Abstract Conditional measurement schemes, which employ linear optical elements and photon detectors, have recently become powerful tools for generating and enriching nonclassical states in single- and multi-mode scenarios. Here, the nonclassical resourcefulness of a simple single-mode conditional measurement (CM) setup, with a coherent state as one input state, is examined. Studying the output of this setup in the form of displaced qudits (DQ) simplifies the complete characterization of nonclassical resources. The figures of merit of the prepared states are evaluated through quadrature squeezing and some of the non-Gaussian measures such as the Hilbert–Schmidt distance, the quantum relative entropy and the Wigner negativity to identify the squeezing and non-Gaussianity of the states, respectively. The squeezing capacity of the DQ output is compared with the achievable squeezing in finite superposed Fock states, since DQ also constitute a finite-dimensional representation. This optimal squeezing is attained when the detector detects the single photons in the CM setup. All the studied non-Gaussian measures confirm the qualitative agreement that the non-Gaussianity of the setup is limited and does not exceed that of the input number state. The interplay of nonclassical resources between non-Gaussianity and squeezing is exemplified, showing that states exhibiting non-Gaussianity do not exhibit squeezing, and vice versa. In addition, experimental imperfections, such as photon-source impurities and detector inefficiencies, are accommodated to analyze the realistic preparation of DQ. The calculated success probabilities are around 15 % to create the maximally squeezed states under experimental conditions. It demonstrates the potential of nonclassical state generation with minimal nonclassical inputs through the CM scheme.
Abstract Conditional measurement schemes, which employ linear optical elements and photon detectors, have recently become powerful tools for generating and enriching nonclassical states in single- and multi-mode scenarios. Here, the nonclassical resourcefulness of a simple single-mode conditional measurement (CM) setup, with a coherent state as one input state, is examined. Studying the output of this setup in the form of displaced qudits (DQ) simplifies the complete characterization of nonclassical resources. The figures of merit of the prepared states are evaluated through quadrature squeezing and some of the non-Gaussian measures such as the Hilbert–Schmidt distance, the quantum relative entropy and the Wigner negativity to identify the squeezing and non-Gaussianity of the states, respectively. The squeezing capacity of the DQ output is compared with the achievable squeezing in finite superposed Fock states, since DQ also constitute a finite-dimensional representation. This optimal squeezing is attained when the detector detects the single photons in the CM setup. All the studied non-Gaussian measures confirm the qualitative agreement that the non-Gaussianity of the setup is limited and does not exceed that of the input number state. The interplay of nonclassical resources between non-Gaussianity and squeezing is exemplified, showing that states exhibiting non-Gaussianity do not exhibit squeezing, and vice versa. In addition, experimental imperfections, such as photon-source impurities and detector inefficiencies, are accommodated to analyze the realistic preparation of DQ. The calculated success probabilities are around 15 % to create the maximally squeezed states under experimental conditions. It demonstrates the potential of nonclassical state generation with minimal nonclassical inputs through the CM scheme.
Conditional Measurement scheme which employs linear optical elements and photon detection is the fertile ground for nonclassical state generation. We consider a simple setup that requires a coherent state and a number state as inputs of the beam splitter, and a photon detector. We show that by tuning the parameters involved in the setup, we can achieve optimal squeezing from the setup. This is facilitated by writing the output state of the conditional measurement as displaced qudits. Setting aside displacement which plays no role in squeezing, the finite-dimensional representation makes it possible to calculate the maximal amount of squeezing. By fixing the detection at one photon level irrespective of any number state input and carefully chosen coherent parameter and beam splitter reflectivity values, one can reach the maximal squeezing at least for lower number state inputs. This is in contrast to the earlier attempts in atom field interaction models etc., where the squeezing obtained was far from saturation. To accommodate the experimental imperfections, we consider the impure nature of the photon source and detector inefficiency.
Generation of highly non-classical quantum states of light is essential for optical quantum information processing and quantum metrology. Given the lack of sufficiently strong nonlinear interactions between optical fields, the commonly employed optical quantum-state preparation schemes are conditional, based on nonlinearity induced by heralding photon number measurement on a part of a multimode squeezed Gaussian state. Development and optimization of such probabilistic quantum-state engineering schemes represents one of the central challenges in current quantum optics. As technology advances and experiments progress to detection of higher numbers of photons, the maximization of the heralding probability becomes essential to ensure sufficiently high state-preparation rates. Here, we show that for the conditional quantum state preparation schemes based on Gaussian states and photon number measurements the maximization of the heralding probability can be formulated as finding solution to a system of polynomial equations, which offers an efficient way to find the optimal configuration and allows us to apply techniques dedicated specifically to solving such systems of equations. Our approach can seamlessly incorporate bounds on the available single-mode quadrature squeezing, which is highly experimentally relevant. We mainly consider generation of finite superpositions of Fock states but show that the approach can be straightforwardly extended to generation of squeezed superpositions of Fock states. We focus on Gaussian states with vanishing coherent displacements, hence the conditionally generated states have well defined photon number parity. We illustrate our general methodology through examples of generation of single-mode states with two and three heralding modes, and generation of two-mode states with two heralding modes.
Non-Gaussian quantum states and operations constitute essential resources for achieving quantum computational advantage and enabling quantum error correction in bosonic platforms. However, their generation in optical settings remains a challenging experimental task, often relying on probabilistic heralded protocols. Here, we present an in-depth analysis of the suitability of photon catalysis between low number Fock states and squeezed states for the generation of squeezed coherent state superpositions. We employ the stellar rank formalism to characterize the non-Gaussian complexity of input resources (including both states and measurements) and the generated states. This enables a systematic comparison of the fidelity between the catalyzed output and the target states to the maximum fidelity achievable by any protocol with the same non-Gaussian input resources. In this sense, we identify instances where the catalysis protocols considered here are provably optimal. We identify parameter regimes in which high-fidelity approximations of the target states can be achieved with minimal resources. Furthermore, we benchmark the performance of photon catalysis against Gaussian boson sampling-inspired protocols in terms of success probability and state quality, highlighting the advantages of deterministic Fock state sources. We also investigate the generation of related non-Gaussian resources including squeezed Fock states, relevant for quantum error correction. To account for experimental imperfections, we model losses across all optical modes using a Hilbert space truncation approach in the Fock basis and analyze the robustness of the generated states under realistic conditions. Our results quantify the trade-offs between non-Gaussian resource complexity, achievable fidelity, and losses in photon catalysis protocols, providing practical guidelines for near-term photonic implementations.
Abstract We introduce a protocol for generating a broad class of non-Gaussian (nG) quantum states via postselected weak measurement techniques. The scheme involves injecting an arbitrary quantum state and a single photon into the signal and idler ports, respectively, of an interference setup that incorporates a third-order nonlinear medium. A nG state is conditionally produced at the signal output, heralded by the detection of a single photon in one of the idler output channels. The protocol exploits a weak cross-Kerr interaction and effective single-photon nonlinearity enhanced by the weak-value amplification. We show that by tuning the weak value of the photon number operator in the idler mode within experimentally feasible parameters, a wide variety of nG states can be generated with high fidelity. As specific examples, we demonstrate the generation of photon-added states, displaced and squeezed number states, and a continuum of intermediate nG states using coherent and squeezed vacuum inputs, respectively. Furthermore, we show that the protocol enables the enhancement of non-Gaussianity and the enlargement of Schrödinger cat (SC) states when ideal SC states are used as the input. Our results provide an alternative route for the conditional generation of tunable nG states, with potential applications in quantum information processing. This approach may also open new avenues for quantum state engineering using postselected weak measurements.
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 This paper investigates the quantum features of non-Gaussian states generated by applying a two-mode squeezing operator S ˆ a b ( s ) to two generalized single-mode squeezed vacuum states (SVSs), each formed by the superposition of an SVS and a single–photon–subtracted SVS. The results show that, in the new states, the two-mode squeezing effect, the Einstein–Podolsky–Rosen (EPR) correlation, the Hillery–Zubairy entanglement, and the linear entropy are all enhanced as the two-mode squeezing parameter s increases. Moreover, both the degrees of squeezing and entanglement are improved and exceed those of the two-mode squeezed vacuum state (TMSVS) for stronger single-mode squeezing parameters. The optimal conditions for achieving such enhancements are identified for different regimes, depending on whether the generalized SVSs are purely Gaussian, maximally non-Gaussian, or intermediate states. In an application, the quantum Cramér–Rao bound (QCRB) is evaluated when the non-Gaussian states are employed as inputs to a Mach–Zehnder interferometer (MZI). The results further demonstrate that the enhanced phase sensitivity in the MZI originates from both the squeezing strengths and the intrinsic photon-subtraction operation. These findings highlight the potential of the new non-Gaussian states as promising resources for quantum metrology and quantum sensing.