This paper establishes the theoretical framework to enable the seamless transfer of digital information from the classical microwave domain to the quantum optical domain in wireless-to-optical converters. It introduces a quantum mechanical network model to characterize digital information mapping from microwave to optical domains in seamless wireless-to-optical converters based on antenna-coupled electro-optic modulators. Key design principles are outlined to optimize information mapping strength, supported by analytical and physical reasoning. The model is further extended to demonstrate phase-space encoding of optical coherent states using classical microwave constellations. In addition, the framework addresses the challenge of inter-symbol overlap in the quantum optical phase-space due to quadrature fluctuations and proposes a potential mitigation technique. The foundational framework established in this paper can also enable the encoding of other nonclassical states of light, such as squeezed states, thereby paving the way for integrating classical microwave and quantum optical links in the near future.
Continuous-variable quantum key distribution is a compelling framework for scalable quantum networks due to its seamless integration with existing optical communication infrastructure. However, a fundamental gap persists between theoretical protocols requiring ideal Gaussian modulation and the constrained, discrete-modulated signals dictated by practical high-speed hardware. Current security proofs for discrete modulation rely on semidefinite programming, which suffers from prohibitive computational overhead for high-order constellations and lacks direct physical insight into non-Gaussian modulation.In this Letter, we overcome this limitation by developing a security framework that obviates semidefinite programming in favor of an approach grounded fundamentally in the Heisenberg uncertainty principle. By introducing a multi-mode entanglement-source model to characterize non-Gaussian state preparation, we establish an explicit mapping between constellation geometry and the secret key rate. This framework effectively quantifies the security implications of hardware-limited, finite state preparation, enabling both numerical and analytical security analysis under high-order constellations. We experimentally validate our method on both discrete-component and integrated photonic platforms, demonstrating that a quadrature amplitude modulation format with 256 constellation points can asymptotically approach the Gaussian capacity limit. Beyond quantum key distribution, the principle of tightening uncertainty-constrained bounds via source-mode expansion offers a paradigm for exploring the information-theoretic properties of complex non-Gaussian systems.
This paper develops a theoretical framework for enabling seamless transfer of digital information from classical microwave domain to the quantum optical domain in wireless-to-optical converters. A quantum mechanical network model is introduced to characterize microwave-to-optical digital information mapping in antenna-coupled electro-optic modulator-based converters. Design guidelines are discussed to maximize the information mapping strength. The derived model is then extended to show phase-space encoding of optical coherent-states with classical wireless microwave constellation. Further, the challenge of inter-symbol overlap in the encoded quantum optical phase-space due to quadrature fluctuations is highlighted. The possibility of erroneous phase-space encoding due to quadrature fluctuations is pointed out, followed by a potential mitigation technique. The presented framework also lays the groundwork for encoding other non-classical states of light such as squeezed states, and hence forms the basis for bridging classical microwave and quantum optical links in the near future.
Squeezed Fock states, photon-subtracted squeezed states, and optical cat states are established non-Gaussian resources in continuous-variable quantum optics. Here we compare these known state families from a task-oriented perspective: matched mean photon number, scalar Wigner negativity, and directional displacement-fidelity response. Starting from squeezed vacuum, single-photon subtraction prepares a state proportional to
S(r,θ)∣1⟩, while two-photon subtraction prepares an even-parity squeezed Fock superposition rather than a pure
S(r,θ)∣2⟩. We benchmark photon-conditioned squeezed states against Fock and coherent-cat references using the integrated Wigner negativity
δ, the energy-normalized metric
δ/⟨n⟩, and fidelity-threshold displacement radii
RF(φ). Cat benchmarks remain strong scalar Wigner-negativity resources, whereas photon-conditioned squeezed states provide an origin-centered alternative with tunable anisotropic displacement response. In particular, the two-photon-subtracted squeezed state shows favorable displacement-fidelity radii over selected quadrature directions at matched
⟨n⟩. These results identify a regime relevant to homodyne-aligned continuous-variable control and anisotropic displacement-noise mitigation, with directional sensing as a natural dual application.
Abstract Optical scalar beams provide a platform to explore classical analogies to quantum mechanics. We introduce a Lie group-theoretic 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.