Science and Technology

Moscow, Russia

We will lecture on modern quantum algorithms, starting with the basics and going through current challenges and recent results related to QAOA, VQE and quantum circuits as machine learning models. Lecture notes and problem sets will be provided.

Laboratoire Kastler Brossel, Sorbonne Université

Ecole Normale Supérieure, CNRS

Paris, France

Photons confined in optical cavities or propagating in paraxial geometries acquire an effective mass and behave like matter particles. Moreover an effective photon-photon interaction can be engineered when the photons propagate in a nonlinear medium, resulting in a collective fluid-like behavior of light.

A few years ago, the superfluid behavior of light was observed in such systems, the so called quantum fluids of light [1].This lecture will show how these properties have been studied and how they can be used to simulate various systems, ranging from condensed matter to astrophysics.

[1] I. Carusotto and C. Ciuti, Quantum Fluids of Light, Rev. Mod. Phys. 85, 299 (2013).

Lebedev Physical Institute

of the Russian Academy of Sciences

Moscow, Russia

Perfect isolation from the environment, long coherent times and strong Coulomb coupling make trapped ions one of the best platforms for quantum logic and quantum computation. Prompt development of ion trapping and cooling technologies, precise addressing of quantum states and single particle manipulation pave a way to complex architectures already demonstrating unprecedented fidelity of quantum operations for tens of ionic qubits. In this Lecture, I will try to give some basics of ion trapping and cooling together with presenting the most recent results in the field.

Research Director

National Institute of Optics — CNR

Florence, Italy

A full control of the state and mode of nonclassical light is among the major challenges in the path of future quantum technologies.

In recent years, quantum state engineering has quickly evolved, with new tools and techniques, such as photon addition and subtraction, which have demonstrated their extreme versatility for performing operations normally unavailable in the realm of Gaussian quantum optics. While photon subtraction can enhance nonclassicality and entanglement in a quantum light state, photon addition has the unique capability of creating nonclassicality and entanglement from scratch, whatever the input.

However, engineering quantum light states in a single, well-defined, mode is rarely enough. In real experiments, states are often prepared in modes that do not coincide with those used for their processing and detection, or for the optimal coupling to matter systems. Gaining access to the rich mode structure of quantum light would also greatly increase the capacity of communicating, manipulating, and storing quantum information. For all these tasks it is of fundamental importance to gain a full control over the modes that host the quantum states.

In this lecture, I will briefly present some recent experimental results towards the controlled generation, manipulation, and characterization of the quantum state and of the mode structure of ultrashort light wavepackets.

RQC

I report methodology for security evaluation of a QKD system that we have recently applied to several commercial devices. Results from one of them, a sub-carrier wave QKD system developed by ITMO University, will be shown [1]. Our audit and the follow-up work by the manufacturer have led to a marked improvement in implementation quality. We hope this methodology contributes to future standards for quantum cryptography.

[1] S. Sajeed, P. Chaiwongkhot, A. Huang, H. Qin, V. Egorov, A. Kozubov, A. Gaidash, V. Chistiakov, A. Vasiliev, A. Gleim, and V. Makarov, arXiv:1909.07898.

Laboratoire Charles Fabry, IOGS, CNRS

France

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