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1. Classical-Nonclassical Polarity of Gaussian States

   https://doi.org/10.1103/PhysRevLett.132.240201  

   Liu, Jiru; Ge, Wenchao; Zubairy, M Suhail (June 2024, Physical Review Letters)

   Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multimode Gaussian states has posed some challenges. To address this, we introduce a unified quantification: the “classical-nonclassical polarity,” represented by P. For a single mode, a positive value of P captures the reduced minimum quadrature uncertainty below the vacuum noise, while a negative value represents an enlarged uncertainty due to classical mixtures. For multimode systems, a positive P indicates bipartite quantum entanglement. We show that the sum of the total classical-nonclassical polarity is conserved under arbitrary linear optical transformations for any two-mode and three-mode Gaussian states. For any pure multimode Gaussian state, the total classical-nonclassical polarity equals the sum of the mean photon number from single-mode squeezing and two-mode squeezing. Our results provide a new perspective on the quantitative relation between single-mode nonclassicality and entanglement, which may find applications in a unified resource theory of nonclassical features. 

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2. Page curves and typical entanglement in linear optics

   https://doi.org/10.22331/q-2023-05-23-1017  

   Iosue, Joseph T.; Ehrenberg, Adam; Hangleiter, Dominik; Deshpande, Abhinav; Gorshkov, Alexey V. (May 2023, Quantum)

   Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the Rényi-2 Page curve (the average Rényi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the Rényi-2 entropy by studying its variance. Using the aforementioned results for the Rényi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity. 

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3. Bosonic pair production and squeezing for optical phase measurements in long-lived dipoles coupled to a cavity

   https://doi.org/10.48550/arXiv.2204.13090  

   Sundar, B.; Barberena, D.; Piñeiro Orioli, A.; Chu, A.; Thompson, J.K.; Rey, A.M.; Lewis-Swan, R.J. (October 2022, ArXivorg)

   We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing (TMS) of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for the observation of continuous variable entanglement in atomic systems and associated applications in next-generation optical atomic clocks. 

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4. Mapping continuous-variable quantum states onto optical scalar beams

   https://doi.org/10.1088/2515-7647/ae2fa4  

   Rodríguez-Lara, B M; Becerra, F E (January 2026, Journal of Physics: Photonics)

   Abstract Optical scalar beams provide a platform to explore classical analogies to quantum mechanics. We introduce a Lie group-theoretic $\mathrm{su}(1,1)$framework to construct optical beam analogs of continuous-variable (CV) quantum states, including one- and two-mode squeezing. Using Fourier methods and the optical Wigner distribution, we investigate how squeezing reshapes the spatial and spectral structure of these beams, and find that the achievable diffraction-limited spatial compression is bounded by the numerical aperture of the optical system. We construct an optical analog of the Duan–Simon inseparability criterion and use marginal optical Wigner distributions, which encode partial phase-space information, as witnesses of CV classical entanglement. Our framework provides a unified approach to quantum-inspired beam engineering with potential applications in optical imaging, metrology, and communication. 

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5. Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing

   https://doi.org/10.22331/q-2024-09-19-1478  

   Brady, Anthony J; Wu, Jing; Zhuang, Quntao (September 2024, Quantum)

   Recent advancements in multi-mode Gottesman-Kitaev-Preskill (GKP) codes have shown great promise in enhancing the protection of both discrete and analog quantum information. This broadened range of protection brings opportunities beyond quantum computing to benefit quantum sensing by safeguarding squeezing — the essential resource in many quantum metrology protocols. However, the potential for quantum sensing to benefit quantum error correction has been less explored. In this work, we provide a unique example where techniques from quantum sensing can be applied to improve multi-mode GKP codes. Inspired by distributed quantum sensing, we propose the distributed two-mode squeezing (dtms) GKP codes that offer benefits in error correction with minimal active encoding operations. Indeed, the proposed codes rely on a $single$(active) two-mode squeezing element and an array of beamsplitters that effectively distributes continuous-variable correlations to many GKP ancillae, similar to continuous-variable distributed quantum sensing. Despite this simple construction, the code distance achievable with dtms-GKP qubit codes is comparable to previous results obtained through brute-force numerical search \cite{lin2023closest}. Moreover, these codes enable analog noise suppression beyond that of the best-known two-mode codes \cite{noh2020o2o} without requiring an additional squeezer. We also provide a simple two-stage decoder for the proposed codes, which appears near-optimal for the case of two modes and permits analytical evaluation. 

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