Quantumassisted approach

Enhanced Hanbury Brown and Twiss interferometry using parametric amplification, Xiaoping Ma et al, EPJ Quantum Technology volume 7, Article number: 10 (2020)
The Hanbury Brown and Twiss (HBT) interferometer was proposed to observe intensity correlations of starlight to measure a star’s angular diameter. As the intensity of light that reaches the detector from a star is very weak, one cannot usually get a workable signaltonoise ratio. We propose an improved HBT interferometric scheme incorporating optical parametric amplifiers (OPA) into the system to amplify the correlation signal. Remarkably, for weak star light, the signaltonoise ratio (SNR) in the new HBT interferometric scheme is much better than that of conventional HBT interferometer. Our work is valuable in measuring a star whose intensity at the detector is low and maybe also applicable in remote sensing and longdistance quantum imaging where the light passed through the object is weak after a long distance transmission.
Estimating the angular separation between two incoherent thermal sources is a challenging task for direct imaging, especially at lengths within the diffraction limit. Moreover, detecting the presence of multiple sources of different brightness is an even more severe challenge. We experimentally demonstrate two tasks for superresolution imaging based on hypothesis testing and quantum metrology techniques. We can significantly reduce the error probability for detecting a weak secondary source, even for small separations. We reduce the experimental complexity to a simple interferometer: we show (1) our setup is optimal for the state discrimination task, and (2) if the two sources are equally bright, then this measurement can superresolve their angular separation. Using a collection baseline of 5.3 mm, we resolve the angular separation of two sources placed 15 μm apart at a distance of 1.0 m with a 1.7% accuracy  an almost 3ordersofmagnitude improvement over shotnoise limited direct imaging.
https://www.nature.com/articles/s41467022329778
We report results of verylongbaseline interferometric imaging using distributed single photons. We demonstrate source autocorrelation reconstruction, and increased signaltonoise ratio per detected coincidence compared to using classical states as phase reference.
 Multiparameter estimation in networked quantum sensors, Timothy J. Proctor, Paul A. Knott and Jacob A. Dunningham
We introduce a general model for a network of quantum sensors, and we use this model to consider the 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 spa tially 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.
 Distributed quantum sensing using continuousvariable multipartite entanglement, Quntao Zhuang, Zheshen Zhang, Jeffrey H. Shapiro
Distributed quantum sensing uses quantum correlations between multiple sensors to enhance the measurement of unknown parameters beyond the limits of unentangled systems. We describe a sensing scheme that uses continuousvariable multipartite entanglement to enhance distributed sensing of fieldquadrature displacement. By dividing a squeezedvacuum state between multiple homodynesensor nodes using a lossless beamsplitter array, we obtain a rootmeansquare (rms) estimation error that scales inversely with the number of nodes (Heisenberg scaling), whereas the rms error of a distributed sensor that does not exploit entanglement is inversely proportional to the square root of number of nodes (standard quantum limit scaling). Our sensor’s scaling advantage is destroyed by loss, but it nevertheless retains an rmserror advantage in settings in which there is moderate loss. Our distributed sensing scheme can be used to calibrate continuousvariable quantum key distribution networks, to perform multiplesensor coldatom temperature measurements, and to do distributed interferometric phase sensing.

Entangled sensornetworks for darkmatter searches, Anthony J. Brady, Christina Gao, Roni Harnik, Zhen Liu, Zheshen Zhang, and Quntao Zhuang
The hypothetical axion particle (of unknown mass) is a leading candidate for dark matter (DM). Many experiments search for axions with microwave cavities, where an axion may convert into a cavity photon, leading to a feeble excess in the output power of the cavity. Recent work [Nature 590, 238 (2021)] has demonstrated that injecting squeezed vacuum into the cavity can substantially accelerate the axion search. Here, we go beyond and provide a theoretical framework to leverage the benefits of quantum squeezing in a network setting consisting of many sensorcavities. By forming a local sensor network, the signals among the cavities can be combined coherently to boost the axion search. Furthermore, injecting multipartite entanglement across the cavities—generated by splitting a squeezed vacuum—enables a global noise reduction. We explore the performance advantage of such a local, entangled sensornetwork, which enjoys both coherence between the axion signals and entanglement between the sensors. Our analyses are pertinent to nextgeneration DMaxion searches aiming to leverage a network of sensors and quantum resources in an optimal way. Finally, we assess the possibility of using a more exotic quantum state, the GottesmanKitaevPreskill (GKP) state. Despite a constantfactor improvement in the scantime relative to a singlemode squeezedstate in the ideal case, the advantage of employing a GKP state disappears when a practical measurement scheme is considered.
 Distributed Quantum Metrology and the Entangling Power of Linear Networks, Wenchao Ge, Kurt Jacobs, Zachary Eldredge, Alexey V. Gorshkov, Michael FossFeig
We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary nonclassical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multiport interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with welldistributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of nonclassicality.
 Distributed quantum sensing in a continuous variable entangled network, Xueshi Guo, Casper R. Breum, Johannes Borregaard, Shuro Izumi, Mikkel V. Larsen, Tobias Gehring, Matthias Christandl, Jonas S. NeergaardNielsen, and Ulrik L. Andersen
Networking is integral to quantum communications and has significant potential for upscaling quantum computer technologies. Recently, it was realized that the sensing performances of multiple spatially distributed parameters may also be enhanced through the use of an entangled quantum network. Here, we experimentally demonstrate how sensing of an averaged phase shift among four distributed nodes benefits from an entangled quantum network. Using a fourmode entangled continuousvariable state, we demonstrate deterministic quantum phase sensing with a precision beyond what is attainable with separable probes. The techniques behind this result can have direct applications in a number of areas ranging from molecular tracking to quantum networks of atomic clocks.

Quantum Indistinguishability by Path Identity: The awakening of a sleeping beauty, Armin Hochrainer, Mayukh Lahiri, Manuel Erhard, Mario Krenn, Anton Zeilinger
Two photonpair creation processes can be arranged such that the paths of the emitted photons are identical. Thereby the path information is not erased but is never born in the first place. In addition to its implications for fundamental physics, this concept has recently led to a series of discoveries in the fields of imaging, spectroscopy, and quantum information science. Here we present the idea of path identity and provide a comprehensive review of the recent developments.

Entanglement enabled telescopic arrays in the presence of decoherence, Siddhartha Santra, Brian Kirby, Vladimir Malinovsky, Michael Brodsky
We consider quantum enhancement of directdetection interferometric measurements to increase telescope resolution. We propose a protocol of measuring interferometric visibility function using imperfectly entangled states shared between remote telescopes. We show how errors in visibility measurement, and in turn, errors in intensity distribution of a distant object depend on the degree of entanglement of the shared quantum resource. We determine that these errors are sufficiently small over a wide range of resource states which makes our technique feasible in practical environments.

Imaging stars with quantum error correction; Zixin Huang, Gavin K. Brennen, Yingkai Ouyang
The development of highresolution, largebaseline optical interferometers would revolutionize astronomical imaging. However, classical techniques are hindered by physical limitations including loss, noise, and the fact that the received light is generally quantum in nature. We show how to overcome these issues using quantum communication techniques. We present a general framework for using quantum error correction codes for protecting and imaging starlight received at distant telescope sites. In our scheme, the quantum state of light is coherently captured into a nonradiative atomic state via Stimulated Raman Adiabatic Passage, which is then imprinted into a quantum error correction code. The code protects the signal during subsequent potentially noisy operations necessary to extract the image parameters. We show that even a small quantum error correction code can offer significant protection against noise. For large codes, we find noise thresholds below which the information can be preserved. Our scheme represents an application for nearterm quantum devices that can increase imaging resolution beyond what is feasible using classical techniques.

Quantum Telescopy Games Robert Czupryniak, Eric Chitambar, John Steinmetz, Andrew N. Jordan
We consider the Clock Game  task formulated in the framework of quantum information theory  that can be used to improve the existing schemes of quantumenhanced telescopy. The problem of learning when a stellar photon reaches a telescope is translated into an abstract game, which we call the Clock Game. A winning strategy is provided that involves performing a quantum nondemolition measurement that verifies which stellar spatiotemporal modes are occupied by a photon without disturbing the phase information. We prove tight lower bounds on the entanglement cost needed to win the Clock Game, with the amount of necessary entangled bits equaling the number of timebins being distinguished. This lower bound on the entanglement cost applies to any telescopy protocol protocol that aims to nondestructively extract the timebin information of an incident photon through local measurements, and our result implies that the protocol of [Khabiboulline et al. Phys. Rev. Lett. 123, 70504 (2019)] is optimal in terms of entanglement consumption. The full task of the phase extraction is also considered, and we show that the quantum Fisher Information of the stellar phase can be achieved by local measurements and shared entanglement without the necessity of nonlinear optical operations. The optimal phase measurement is achieved asymptotically with increasing number of ancilla qubits, whereas a single qubit pair is required if nonlinear operations are allowed.

Optimal photonic gates for quantumenhanced telescopes, Robert Czupryniak, John Steinmetz, Paul G. Kwiat, Andrew N. Jordan.
We propose two optimal phaseestimation schemes that can be used for quantumenhanced longbaseline interferometry. By using distributed entanglement, it is possible to eliminate the loss of stellar photons during transmission over the baselines. The first protocol is a sequence of gates using nonlinear optical elements, optimized over all possible measurement schemes to saturate the CramérRao bound. The second approach builds on an existing protocol, which encodes the time of arrival of the stellar photon into a quantum memory. Our modified version reduces both the number of ancilla qubits and the number of gate operations by a factor of two. https://arxiv.org/pdf/2108.01170.pdf

Quantum memories and the doubleslit experiment: implications for astronomical interferometry, Joss BlandHawthorn (U Sydney), Matt Sellars (ANU), John Bartholomew (U Sydney). https://arxiv.org/abs/2103.07590
Thomas Young's slit experiment lies at the heart of classical interference and quantum mechanics. Over the last fifty years, it has been shown that particles (e.g. photons, electrons, large molecules), even individual particles, generate an interference pattern at a distant screen after passage through a double slit, thereby demonstrating waveparticle duality. We revisit this famous experiment by replacing both slits with singlemode fibre inputs to two independent quantum memories that are capable of storing the incident electromagnetic field's amplitude and phase as a function of time. At a later time, the action is reversed: the quantum memories are read out in synchrony and the singlemode fibre outputs are allowed to interact consistent with the original observation. In contrast to any classical memory device, the write and read processes of a quantum memory are nondestructive and hence, preserve the photonic quantum states. In principle, with sufficiently long storage times and sufficiently high photonic storage capacity, quantum memories operating at widely separated telescopes can be brought together to achieve optical interferometry over arbitrarily long baselines.
 LongerBaseline Telescopes Using Quantum Repeaters Daniel Gottesman, Thomas Jennewein, Sarah Croke; Phys. Rev. Lett. 109, 070503 (2012), DOI:10.1103/PhysRevLett.109.070503, https://arxiv.org/abs/1107.2939 synopsis in APS Physics
We present an approach to building interferometric telescopes using ideas of quantum information. Current optical interferometers have limited baseline lengths, and thus limited resolution, because of noise and loss of signal due to the transmission of photons between the telescopes. The technology of quantum repeaters has the potential to eliminate this limit, allowing in principle interferometers with arbitrarily long baselines.
 QuantumAssisted Telescope Arrays, Emil T. Khabiboulline, Johannes Borregaard, Kristiaan De Greve, Mikhail D. Lukin; Phys. Rev. A 100, 022316 (2019), DOI:10.1103/PhysRevA.100.022316; arxiv.org/abs/1809.03396
Quantum networks provide a platform for astronomical interferometers capable of imaging faint stellar objects. In a recent work [arXiv:1809.01659], we presented a protocol that circumvents transmission losses with efficient use of quantum resources and modest quantum memories. Here we analyze a number of extensions to that scheme. We show that it can be operated as a truly broadband interferometer and generalized to multiple sites in the array. We also analyze how imaging based on the quantum Fourier transform provides improved signaltonoise ratio compared to classical processing. Finally, we discuss physical realizations including photondetectionbased quantum state transfer.
 Optical Interferometry with Quantum Networks, Emil T. Khabiboulline, Johannes Borregaard, Kristiaan De Greve, Mikhail D. Lukin; Phys. Rev. Lett. 123, 070504 (2019), DOI:10.1103/PhysRevLett.123.070504, arXiv:1809.01659
We propose a method for optical interferometry in telescope arrays assisted by quantum networks. In our approach, the quantum state of incoming photons along with an arrival time index is stored in a binary qubit code at each receiver. Nonlocal retrieval of the quantum state via entanglementassisted parity checks at the expected photon arrival rate allows for direct extraction of the phase difference, effectively circumventing transmission losses between nodes. Compared to prior proposals, our scheme (based on efficient quantum data compression) offers an exponential decrease in required entanglement bandwidth. Experimental implementation is then feasible with nearterm technology, enabling optical imaging of astronomical objects akin to wellestablished radio interferometers and pushing resolution beyond what is practically achievable classically.
Early quantum optics for astronomy attempts: ESO QuantEYE proposal