arXiv subjects

Gniewomir Sarbicki

Publications and source records attributed to Gniewomir Sarbicki.

At least 19 recordsLinked to original sources

arXiv2026

Finite-size Entanglement Certification via Third-Order Local Randomized Measurements

Certifying entanglement in high-dimensional systems usually requires full state tomography, whose cost grows rapidly with the system dimension. Local randomized measurements offer a scalable alternative, but existing tests based on second-order correlations access only limited information about the state. Here, we derive a finite-size entanglement certificate that extends local randomized measurements to third order. The additional third-order information reveals entanglement that remains undetected at second order, while a dimension-independent concentration bound provides rigorous control of finite-sample errors. Our result opens a practical route to extracting stronger entanglement information from experimental platforms without the dimension-dependent overhead of state tomography.

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arXiv2026

Optimization of two-photon excitation by indistinguishable photons in a three-level atom

We investigate the excitation of a three-level ladder-type atom by a unidirectional field with a pair of indistinguishable photons. Starting from an analytical expression for the two-photon absorption probability, we determine the two-photon state that maximizes the population of the upper atomic state at a chosen time and show that in the limit of an infinitely long pulse, perfect excitation is possible. The optimal state is identified as the time-reversed counterpart of the two-photon state emitted in spontaneous cascade decay. We then compare this ideal excitation strategy with experimentally accessible families of states, including symmetrized Gaussian product states, temporally correlated Gaussian states, and coherent pulses. We analyze how the optimal excitation conditions depend on the ratio of atomic decay rates and on the separation of the atomic transition frequencies. For indistinguishable photons, quantum interference may shift the maxima of the marginal spectral distribution away from the atomic resonances and qualitatively modify the optimal excitation strategy. Our results clarify the role of indistinguishability and correlations in two-photon absorption and provide guidance for designing realistic excitation schemes in quantum-optical light-matter interfaces.

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arXiv2026

Third-Order Local Randomized Measurements for Finite-size Entanglement Certification

Randomized measurements access nonlinear functionals without full tomography, yet turning third-order local single-copy data into a strong entanglement test remains difficult. We convert the reduction criterion into an experimentally measurable separability criterion by testing it on squared affine combinations of the identity, the local marginals, and the state itself. This yields a $4\times4$ matrix $\bar{\mathfrak{M}}(ρ)$ built from experimentally accessible second- and third-order local invariants. Entanglement is certified when its minimum eigenvalue $\mathcal{E}_4(ρ)$ becomes negative. We prove that all separable states satisfy $\bar{\mathfrak{M}}(ρ)\succeq0$, and that the sign of $\mathcal{E}_4(ρ)$ can be inferred from single-copy randomized measurements with dimension-independent sample complexity. For isotropic states on $d\times d$, the second-order purity criterion detects entanglement only for $p\sim d^{-1/2}$, whereas our third-order witness reaches $p\sim 2/d$, close to the separability threshold $p\sim 1/d$. A complementary nonisotropic benchmark shows that the affine marginal directions become essential once the local states are not maximally mixed.

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arXiv2025

Entanglement detection via third-order local invariants from randomized measurements

We compute all third-order local invariants accessible via randomised measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite states with arbitrary local dimensions. The results show that third-order invariants capture inter-subsystem correlations beyond second-order spectral criteria within more feasible entanglement detection protocols than full tomography. As an example, Werner states in $d=3$ the entanglement is detected for $p>\frac 12$ at the second-order correlations, and it is improved to $p>\frac 1{\sqrt[3]{10}}$ at the third-order.

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arXiv2025

Optimization of two-photon absorption for three-level atom

This work discusses the problem of optimal excitation of a three-level atom of ladder-configuration by light in the two-photon state and coherent light carrying an average of two photons. The applied atom-light interaction model is based on the Wigner-Weisskopf approximation. We characterize the properties of the optimal two-photon state that excites an atom perfectly, i.e. with probability equal to one: We find that the spectro-temporal shape of the optimal state of light is determined by the lifetimes of the atomic states, with the degree of photonic entanglement in the optimal state depends on the lifetime ratio. In consequence, two distinct interaction regimes can be identified in which the entanglement of the input state of light has qualitatively different impact. As the optimal states may be challenging to prepare in general, we compare the results with those obtained for photon pairs of selected experimentally-relevant pulse shapes. As these shapes are optimized for maximal atomic excitation probability, the results can be interpreted in terms of the overlap between the optimal and investigated pulse shapes.

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arXiv2025

Quantum trajectories and output field properties for two-photon input field

The excitation of atomic and molecular systems by propagating light in a two-photon state within the Wigner-Weisskopf approximation has been described using stochastic tools. The problem of a stochastic evolution of the quantum system, depending on the results of the measurement of the output field, was formulated and solved making use of the model of repeated interactions and measurement. We defined the discrete in-time interaction between the quantum system and its environment being the electromagnetic field approximated by a chain or chains of harmonic oscillators. We determined analytical formulae for quantum trajectories associated with one-dimensional and two-dimensional counting processes, corresponding respectively to unidirectional or bidirectional input field prepared in the two-photon states. We derived the formulae for the exclusive probability densities of photon counts that allow us to completely characterize the photon statistics of the output field. Finally, we showed how to apply the quantum trajectories to obtain the formula for the probability of the two-photon absorption for a three-level atom in a ladder configuration. The paper also includes a discussion on the optimal two-photon state that maximizes the two-photon absorption probability.

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arXiv2024

Signatures of superradiance in intensity correlation measurements in a two-emitter solid-state system

We perform intensity correlation ($g^{(2)}(τ)$) measurements on nitrogen-vacancy (NV) emitters embedded in diamond nanopillars. We observe an increase in transition rates from both the singlet and triplet states by a factor of $\approx 6$, indicating cooperative effects between the multiple emitters in the pillar, at room temperature. We simultaneously observe a $g^{(2)}(0) > 0.5 (\to 1$) as opposed to $g^{(2)}(0) < 0.5$ for others (and as expected for single emitters), indicating the presence of at least two emitters. Furthermore, we observe a triple exponential behaviour for the $g^{(2)}$ in contrast to the standard double exponential behaviour seen for single NV emitters. To understand our experimental observations, we developed a theoretical model. We solve the Lindblad master equation, tailored for single and two NV centers, to study their dissipative dynamics when coupled to a common electromagnetic field, at a finite temperature. Through this, we identify superradiant emission from a two-emitter system as the most likely explanation for our observed data. We also find that random number generation using the coupled emitter system performs better under the NIST test suite and explain it in terms of an entropy-driven model for a coupled emitter system. Our results provide a new signature for multiphotonic states, such as superradiant states, using intensity correlation measurements, that will become important for quantum photonic technologies progress.

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arXiv2023

Optimality of generalized Choi maps in $M_3$

A family of linear positive maps in the algebra of $3 \times 3$ complex matrices proposed recently in Bera et al. arXiv:2212.03807 is further analyzed. It provides a generalization of a seminal Choi nondecomposable extremal map in $M_3$. We investigate when generalized Choi maps are optimal, i.e. cannot be represented as a sum of positive and completely positive maps. This property is weaker than extremality, however, it turns out that it plays a key role in detecting quantum entanglement.

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arXiv2023

Optimizing positive maps in the matrix algebra $M_n$

We present an optimization procedure for a seminal class of positive maps $τ_{n,k}$ in the algebra of $n \times n$ complex matrices introduced and studied by Tanahasi and Tomiyama, Ando, Nakamura and Osaka. Recently, these maps were proved to be optimal whenever the greatest common divisor $GCD(n,k)=1$. We attain a general conjecture how to optimize a map $τ_{n,k}$ when $GCD(n,k)=2$ or 3. For $GCD(n,k)=2$, a series of analytical results are derived and for $GCD(n,k)=3$, we provide a suitable numerical analysis.

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arXiv2023

Synchronized Bell protocol for detecting non-locality between modes of light

In the following paper, we discuss a possible detection of non-locality in two-mode light states in the Bell protocol, where the local observables are constructed using displacement operators, implemented by Mach-Zender Interferometers fed by strong coherent states. We report numerical results showing that maximizing the Braunstein-Caves Chained Bell (BCCB) inequalities requires equal phases of displacements. On the other hand, we prove that non-locality cannot be detected if the phases of displacements are unknown. Hence, the Bell experiment has to be equipped with a synchronization mechanism. We discuss such a mechanism and its consequences.

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arXiv2023

A class of optimal positive maps in $M_n$

It is proven that a certain class of positive maps in the matrix algebra $M_n$ consists of optimal maps, i.e. maps from which one cannot subtract any completely positive map without loosing positivity. This class provides a generalization of a seminal Choi positive map in $M_3$.

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arXiv2022

Generalizing Choi map in $M_3$ beyond circulant scenario

We present a generalization of the family of linear positive maps in $M_3$ proposed thirty years ago by Cho et al. (Linear Algebra Appl. ${\bf 171}$, 213 (1992)) as a generalization of the seminal Choi non-decomposable map. The necessary and sufficient conditions for decomposability are provided.

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arXiv2022

Detecting Entanglement Between Modes of Light

We consider a subgroup of unitary transformations on a mode of light induced by a Mach-Zehnder Interferometer and an algebra of observables describing a photon-number detector proceeded by an interferometer. We explore the uncertainty principles between such observables and their usefulness in performing a Bell-like experiment to show a violation of the CHSH inequality, under physical assumption that the detector distinguishes only zero from non-zero number of photons. We show which local settings of the interferometers lead to a maximal violation of the CHSH inequality.

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arXiv2021

A class of Bell diagonal entanglement witnesses in $\mathbb{C}^4 \otimes \mathbb{C}^4$: optimization and the spanning property

Two classes of Bell diagonal indecomposable entanglement witnesses in $\mathbb{C}^4 \otimes \mathbb{C}^4$ are considered. Within the first class, we find a generalization of the well-known Choi witness from $\mathbb{C}^3 \otimes \mathbb{C}^3$, while the second one contains the reduction map. Interestingly, contrary to $\mathbb{C}^3 \otimes \mathbb{C}^3$ case, the generalized Choi witnesses are no longer optimal. We perform an optimization procedure of finding spanning vectors, that eventually gives rise to optimal witnesses. Operators from the second class turn out to be optimal, however, without the spanning property. This analysis sheds a new light into the intricate structure of optimal entanglement witnesses.

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arXiv2021

Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket

An evolution of a two-level system (qubit) interacting with a single-photon wave packet is analyzed. It is shown that a hierarchy of master equations gives rise to phase covariant qubit evolution. The temporal correlations in the input field induce nontrivial memory effects for the evolution of a qubit. It is shown that in the resonant case whenever time-local generator is regular (does not display singularities) the qubit evolution never displays information backflow. However, in general the generator might be highly singular leading to intricate non-Markovian effects. A detailed analysis of the exponential profile is provided which allows to illustrate all characteristic feature of the qubit evolution.

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arXiv2020

Detection power of separability criteria based on a correlation tensor: a case study

Detection power of separability criteria based on a correlation tensor is tested within a family of generalized isotropic state in $d_1 \otimes d_2$. For $d_1 \neq d_2$ all these criteria are weaker than positive partial transposition (PPT) criterion. Interestingly, our analysis supports the recent conjecture that a criterion based on symmetrically informationaly complete positive operator-valued measure (SIC-POVMs) is stronger than realignment criterion.

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arXiv2020

On the Alberti-Uhlmann Condition for Unital Channels

We address the problem of existence of completely positive trace preserving (CPTP) maps between two sets of density matrices. We refine the result of Alberti and Uhlmann and derive a necessary and sufficient condition for the existence of a unital channel between two pairs of qubit states which ultimately boils down to three simple inequalities.

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arXiv2020

Enhanced realignment criterion vs. linear entanglement witnesses

It is shown that the enhanced (nonlinear) realignment criterion is equivalent to the family of linear criteria based on correlation tensor. These criteria generalize the original (linear) realignment criterium and give rise to the family of entanglement witnesses. An appropriate limiting procedure is proposed which leads to a novel class of witnesses which are as powerful as the enhanced realignment criterion.

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