arXiv subjects

Petr Marek

Publications and source records attributed to Petr Marek.

At least 19 recordsLinked to original sources

arXiv2026

Higher-order covariance matrices for non-Gaussian quantum states

Covariance matrices lie at the heart of the powerful and well-established symplectic framework for describing continuous-variable Gaussian quantum states. However, since this framework only relies on first- and second-order moments, it is not sufficient for the analysis of non-Gaussian states because their higher-order moments are essential to capture some of their key properties. Here, we define higher-order covariance matrices -- more precisely, covariance matrices built from higher-order quadrature monomials -- which provide a simple way to evaluate the effect of Gaussian transformations on non-Gaussian states and can be used, for example, to address nonlinear squeezing or non-Gaussian nullifiers. Higher-order covariance matrices can be estimated from homodyne measurement data using only a limited number of quadrature angles, which involves matrices of moderate dimension compared with a full simulation in the Fock basis. The dimension of a higher-order covariance matrix does not depend on the span of the quantum states in Fock basis and, furthermore, scales only polynomially with the number of modes.

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arXiv2026

Picosecond Schr\"odinger cat states for ultrafast optical quantum processing

Non-Gaussian states are essential resources for universal, fault-tolerant optical quantum computing, but their generation rate remains limited by low heralding probabilities and operation in nanosecond temporal modes. Here, we demonstrate multi-photon generalized photon subtraction in picosecond optical wave packets, establishing the state-generation capability required for high-rate operation by addressing the temporal-mode bottleneck that has constrained the achievable rate. Two interfering ultrashort squeezed vacua are heralded by photon-number-resolving detection with a high-speed transition-edge sensor and characterized by pulsed homodyne detection matched to 10-ps temporal modes at a 5-MHz pump repetition rate. We reconstruct Wigner functions without loss correction that exhibit up to four distinct negative regions for four-photon heralding, together with an effective cat-state amplitude of $\alpha_{\mathrm{eff}} = 1.69$. This amplitude approaches the range of practical relevance for fault-tolerant cat-code architectures and for adaptive breeding toward logical-qubit generation, while the picosecond temporal mode establishes a platform compatible with high-rate, scalable time-multiplexed photonic architectures.

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arXiv2026

Generalization of catability for parity-less cat states

We extend the nullifier-based certification framework of catability from parity-defined coherent cat states to parity-less Kerr cat states. Since Kerr cats cannot be distinguished by parity alone, we replace the parity component of the original nullifier with a displaced-parity operator that captures their characteristic interference structure. The resulting generalized catability remains directly observable and can be evaluated from a finite number of photon-number measurements without full state tomography. Numerical benchmarks show that the method faithfully certifies Kerr-cat features, produces accurate approximations of ideal Kerr cat states, and is more resilient to optical loss than fidelity-based certification. We also identify an exact anti-linear nullifier based on complex conjugation, providing an ideal algebraic description of Kerr cat states. Our results broaden the scope of catability and provide an experimentally practical approach to the characterization of Kerr cat states.

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arXiv2026

Efficient characterization of general Gottesman-Kitaev-Preskill qubits

Practical utilization of Gottesman-Kitaev-Preskill (GKP) qubits requires not only the preparation of logical basis states, but also the ability to prepare and evaluate arbitrary logical qubit superpositions. Currently, this is typically done via quantum state tomography, which is resource-intensive. We introduce a family of positive semidefinite Hermitian operators, one for each point on the logical Bloch sphere, whose unique zero-eigenvalue ground states are the corresponding ideal GKP qubit states. We show that the expectation value of each operator serves as a witness of non-Gaussianity, and corresponds to twice the logical infidelity for states in the ideal logical GKP subspace. Furthermore, the truncated finite-dimensional counterparts of these operators yield physical approximations of arbitrary logical GKP states as their ground states. The evaluation of the proposed operators requires only three quadrature measurements, making this framework practical for both the experimental characterization and numerical optimization of GKP state preparation circuits.

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arXiv2026

Environment-Assisted Decoherence Suppression of Optical Non-Gaussian States

Optical loss is a common bottleneck in photonic quantum information processing, undermining the quantum advantage over classical approaches. Although several countermeasures, such as quantum distillation and error correction, have been proposed, they typically require experimentally demanding non-Gaussian operations. Here, we demonstrate a Gaussian-only scheme that suppresses loss-induced decoherence for general, unknown optical quantum states. By injecting a squeezed vacuum state into an environment of the loss channel and performing feedforward based on environmental monitoring, the scheme effectively suppresses loss-induced noise. Our programmable loop-based optical circuit allows us to implement the scheme for several types of loss-sensitive non-Gaussian states under various loss conditions for up to five steps, and directly compare the results with the unsuppressed case. Our results show that the scheme consistently mitigates state degradation, preserving higher fidelity and Wigner negativity than without suppression. This approach can be applied to mitigating a broad class of errors in optical systems and extending quantum memory lifetimes. Moreover, it is compatible with other loss-suppression techniques and extendable to physical platforms beyond optics, offering a promising route toward reducing the overhead required for fault-tolerant quantum information processing.

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arXiv2026

Witnesses of non-Gaussian features as lower bounds of stellar rank

Quantum non-Gaussian states and operations serve as fundamental resources for universal quantum computation, error correction, and high-precision metrology, extending beyond the Gaussian limits. While the stellar rank provides a rigorous hierarchical measure of non-Gaussianity, it remains challenging to determine experimentally. Conversely, witnesses of non-Gaussian features, based on the expectation values and variances of measurable observables, offer an accessible method for certifying non-Gaussian behavior but lack a direct connection to stellar rank. In this work, we establish a quantitative connection between these witnesses and stellar rank, demonstrating that the former can provide certifiable lower bounds on stellar rank. We introduce normalized expectation value and variance-based quantifiers and show that these witnesses form a consistent hierarchy of thresholds corresponding to stellar rank. Our results bridge the gap between abstract hierarchical measures and experimentally accessible quantifiers, enabling scalable certification of non-Gaussian states.

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arXiv2026

Tuning Wave-Particle Duality of Quantum Light by Generalized Photon Subtraction

Wave--particle duality is a hallmark of quantum mechanics. For bosonic systems, there exists a continuum of intermediate states bridging wave-like Schr\"odinger cat states and particle-like Fock states. Such states have recently been recognized as valuable resources for enhancing fault-tolerant quantum computation (FTQC) with propagating light. Here we experimentally demonstrate tunable generation of these intermediate states by employing generalized photon subtraction (GPS). By detecting up to three photons from squeezed-light sources with a photon-number-resolving detector, we continuously control the balance between wave- and particle-like features. This approach allows us to construct a spectral family of quantum states with high generation rates, optimized according to the required fault-tolerance threshold. Our results establish GPS as a versatile toolbox for tailoring non-Gaussian resources, opening a pathway to efficient Gottesman--Kitaev--Preskill (GKP) qubit generation and addressing a central bottleneck in optical quantum computing.

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arXiv2025

Teleportation-based squeezer for bosonic cluster states

The one-way quantum computation utilizing bosonic modes of light offers unmatched scalability of light modes, and it has seen rapid experimental development recently. Scalability requires robust and low-error gates and measurements. Squeezing gate is one of the necessary Gaussian operations. We find the optimal squeezing gate in cluster state architecture. Our approach newly uses amplitude transmission coefficients of unbalanced beam splitters and homodyne detection with subsequent unity-gain feed-forward to squeeze the input state. The approach outperforms the current method based on optimally rotated homodyne detection, but with fixed balanced beam splitters. The performance of both cluster state squeezers is evaluated for Gaussian and non-Gaussian input states. We use different metrics to benchmark the quality of squeezed output states. The result opens a road to low-noise squeezing gates in experimentally achievable cluster states.

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arXiv2025

Beyond Stellar Rank: Control Parameters for Scalable Optical Non-Gaussian State Generation

Advanced quantum technologies rely on non-Gaussian states of light, essential for universal quantum computation, fault-tolerant error correction, and quantum sensing. Their practical realization, however, faces hurdles: simulating large multi-mode generators is computationally demanding, and benchmarks such as the \emph{stellar rank} do not capture how effectively photon detections yield useful non-Gaussianity. We address these challenges by introducing the \emph{non-Gaussian control parameters} $(s_0,\delta_0)$, a continuous and operational measure that goes beyond stellar rank. Leveraging these parameters, we develop a universal optimization method that reduces photon-number requirements and greatly enhances success probabilities while preserving state quality. Applied to the Gottesman--Kitaev--Preskill (GKP) state generation, for example, our method cuts the required photon detections by a factor of three and raises the preparation probability by nearly $10^8$. Demonstrations across cat states, cubic phase states, GKP states, and even random states confirm broad gains in experimental feasibility. Our results provide a unifying principle for resource-efficient non-Gaussian state generation, charting a practical route toward scalable optical quantum technologies and fault-tolerant quantum computation.

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arXiv2025

Nonlinear squeezing of superpositions of quadrature eigenstates

We introduce a family of operators exploiting the symmetry of superpositions of quadrature eigenstates (SQE) and demonstrate how the associated nonlinear squeezing, quantified by the expectation value of such operators, serves both as a witness of non-Gaussianity and as an indicator of the quality of SQE approximations. To establish the usefulness of this measure, we connect it to quantum state fidelity and evaluate its implications in breeding protocols. Finally, we construct optimal approximations of SQE states in truncated Fock spaces.

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arXiv2025

Optical states with higher stellar rank

Quantum non-Gaussian states of traveling light fields are crucial components of quantum information processing protocols; however, their preparation is experimentally challenging. In this paper, we discuss the minimal requirements imposed on the quantum efficiency of photon number resolving detectors and the quality of the squeezing operation in an experimental realization of certifiable quantum non-Gaussian states of individual photonic states with three, four, and five photons.

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arXiv2025

Nullifiers of non-Gaussian cluster states through homodyne measurement

In continuous variable optical platforms, large-scale Gaussian cluster states have already been demonstrated, but non-Gaussian resources are essential to achieve universality and fault tolerance in measurement-based quantum computation. However, characterizing and certifying non-Gaussian cluster states remains an outstanding challenge. Here, we introduce a general framework for the characterization of non-Gaussian cluster states based on non-Gaussian nullifiers, extending the widely used Gaussian nullifier concept. We show that these nullifiers can be directly evaluated from homodyne measurement data, making them experimentally accessible. As an illustration, we derive and experimentally demonstrate non-Gaussian nullifiers for photon-subtracted squeezed states. Our results provide a practical and operational tool for certifying quantum non-Gaussianity in large-scale optical cluster states.

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arXiv2025

Catability as a metric for evaluating superposed coherent states

Superposed coherent states are central to quantum technologies, yet their reliable identification remains a challenge, especially in noisy or resource-constrained settings. We introduce a novel, directly measurable criterion for detecting cat-like features in quantum states, rooted in the concept of nonlinear squeezing. This approach bypasses the need for full state tomography and reveals structure where fidelity fails. The numerical results confirm its robustness under loss and its potential for experimental implementation. The method naturally generalizes to more exotic superpositions, including multiheaded cat states.

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arXiv2025

Generalized squeezing as a witness

Quantum systems can be prepared in an infinite continuum of states, but only some of them can be used as resources for quantum technologies. Discerning whether a specific quantum state falls into this class, is often a challenging task. We show that it can be performed by looking at the squeezing of the quantum states - a scenario in which the variance of some observable operator is suppressed below the threshold given by the non-useful states. We discuss the general concept first; then we illustrate the approach by evaluating cubic nonlinear squeezing in the system of collective atomic spins.

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arXiv2025

Genuine Continuous Quantumness

Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus is currently shifting towards genuinely quantum non-Gaussian states. However, while genuine quantum behavior comes naturally to discrete variable systems, its preparation and verification are difficult in continuous ones. Simultaneously, a unifying theoretical framework based on the continuous nature is missing. Here, we introduce nonlinear squeezing as a general framework to describe and verify genuine quantumness in the noise of continuous quantum states. Using this approach, we certify the non-Gaussianity of experimentally prepared multi-photon-added coherent states of light for the first time. Chiefly, we demonstrated the nonlinear squeezing corresponding to third- and fifth-order quantum nonlinearities, going significantly beyond the current state-of-the-art in quantum technology. This framework enables uncovering intricate quantum properties in cutting-edge experiments and provides an efficient tool for further development of quantum technologies.

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arXiv2025

High-Rate Four Photon Subtraction from Squeezed Vacuum: Preparing Cat State for Optical Quantum Computation

Generating logical qubits, essential for error detection and correction in quantum computation, remains a critical challenge in continuous-variable (CV) optical quantum information processing. The Gottesman-Kitaev-Preskill (GKP) code is a leading candidate for logical qubits, and its generation requires large-amplitude coherent state superpositions -- Schr\"{o}dinger cat states. However, experimentally producing these resource states has been hindered in the optical domain by technical challenges. The photon subtraction method, a standard approach for generating cat states using a squeezed vacuum and a photon number-resolving detector, has proven difficult to scale to multi-photon operations. While the amplitude of the generated cat states increases with the number of subtracted photons, limitations in the generation rate have restricted the maximum photon subtraction to $n=3$ for over a decade. In this work, we demonstrate high-rate photon subtraction of up to four photons from a squeezed vacuum with picosecond wavepackets generated by a broadband optical parametric amplifier. Using a Ti-Au superconducting-transition-edge sensor, we achieve high-speed, high-resolution photon number discrimination. The resulting states exhibit Wigner function negativity without loss correction, and their quantum coherence is verified through off-diagonal density matrix elements in CV representation. These results overcome long-standing limitations in multi-photon operations, providing a critical foundation for generating quantum resources essential for fault-tolerant quantum computing and advancing ultrafast optical quantum processors.

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arXiv2024

Nonlinear squeezing generation via multimode PDC and single photon measurement

Nonlinear squeezing is a property of non-Gaussian states of light with an important application in continuous variable quantum computing. We study the generation of nonlinear squeezing in multimode systems produced by the photon-added coherent state technique. We present a protocol and find a regime in which the nonlinear squeezing appears in two modes simultaneously, even for a weak non-Gaussianity induced by the single-photon addition. We explore the properties of nonlinear squeezing depending on the modal structure of light, as well as the seed and local oscillator profiles, and present an optimal measurement strategy.

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arXiv2024

Adapting coherent-state superpositions in noisy channels

Quantum non-Gaussian states are crucial for the fundamental understanding of non-linear bosonic systems and simultaneously advanced applications in quantum technologies. In many bosonic experiments the important quantum non-Gaussian feature is the negativity of the Wigner function, a cornerstone for quantum computation with bosons. Unfortunately, the negativities present in complex quantum states are extremely vulnerable to the effects of decoherence, such as energy loss, noise and dephasing, caused by the coupling to the environment, which is an unavoidable part of any experimental implementation. An efficient way to mitigate its effects is by adapting quantum states into more resilient forms. We propose an optimal protection of superpositions of coherent states against a sequence of asymmetric thermal lossy channels by suitable squeezing operations.

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