Quantum sensing and communication (QSC) is pivotal for developing next-generation networks with unprecedented performance. Many implementations of existing QSC systems employ Gaussian states as they can be easily realized using current technologies. However, Gaussian states lack non-classical properties necessary to unleash the full potential of QSC. This motivates the use of non-Gaussian states, which have non-classical properties beneficial for QSC. This paper establishes a theoretical foundation for QSC employing photon-varied Gaussian states (PVGSs). The PVGSs are non-Gaussian states that can be generated from Gaussian states using current technologies. First, we derive a closed-form expression for the generalized bilinear generating function of ordinary Hermite polynomials and show how it can be used to describe PVGSs. Then, we characterize PVGSs by deriving their Fock representation and their inner product. We also determine equivalence conditions for Gaussian states obtained from arbitrary permutations of rotation, displacement, and squeezing operators. Finally, we explore the use of PVGSs for QSC in several case studies.
Quantum communication systems exchange information between a source and a destination by encoding such information into quantum states according to modulation techniques. The design of quantum modulation techniques, including quantum quadrature amplitude modulation (QAM), requires choosing and characterizing quantum states. This paper explores the use of non-Gaussian photon-added Gaussian states (PAGSs) for quantum QAM communications. First, we characterize pure PAGSs in the Fock space and derive a closed-form expression for their inner product. Then, we develop a quantum QAM technique employing PAGSs. In particular, we show how to construct quantum QAM constellations of PAGSs. Finally, we evaluate the performance of the developed quantum QAM technique with PAGSs, when a square root measurement (SRM) receiver is employed, and compare such performance with that of existing coherent states. Results show that PAGSs can provide a performance gain with respect to coherent states.
Quantum non-Gaussian states of photons and phonons are conclusive and direct witnesses of higher-than-quadratic nonlinearities in optical and mechanical processes. Moreover, they are proven resources for quantum sensing, communication and error correction with diverse continuous-variable systems. This review introduces theoretical analyses of nonclassical and quantum non-Gaussian states of photons and phonons. It recapitulates approaches used to derive operational criteria for photons tolerant to optical losses, their application in experiments and their nowadays extension to quantum non-Gaussian photon coincidences. It extends to a recent comparison of quantum non-Gaussianity, including robustness to thermal noise, and sensing capability for high-quality phononic Fock states of single trapped cooled ions. The review can stimulate further development in the criteria of quantum non-Gaussian states and experimental effort to prepare and detect such useful features, navigating the community to advanced quantum physics and technology.
We present a framework for studying linear bosonic non-Gaussian channels. Our emphasis is on a class of channels that we call photon-added Gaussian channels and these are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian regime for numerous tasks in continuous-variable quantum information processing including universal quantum computation. These channels are obtained by extending Gaussian channels with photon addition applied to the ancilla ports giving rise to a one-parameter family of non-Gaussian channels indexed by photon number
n≥1. We derive its operator-sum representation which is indispensable in the present context. We observe that these channels are Fock-preserving (or coherence non-generating in the Fock basis). Further, noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We then report examples of activation of nonclassicality, using this method of photon-addition, at outputs of channels that would otherwise output only classical states. We also derive many structure theorems and information theoretic properties of these channels.
Quantum noise limits high-precision sensing, such as in gravitational wave detectors. Caves first proposed beating this shot-noise limit by injecting squeezed vacuum at the dark port of an interferometer. Frequency-dependent squeezing through a filter cavity now delivers broadband quantum noise reductions of up to 5.2 dB at Hanford and 6.1 dB at Livingston in the LIGO detectors' fourth observing run. Building on these advances, this thesis develops techniques for interferometric sensing under realistic loss and phase noise, spanning Gaussian state preparation, optomechanical readout and feedback control, and non-Gaussian state preparation. In Parts I and II, we work in the two-photon formalism, where states are Gaussian and dynamics are linear. In Part I, we present a waveguide squeezer as an alternative to the traditional bulk cavity-based source; it is single-pass, broadband, and compact, and its modularity opens a path to non-Gaussian state generation. We report the detection of squeezed light from waveguide sources at 1064 nm in the sub-MHz regime, and we phase-stabilize the squeezed vacuum with quantum noise locking. We also analyze the loss and phase-noise tolerance of Gaussian states. In Part II, we design a tabletop phase-sensitive optomechanical amplifier and analyze its performance in terms of cavity stability, control system, and noise budget. We then implement the locking scheme, including Pound-Drever-Hall locking of the cavity, and characterize the noise budget at the initial stage. We also propose using optomechanics for coherent feedback control, which could evade back-action and broaden the detection bandwidth of future gravitational wave detectors. In Part III, we turn to non-Gaussian states. Phase noise does not preserve Gaussianity, so the best input state under combined loss and phase noise need not be Gaussian. We numerically optimize the input state for displacement sensing over the
(η,σϕ) landscape, integrating the Lindblad master equation in a truncated Fock basis and computing the quantum Fisher information. Within the Gaussian sub-family, the optimizer returns a displaced squeezed state once phase noise is appreciable, rather than pure squeezed vacuum. Without the Gaussian restriction, the optimized states sort roughly into four classes (Fock-like, cubic-phase-like, discrete-rotational, and squeezed), each dominant in a different region of the parameter space. In the experimentally relevant region of 1% loss and 100 mrad phase noise, cat states outperform squeezed vacuum even with balanced homodyne readout, an improvement implementable in the near term. We also show that the non-Gaussian advantage persists at higher photon budgets, well above
Nˉ=5. Together, these results show how state preparation, readout, and feedback choices trade off against realistic loss and phase noise, and identify the regimes where non-Gaussian states perform better.
As a cornerstone of quantum science and technology, quantum precision measurement aims to transcend the standard quantum limit (SQL) and achieve sensitivities unattainable by classical approaches by harnessing distinctive quantum resources such as entanglement, squeezing and non-Gaussianity. Within this framework, Gaussian states have historically played a central role, underpinning a series of seminal experimental advances; however, their utility in metrology is fundamentally bounded by theoretical constraints that preclude unlimited gains in measurement precision. In contrast, a growing body of recent research has revealed that non-Gaussian states–endowed with stronger quantum correlations and more pronounced non-classical characteristics — can significantly surpass Gaussian counterparts in key tasks such as phase estimation, quantum imaging and quantum sensing. Under specific conditions, these states even exhibit the potential to approach or saturate the ultimate Heisenberg limit. This review offers a comprehensive overview of the theoretical underpinnings, representative preparation methodologies, experimental progress and emerging applications of non-Gaussian states in quantum metrology. Special attention is devoted to illustrating their transformative potential for the development of next-generation quantum sensors and high-precision measurement instruments, while also addressing prevailing challenges and delineating promising future research trajectories in this rapidly advancing field.
Quantum technologies, encompassing communication, computation, and metrology, rely on the generation and control of non-Gaussian states of light. These states enable secure quantum communication, fault-tolerant quantum computation, and precision sensing beyond classical limits, yet their practical realisation remains a major challenge due to reliance on high-photon-number Fock states or strong non-linearities. Here we introduce a unified optical framework that removes this constraint, using only Gaussian inputs, optical parametric amplification, and heralded photon detection. Within a single architecture, we demonstrate the generation of photon-added squeezed states with near unit fidelity, cubic-phase-like states with strong non-linearities and fidelities above 98.5%, and squeezed-cat states exceeding 99% fidelity that can be iteratively bred into GKP grid states surpassing the 9.75 dB fault-tolerance threshold. Operating entirely below 3 dB of input squeezing, the approach provides a scalable, experimentally accessible platform that unites the state resources required for quantum communication, metrology, and computation within one coherent optical framework.