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arXiv:2309.09841 · Physical Review Research

Photonic quantum metrology with variational quantum optical nonlinearities

A. Muñoz de las Heras, Cristian Tabares, J. T. Schneider, Luca Tagliacozzo, Diego Porras, Alejandro González-Tudela

Published Mar 19, 2024• 9 citations
arXivHTMLPDF

Abstract

Photonic quantum metrology harnesses quantum states of light, such as NOON or twin-Fock states, to measure unknown parameters beyond classical precision limits. Current protocols suffer from two severe limitations that preclude their scalability: the exponential decrease in fidelities (or probabilities) when generating states with large photon numbers due to gate errors and the increased sensitivity of such states to noise. Here, we develop a deterministic protocol combining quantum optical nonlinearities and variational quantum algorithms that provides a substantial improvement on both fronts. First, we show how the variational protocol can generate metrologically relevant states with a small number of operations which do not significantly depend on photon number, resulting in exponential improvements in fidelities when gate errors are considered. Second, we show that such states offer a better robustness to noise compared to other states in the literature. Since our protocol harnesses interactions already appearing in state-of-the-art setups, such as cavity QED, we expect that it will lead to more scalable photonic quantum metrology in the near future. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.013299

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Quantum entanglement is a fascinating physical resource that is central to the field of quantum information processing with important applications in such areas as quantum computing, quantum communication, quantum metrology, and quantum imaging. \nIt describes the physical phenomenon in which the quantum state of a multipartite system cannot be written as consisting of constituents that are independent of each other. In this case, the state of the system is called an entangled state. In this \ndissertation, the entanglement of photons--the elementary excitations of the quantized electromagnetic field--is studied. A focus is made on a particular type of entangled states of light called the d-mode N-photon NOON state, which consists of N photons with the N photons as an ensemble appearing at d orthogonal modes simultaneously and are inseparable. \nIn quantum metrology, a field that investigates the ultimate precision of measurements of unknown physical parameters, the two-mode NOON state has been studied extensively with respect to its ability to achieve super-resolution and super-sensitivity in the estimation of a single parameter. A lot of theoretical research has been conducted on the generation of two-mode NOON states, and two-mode NOON states with up to 4 photons have been experimentally and efficiently produced. On the other hand, recently there has been increasing interest in the study of the simultaneous estimation of multiple parameters. Accordingly, the multi-mode NOON state has been attracting more and more attention in view of its potential for enhanced efficiency as compared to using multiple two-mode NOON states separately to estimate the parameters. Nevertheless, no known generation method of multi-mode NOON states with more than 2 photons or 2 modes exists so far. \nIn this dissertation, several scalable generation methods of multi-mode NOON states are proposed. These methods take advantage of multi-photon quantum interference and they can theoretically be applied to produce NOON states with an \narbitrary number of modes and an arbitrary number of photons. The intrinsic generation probability for each method is calculated, and the methods are compared in regards to their feasibility and efficiency. The advantages of using multi-mode NOON \nstates in quantum metrology are also analyzed and discussed in detail.

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Photonic quantum metrology harnesses quantum states of light, such as NOON or twin-Fock states, to measure unknown parameters beyond classical precision limits. Current protocols suffer from two severe limitations that preclude their scalability: the exponential decrease in fidelities (or probabilities) when generating states with large photon numbers due to gate errors and the increased sensitivity of such states to noise. Here, we develop a deterministic protocol combining quantum optical nonlinearities and variational quantum algorithms that provides a substantial improvement on both fronts. First, we show how the variational protocol can generate metrologically relevant states with a small number of operations which do not significantly depend on photon number, resulting in exponential improvements in fidelities when gate errors are considered. Second, we show that such states offer a better robustness to noise compared to other states in the literature. Since our protocol harnesses interactions already appearing in state-of-the-art setups, such as cavity QED, we expect that it will lead to more scalable photonic quantum metrology in the near future. Published by the American Physical Society 2024
Photonic quantum metrology enables the measurement of physical parameters with precision surpassing classical limits by using quantum states of light. However, generating states providing a large metrological advantage is hard because standard probabilistic methods suffer from low generation rates. Deterministic protocols using non-linear interactions offer a path to overcome this problem, but they are currently limited by the errors introduced during the interaction time. Thus, finding strategies to minimize the interaction time of these non-linearities is still a relevant question. In this work, we introduce and compare different deterministic strategies based on continuous and programmable Jaynes-Cummings and Kerr-type interactions, aiming to maximize the metrological advantage while minimizing the interaction time. We find that programmable interactions provide a larger metrological advantage than continuous operations at the expense of slightly larger interaction times. We show that while for Jaynes-Cummings non-linearities the interaction time grows with the photon number, for Kerr-type ones it decreases, favoring the scalability to big photon numbers. Finally, we also optimize different measurement strategies for the deterministically generated states based on photon-counting and homodyne detection.
Photonic states with large and fixed photon numbers, such as Fock states, enable quantum-enhanced metrology but remain an experimentally elusive resource. A potentially simple, deterministic, and scalable way to generate these states consists of fully exciting NNN quantum emitters equally coupled to a common photonic reservoir, which leads to a collective decay known as Dicke superradiance. The emitted NNN-photon state turns out to be a highly entangled multimode state, and to characterize its metrological properties in this work we (i) develop theoretical tools to compute the quantum Fisher information of general multimode photonic states, (ii) use it to show that Dicke superradiant photons in one-dimensional waveguides achieve Heisenberg scaling, which can be saturated by a parity measurement, and (iii) study the robustness of these states to experimental limitations in state-of-the-art atom-waveguide QED setups.
Quantum metrology exploits quantum correlations to perform measurements with precision higher than can be achieved with classical approaches [1]. Photonic approaches promise transformative advances in the family of interferometric phase measurement techniques, a vital toolset used to precisely determine quantities including distance, velocity, acceleration and materials properties. Without quantum enhancement, the precision limit in optical phase sensing (i.e. the minimum uncertainty) is the shot noise limit (SNL): 1/sqrt(N) where N is the number of resources (e.g. photons) used. Entangled photons promise sensitivity surpassing the shot noise limit achievable with classical probes. The maximally phase-sensitive state is the NOON state [2], a path-entangled state of definite photon number N. Despite theoretical proposals stretching back decades [3], no measurement using such photonic (i.e. definite photon number) states has unconditionally surpassed the shot noise limit: by contrast, all such demonstrations employed postselection to discount photon loss in the source, interferometer or detectors. Here, we use the state of art single photon generation and detection technology to respectively make and measure a two-photon NOON state, and use it to perform unconditional phase sensing beyond the shot noise limit — that is, without artificially correcting for loss or any other source of imperfection [4]. We performed a two-photon NOON state polarisation interferometry measurement on a birefringent test phase. We use photons generated from a high-heralding-efficiency, high purity source of telecom-wavelength photon pairs [5], and we employ high efficiency superconducting photon detectors. Unlike previous experiments, our apparatus does not require postselection to achieve phase uncertainty below that achievable in an ideal, lossless classical interferometer. Our results show a clear violation (for a range of phases) of the stringent SNL Fisher-information bound, F_{SNL} = 2.09635, that takes into account the information in unrecorded trials arising from loss and higher order terms — making our demonstration unconditional. We also performed a direct phase sensing measurement and observed phase uncertainties more than 10 standard deviations below the SNL [4]. Our results enable quantum-enhanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances. References [1] V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011). [2] J. P. Dowling, “Quantum optical metrology–the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008). [3] R. Demkowicz-Dobrzanski, M. Jarzyna, and J. Kołodynski, “Quantum limits in optical interferometry,” Prog. Opt. 60, 345–435 (2015). [4] S. Slussarenko, M. M.Weston, H. M. Chrzanowski, L. K. Shalm, V. B. Verma, S.W. Nam, and G. J. Pryde, “Unconditional violation of the shot noise limit in photonic quantum metrology,” Nat. Photon. 11, 700-703 (2017). [5] M. M. Weston, H. M. Chrzanowski, S. Wollmann, A. Boston, J. Ho, L. K. Shalm, V. B. Verma, M. S. Allman, S. W. Nam, R. B. Patel, S. Slussarenko, and G. J. Pryde, “Efficient and pure femtosecond-pulse length source of polarization-entangled photons,” Opt. Express 24, 10,869–10,879 (2016).
Quantum entanglement is a fascinating physical resource that is central to the field of quantum information processing with important applications in such areas as quantum computing, quantum communication, quantum metrology, and quantum imaging. \nIt describes the physical phenomenon in which the quantum state of a multipartite system cannot be written as consisting of constituents that are independent of each other. In this case, the state of the system is called an entangled state. In this \ndissertation, the entanglement of photons--the elementary excitations of the quantized electromagnetic field--is studied. A focus is made on a particular type of entangled states of light called the d-mode N-photon NOON state, which consists of N photons with the N photons as an ensemble appearing at d orthogonal modes simultaneously and are inseparable. \nIn quantum metrology, a field that investigates the ultimate precision of measurements of unknown physical parameters, the two-mode NOON state has been studied extensively with respect to its ability to achieve super-resolution and super-sensitivity in the estimation of a single parameter. A lot of theoretical research has been conducted on the generation of two-mode NOON states, and two-mode NOON states with up to 4 photons have been experimentally and efficiently produced. On the other hand, recently there has been increasing interest in the study of the simultaneous estimation of multiple parameters. Accordingly, the multi-mode NOON state has been attracting more and more attention in view of its potential for enhanced efficiency as compared to using multiple two-mode NOON states separately to estimate the parameters. Nevertheless, no known generation method of multi-mode NOON states with more than 2 photons or 2 modes exists so far. \nIn this dissertation, several scalable generation methods of multi-mode NOON states are proposed. These methods take advantage of multi-photon quantum interference and they can theoretically be applied to produce NOON states with an \narbitrary number of modes and an arbitrary number of photons. The intrinsic generation probability for each method is calculated, and the methods are compared in regards to their feasibility and efficiency. The advantages of using multi-mode NOON \nstates in quantum metrology are also analyzed and discussed in detail.
The quantum statistical fluctuations of electromagnetic fields establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here, we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric downconversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling, and quantum networks.
Quantum metrology aims at achieving enhanced performance in measuring unknown parameters by utilizing quantum resources. Thus, quantum metrology is an important application of quantum technologies. Photonic systems can implement these metrological tasks with simpler experimental techniques. We present a scheme for improved parameter estimation by introducing entangled generalized coherent states (EGCS) for photonic quantum metrology. These states show enhanced sensitivity beyond the classical and Heisenberg limits and prove to be advantageous as compared to the entangled coherent and NOON states. Further, we also propose a scheme for experimentally generating certain entangled generalized coherent states with current technology.