arXiv subjects

Jaromír Fiurášek

Publications and source records attributed to Jaromír Fiurášek.

At least 19 recordsLinked to original sources

arXiv2026

Direct estimation of $g^{(2)}(0)$ from click statistics of a multiplexed detector

We present and theoretically analyze a method for direct estimation of the second-order correlation function $g^{(2)}(0)$ from the click statistics of a multiplexed detector composed of M binary on-off detection channels. The method uses linear estimators of the first and second moments of the photon-number operator and can provide accurate results even for optical fields with substantial mean photon numbers. For a fixed number of channels, the detection range can be extended by introducing additional losses before the detector. We demonstrate the performance of the method for coherent, thermal, amplitude-squeezed, and photon-added coherent states. We also derive a nonclassicality criterion based on the estimated correlation function and show how the method can be adapted to unbalanced detectors. Our work establishes direct estimation of $g^{(2)}(0)$ as a simple and versatile method for quantitatively characterizing quantum light using multiplexed click detectors.

quant-ph↗

arXiv2026

Heralding probability optimization for nonclassical light generated by photon counting measurements on multimode Gaussian states

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.

quant-ph↗

arXiv2026

Maximum heralding probabilities of nonclassical-state generation from a two-mode Gaussian state via photon-counting measurements

Highly nonclassical states of light - such as the approximate Gottesman-Kitaev-Preskill states, states exhibiting cubic nonlinear squeezing, or cat-like states - can be generated from experimentally accessible Gaussian states via photon counting measurements on selected modes, conditioned on specific outcomes of these heralding events. A simplest yet important example of this approach involves performing photon number measurements on one mode of a two-mode entangled Gaussian state. The heralding probability of this scheme is a key figure of merit, as it determines the generation rate of the target nonclassical state. In this work we show that the maximum heralding probability for the two-mode setting can be calculated analytically, and we investigate its dependence on the number of detected photons n. Our results show that the number of required experimental trials scales only polynomially with n. Generation of highly complex optical quantum states with high stellar rank is thus in principle possible in this setting, given access to sufficiently strong squeezing.

quant-ph↗

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.

quant-ph↗

arXiv2026

Fundamental limits on determination of photon number statistics from measurements with multiplexed on/off detectors

We investigate fundamental bounds on the ability to determine photon number distribution and other related quantities from tomographically incomplete measurements with an array of M detectors that can only distinguish the absence or presence of photons. We show that the lower and upper bounds on photon number probabilities can be determined by solving a linear program. We present and discuss numerical results for various input states including thermal states, coherent states, squeezed states, and highly non-classical single-photon subtracted squeezed vacuum states. Besides photon number probabilities we also investigate bounds on the parity of photon number distribution that determines the value of Wigner function of the state at the origin of phase space. Moreover, we also discuss estimation of mean photon number as an example of a quantity described by an unbounded operator. Our approach and results can provide quantitative guidance on the number of detection channels required to determine the photon number distribution with a given precision.

quant-ph↗

arXiv2026

Certification of stellar ranks of quantum states of light with a pair of click detectors

Stellar rank of quantum state of light quantifes the amount of non-Gaussian resources required for its generation. One popular and practical approach to certification of stellar rank is based on measurement of click statistics with an array of binary detectors that can only distinguish the presence and absence of photons. Specifically, it was shown that measurements with an array of m+1 detectors allow one to certify stellar rank m of approximate Fock state $|m\rangle$, even when the state is subjected to losses or certain noise. Here we address the question as to how many click detectors are in principle required to certify stellar ranks higher than one. We show that two click detectors arranged in a Hanbury Brown-Twiss setup suffice. Interestingly, detection of stellar ranks higher than one is greatly facilitated by making the total detection efficiency of the detectors sufficiently low but well calibrated. Losses affect the response of the detection scheme in a way that can be exploited to certify stellar rank of higher Fock states. We explicitly construct the corresponding stellar rank witnesses and discuss dependence of the stellar rank thresholds on parameters of the considered setup. Our results reveal that it is possible to certify stellar ranks higher than 1 even with a minimalistic scheme that provides only very coarse-grained information about the photon number statistics of the characterized state.

quant-ph↗

arXiv2025

Simplified scheme for continuous-variable entanglement distillation: multicopy distillation of Gaussian entanglement without heralding Gaussian measurements

Entanglement of continuous-variable Gaussian states can be distilled by combination of de-Gaussifying operation such as single-photon subtraction and iterative heralded Gaussification. Here we present and analyze a simplified equivalent version of such entanglement distillation protocol, where the Gaussian measurements utilized in heralded Gaussification are eliminated and are absorbed into the preparation of suitable input Gaussian states of the simplified protocol. The simplified scheme contains less detectors and its overall success probability increases in comparison with the original scheme, while producing completely equivalent outputs. Our simplification of the entanglement distillation protocol closely parallels the recently proposed simplification of a scheme for breeding optical single-mode Gottesman-Kitaev-Preskill states [H. Aghaee Rad et al., Nature 638, 912 (2025)]. We investigate operation of the simplified entanglement distillation scheme for both pure and mixed input states and clarify how multicopy distillation of Gaussian entanglement emerges in a setup without any heralding Gaussian measurements.

quant-ph↗

arXiv2025

Extended analysis of distillation and purification of squeezed states of light

Squeezed states of light are one of the most important fundamental resources for quantum optics, optical quantum information processing and quantum sensing. Recently, it has been experimentally demonstrated that the squeezing of single-mode squeezed vacuum states can be enhanced by probabilistic two-photon subtraction. A further enhancement of the squeezing is subsequently possible by heralded Gaussification that distills a Gaussian state from the de-Gaussified two-photon subtracted state. Here we provide an extended theoretical analysis of squeezing distillation and purification. We consider a more general scheme in which photon subtraction is combined with a weak coherent displacement. This more flexible scheme allows to enhance squeezing for arbitrary input squeezing value. Moreover, if the modified two-photon subtraction operation is properly chosen, then arbitrary strong squeezing can be distilled by subsequent Gaussification. We go beyond pure states and show that the combination of photon subtraction and heralded Gaussification cannot suppress losses that have affected the input state. To overcome this limitation, we propose an alternative de-Gaussifying operation based on a Fock-state filter that removes the single-photon state. With this de-Gaussifying operation and subsequent re-Gaussification, pure single-mode squeezed states can be distilled from a large class of mixed input states. Interestingly, we have found that squeezing distillation by two-photon subtraction is closely related to certain methods for generating Gottesman-Kitaev-Preskill (GKP) states, which are crucial for optical quantum computing.

quant-ph↗

arXiv2024

Efficient construction of witnesses of stellar rank of nonclassical states of light

The stellar hierarchy of quantum states of light classifies the states according to the Fock-state resources that are required for their generation together with unitary Gaussian operations. States with stellar rank n can be also equivalently referred to as genuinely n-photon quantum non-Gaussian states. Here we present an efficient method for construction of general witnesses of the stellar rank. The number of parameters that need to be optimized in order to determine the witness does not depend on the stellar rank and it scales quadratically with the number of modes. We illustrate the procedure by constructing stellar rank witnesses based on pairs of Fock state probabilities and also based on pairs of fidelities with superpositions of coherent states.

quant-ph↗

arXiv2024

Experimental noiseless quantum amplification of coherent states of light by two-photon addition and subtraction

Noiseless quantum amplifiers are probabilistic quantum devices that enhance amplitude of coherent states without adding any noise, which has far reaching applications in quantum optics and quantum information processing. Here, we report on experimental implementation of an advanced noiseless quantum amplifier for coherent states of light that is based on conditional addition of two photons followed by conditional subtraction of two photons. We comprehensively characterize the noiselessly amplified coherent states via quantum state tomography and analyze the amplification gain and noise properties of the amplifier. We observe very good agreement between the experiment and theoretical predictions. Our work reveals that sequences of multiple photon additions and subtractions represent an efficient and experimentally feasible alternative to multiplexing that was originally proposed to boost the performance of noiseless quantum amplifiers. Beyond noiseless quantum amplification, our experiment represents a significant step forward towards engineering complex quantum operations on traveling light beams by coherent combinations of various sequences of multiphoton additions and subtractions.

quant-ph↗

arXiv2024

Experimental investigation of heralded Gaussification of phase-randomized coherent states of light

Probabilistic heralded Gaussification of quantum states of light is an important ingredient of protocols for distillation of continuous variable entanglement and squeezing. An elementary step of heralded Gaussification protocol consists of interference of two copies of the state at a balanced beam splitter, followed by conditioning on outcome of a suitable Gaussian quantum measurement on one output mode. When iterated, the protocol either converges to a Gaussian state, or diverges. Here we report on experimental investigation of the convergence properties of iterative heralded Gaussification. We experimentally implement two iterations of the protocol, which requires simultaneous processing of four copies of the input state. We utilize the phase-randomized coherent states as the input states, which greatly facilitates the experiment, because these states can be generated deterministically and their mean photon number can easily be tuned. We comprehensively characterize the input and partially Gaussified states by balanced homodyne detection and quantum state tomography. Our experimental results are in good agreement with theoretical predictions and they provide new insights into the convergence properties of heralded quantum Gaussification.

quant-ph↗

arXiv2024

Experimental preparation of multiphoton-added coherent states of light

Conditional addition of photons represents a crucial tool for optical quantum state engineering and it forms a fundamental building block of advanced quantum photonic devices. Here we report on experimental implementation of the conditional addition of several photons. We demonstrate the addition of one, two, and three photons to input coherent states with various amplitudes. The resulting highly nonclassical photon-added states are completely characterized with time-domain homodyne tomography, and the nonclassicality of the prepared states is witnessed by the negativity of their Wigner functions. We experimentally demonstrate that the conditional addition of photons realizes approximate noiseless quantum amplification of coherent states with sufficiently large amplitude. We also investigate certification of the stellar rank of the generated multiphoton-added coherent states, which quantifies the non-Gaussian resources required for their preparation. Our results pave the way towards the experimental realization of complex optical quantum operations based on combination of multiple photon additions and subtractions.

quant-ph↗

arXiv2022

Quantum non-Gaussianity certification of photon-number-resolving detectors

We report on direct experimental certification of the quantum non-Gaussian character of a photon-number resolving detector. The certification protocol is based on an adaptation of the existing quantum non-Gaussianity criteria for quantum states to quantum measurements. In our approach, it suffices to probe the detector with a vacuum state and two different thermal states to test its quantum non-Gaussianity. The certification is experimentally demonstrated for the detector formed by a spatially multiplexed array of ten single-photon avalanche photodiodes. We confirm the quantum non-Gaussianity of POVM elements $\hatΠ_m$ associated with the $m$-fold coincidence counts, up to $m=7$. The experimental ability to certify from the first principles the quantum non-Gaussian character of $\hatΠ_m$ is for large $m$ limited by low probability of the measurement outcomes, especially for vacuum input state. We find that the injection of independent Gaussian background noise into the detector can be helpful and may reduce the measurement time required for reliable confirmation of quantum non-Gaussianity. In addition, we modified and experimentally verified the quantum non-Gaussianity certification protocol employing a third thermal state instead of a vacuum to speed up the whole measurement. Our findings demonstrate the existence of efficient tools for the practical characterization of fundamental non-classical properties and benchmarking of complex optical quantum detectors.

physics.optics↗

arXiv2021

Teleportation-based noiseless quantum amplification of coherent states of light

We propose and theoretically analyze a teleportation-based scheme for high-fidelity noiseless quantum amplification of coherent states of light. In our approach, the probabilistic noiseless quantum amplification operation is encoded into a suitable auxiliary two-mode entangled state and then applied to the input coherent state via continuous-variable quantum teleportation. The scheme requires conditioning on the outcomes of homodyne measurements in the teleportation protocol. In contrast to high-fidelity noiseless quantum amplifiers based on combination of conditional single-photon addition and subtraction, the present scheme requires only photon subtraction in combination with auxiliary Gaussian squeezed vacuum states. We first provide a pure-state description of the protocol which allows us to to clearly explain its principles and functioning. Next we develop a more comprehensive model based on phase-space representation of quantum states, that accounts for various experimental imperfections such as excess noise in the auxiliary squeezed states or limited efficiency of the single-photon detectors that can only distinguish the presence or absence of photons. We present and analyze predictions of this phase-space model of the noiseless tele-amplifier.

quant-ph↗

arXiv2021

Experimental demonstration of optimal probabilistic enhancement of quantum coherence

We theoretically and experimentally investigate conditional enhancement of overall coherence of quantum states by probabilistic quantum operations that apply to the input state a quantum filter diagonal in the basis of incoherent states. We identify the optimal filters that for a given probability of successful filtering maximize the output coherence. We verify the performance of the studied quantum filters in a proof-of-principle experiment with linear optics, where a pair of two-level quantum systems is represented by polarization states of two photons. We comprehensively characterize the implemented two-qubit linear optical quantum filters by full quantum process tomography and we experimentally observe the optimal quantum coherence enhancement by quantum filtering.

quant-ph↗

arXiv2021

Quantum non-Gaussianity criteria based on vacuum probabilities of original and attenuated state

Quantum non-Gaussian states represent an important class of highly non-classical states whose preparation requires quantum operations or measurements beyond the class of Gaussian operations and statistical mixing. Here we derive criteria for certification of quantum non-Gaussianity based on probability of vacuum in the original quantum state and a state transmitted through a lossy channel with transmittance T. We prove that the criteria hold for arbitrary multimode states, which is important for their applicability in experiments with broadband sources and single-photon detectors. Interestingly, our approach allows to detect quantum non-Gaussianity using only one photodetector instead of complex multiplexed photon detection schemes, at the cost of increased experimental time. We also formulate a quantum non-Gaussianity criterion based on the vacuum probability and mean photon number of the state and we show that this criterion is closely related to the criteria based on pair of vacuum probabilities. We illustrate the performance of the obtained criteria on the example of realistic imperfect single-photon states modeled as a mixture of vacuum and single-photon states with background Poissonian noise.

quant-ph↗

arXiv2021

Optimal implementation of two-qubit linear optical quantum filters

We design optimal interferometric schemes for implementation of two-qubit linear optical quantum filters diagonal in the computational basis. The filtering is realized by interference of the two photons encoding the qubits in a multiport linear optical interferometer, followed by conditioning on presence of a single photon in each output port of the filter. The filter thus operates in the coincidence basis, similarly to many linear optical unitary quantum gates. Implementation of the filter with linear optics may require an additional overhead in terms of reduced overall success probability of the filtering and the optimal filters are those that maximize the overall success probability. We discuss in detail the case of symmetric real filters and extend our analysis also to asymmetric and complex filters.

quant-ph↗

arXiv2021

Direct experimental certification of quantum non-Gaussian character and Wigner function negativity of single-photon detectors

Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical states.

quant-ph↗