arXiv subjects

Pavel Sekatski

Publications and source records attributed to Pavel Sekatski.

At least 37 records · Page 2Linked to original sources

arXiv2025

Noise-robust proofs of quantum network nonlocality

Quantum networks allow for novel forms of quantum nonlocality. By exploiting the combination of entangled states and entangled measurements, strong nonlocal correlations can be generated across the entire network. So far, all proofs of this effect are essentially restricted to the idealized case of pure entangled states and projective local measurements. Here we present noise-robust proofs of network quantum nonlocality, for a class of quantum distributions on the triangle network that are based on entangled states and entangled measurements. The key ingredient is a result of approximate rigidity for local distributions that satisfy the so-called ``parity token counting'' property with high probability. Our methods can be applied to any type of noise. As illustrative examples, we consider quantum distributions obtained with imperfect sources and obtain a noise robustness up to $\sim 80\%$ for dephasing noise and up to $\sim 0.5\%$ for white noise. Additionally, we prove that all distributions in the vicinity of some ideal quantum distribution are nonlocal, with a bound on the total-variation distance $\sim 0.25\%$. Our work opens interesting perspectives towards the practical implementation of quantum network nonlocality.

quant-ph↗

arXiv2025

On the entropy growth of sums of iid discrete random variables

We derive an asymptotic lower bound on the Shannon entropy $H$ of sums of $N$ arbitrary iid discrete random variables. The derived bound $H \geq \frac{r(X)}{2}\log(N) + {\it cst}$ is given in terms of the incommensurability rank $r(X)$ of the random variable -- a positive integer quantity that we introduce. The derivation does not rely on central limit theorems, but builds upon the known expressions of the asymptotic entropy of the multinomial distribution and sums of iid lattice random variables, which correspond to the case $r(X)=1$.

cs.IT↗

arXiv2025

From dynamical to steady-state many-body metrology: Precision limits and their attainability with two-body interactions

We consider the estimation of an unknown parameter $θ$ via a many-body probe. The probe is initially prepared in a product state and many-body time-independent interactions enhance its $θ$-sensitivity during the dynamics and/or in the steady state. We present bounds on the Quantum Fisher Information, and corresponding optimal interacting Hamiltonians, for two paradigmatic scenarios for encoding~$θ$: (i)~via unitary Hamiltonian dynamics (dynamical metrology), and (ii)~in the Gibbs and diagonal ensembles (time-averaged dephased state), two ubiquitous steady states of many-body open dynamics. We then move to the specific problem of estimating the strength of a magnetic field via interacting spins and derive two-body interacting Hamiltonians that can approach the fundamental precision bounds. In this case, we additionally analyze the transient regime leading to the steady states and characterize tradeoffs between equilibration times and measurement precision. Overall, our results provide a comprehensive picture of the potential of many-body control in quantum sensing.

quant-ph↗

arXiv2025

Certification of quantum correlations and DIQKD at arbitrary distances through routed Bell tests

Transmission loss represents a major obstacle to the device-independent certification of quantum correlations over long distances, limiting applications such as device-independent quantum key distribution (DIQKD). In this work, we investigate the recently proposed concept of routed Bell experiments, in which a particle sent to one side can be measured either near or far from the source. We prove that routed Bell tests involving only entangled qubits can certify quantum correlations even in the presence of arbitrary loss on the channel to the distant device. This is achieved by adapting concepts from self-testing and quantum steering to the routed Bell test framework. Finally, as a natural extension of our approach, we outline a DIQKD protocol that, in principle, is secure over arbitrary distances.

quant-ph↗

arXiv2025

An information-theoretic proof of the Planckian bound for thermalization

We demonstrate that quantum mechanics entails a fundamental lower bound on the thermalization time $τ$ of any system. At finite temperature, we show that $τ$ is bounded by half the Planckian dissipation time, $τ\geq τ_{\rm Pl}/2$ with $τ_{\rm Pl} = \hbar/(k_{\rm B} T)$. In the low-temperature regime, our bound takes the form $τ\geq \hbar / Δ$ with $Δ$ the spectral gap, in close connection with the quantum adiabatic theorem. These bounds, rooted in Hamiltonian estimation, hold for arbitrary quantum processes that output states close to the corresponding thermal ensemble for a nontrivial class of Hamiltonians.

quant-ph↗

arXiv2025

Bell nonlocality in quantum networks with unreliable sources: Loophole-free postelection via self-testing

We discuss Bell nonlocality in quantum networks with unreliable sources. Our main result is a condition on the observed data which ensures that inconclusive events can be safely discarded, without introducing any loophole. More formally, we characterize the fair-sampling property for measurements in a network. When all measurements are fair-sampling, we show that the post-selection of conclusive outcomes does not compromise the assumption of source independence, hence avoiding the detection loophole. Furthermore, we show that in some cases, the fair-sampling property can in fact be guaranteed based only on observed data. To show this, we prove that saturation of the Finner inequality provides a self-test of the underlying quantum model. We illustrate the relevance of our results by demonstrating an improvement in device-independent randomness generation for a photonic Bell test with a probabilistic source and for the triangle network.

quant-ph↗

arXiv2024

Joint-measurability and quantum communication with untrusted devices

Photon loss represents a major challenge for the implementation of quantum communication protocols with untrusted devices, e.g. in the device-independent (DI) or semi-DI approaches. Determining critical loss thresholds is usually done in case-by-case studies. In the present work, we develop a general framework for characterizing the admissible levels of loss and noise in a wide range of scenarios and protocols with untrusted measurement devices. In particular, we present general bounds that apply to prepare-and-measure protocols for the semi-DI approach, as well as to Bell tests for DI protocols. A key step in our work is to establish a general connection between quantum protocols with untrusted measurement devices and the fundamental notions of channel extendibility and joint-measurability, which capture essential aspects of the communication and measurement of quantum information. In particular, this leads us to introduce the notion of partial joint-measurability, which naturally arises within quantum cryptography.

quant-ph↗

arXiv2024

Selective and noise-resilient wave estimation with quantum sensor networks

We consider the selective sensing of planar waves in the presence of noise. We present different methods to control the sensitivity of a quantum sensor network, which allow one to decouple it from arbitrarily selected waves while retaining sensitivity to the signal. Comparing these methods with classical (non-entangled) sensor networks we demonstrate two advantages. First, entanglement increases precision by enabling the Heisenberg scaling. Second, entanglement enables the elimination of correlated noise processes corresponding to waves with different propagation directions, by exploiting decoherence-free subspaces. We then provide a theoretical and numerical analysis of the advantage offered by entangled quantum sensor networks, which is not specific to waves and can be of general interest. We demonstrate an exponential advantage in the regime where the number of sensor locations is comparable to the number of noise sources. Finally, we outline a generalization to other waveforms, e.g., spherical harmonics and general time-dependent fields.

quant-ph↗

arXiv2024

Fundamental limits of metrology at thermal equilibrium

We consider the estimation of an unknown parameter $θ$ through a quantum probe at thermal equilibrium. The probe is assumed to be in a Gibbs state according to its Hamiltonian $H_θ$, which is divided in a parameter-encoding term $H^{\rm P}_θ$ and an additional, parameter-independent, control $H^{\rm C}$. Given a fixed encoding, we find the maximal Quantum Fisher Information attainable via arbitrary $H^{\rm C}$, which provides a fundamental bound on the measurement precision. We elucidate the role of quantum coherence between encoding and control in different temperature regimes, which include ground state metrology as a limiting case. In the case of locally-encoded parameters, the optimal sensitivity presents a $N^2$-scaling in terms of the number of particles of the probe, which can be reached, at finite temperature, with local measurements and no entanglement. We apply our results to paradigmatic spin chain models, showing that these fundamental limits can be approached using local two-body interactions. Our results set the fundamental limits and optimal control for metrology with thermal and ground state probes, including probes at the verge of criticality.

quant-ph↗

arXiv2024

Information plane and compression-gnostic feedback in quantum machine learning

The information plane (Tishby et al. arXiv:physics/0004057, Shwartz-Ziv et al. arXiv:1703.00810) has been proposed as an analytical tool for studying the learning dynamics of neural networks. It provides quantitative insight on how the model approaches the learned state by approximating a minimal sufficient statistics. In this paper we extend this tool to the domain of quantum learning models. In a second step, we study how the insight on how much the model compresses the input data (provided by the information plane) can be used to improve a learning algorithm. Specifically, we consider two ways to do so: via a multiplicative regularization of the loss function, or with a compression-gnostic scheduler of the learning rate (for algorithms based on gradient descent). Both ways turn out to be equivalent in our implementation. Finally, we benchmark the proposed learning algorithms on several classification and regression tasks using variational quantum circuits. The results demonstrate an improvement in test accuracy and convergence speed for both synthetic and real-world datasets. Additionally, with one example we analyzed the impact of the proposed modifications on the performances of neural networks in a classification task.

quant-ph↗

arXiv2024

Quantum computation with logical gates between hot systems

We consider quantum computer architectures where interactions are mediated between hot qubits that are not in their mechanical ground state. Such situations occur, e.g., when not cooling ideally, or when moving ions or atoms around. We introduce quantum gates between logically encoded systems that consist of multiple physical ones and show how the encoding can be used to make these gates resilient against such imperfections. We demonstrate that, in this way, one can improve gate fidelities by enlarging the logical system, and counteract the effect of unknown positions or position fluctuations of involved particles. We consider both a classical treatment of positions in terms of probability distributions, as well a quantum treatment using mechanical eigenmodes. We analyze different settings including a cool logical system mediating interactions between two hot systems, as well as two logical systems consisting of hot physical systems whose positions fluctuate collectively or individually. In all cases, we demonstrate a significant improvement of gate fidelities, which provides a platform-independent tool to mitigate thermal noise.

quant-ph↗

arXiv2024

Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations

Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal protocol, i.e., the most precise one. It has been solved for some specific instances of the problem, but in general even numerical methods are not known. Here, we focus on the single-shot Bayesian setting, where the goal is to find the optimal initial state of the probe (which can be entangled with an auxiliary system), the optimal measurement, and the optimal estimator function. We leverage the formalism of higher-order operations to develop a method based on semidefinite programming that finds a protocol that is close to the optimal one with arbitrary precision. Crucially, our method is not restricted to any specific quantum evolution, cost function or prior distribution, and thus can be applied to any estimation problem. Moreover, it can be applied to both single or multiparameter estimation tasks. We demonstrate our method with three examples, consisting of unitary phase estimation, thermometry in a bosonic bath, and multiparameter estimation of an SU(2) transformation. Exploiting our methods, we extend several results from the literature. For example, in the thermometry case, we find the optimal protocol at any finite time and quantify the usefulness of entanglement.

quant-ph↗

arXiv2024

Topologically Robust Quantum Network Nonlocality

We discuss quantum network Bell nonlocality in a setting where the network structure is not fully known. More concretely, an honest user may trust their local network topology, but not the structure of the rest of the network, involving distant (and potentially dishonest) parties. We demonstrate that quantum network nonlocality can still be demonstrated in such a setting, hence exhibiting topological robustness. Specifically, we present quantum distributions obtained from a simple network that cannot be reproduced by classical models, even when the latter are based on more powerful networks. In particular, we show that in a large ring network, the knowledge of only a small part of the network structure (involving only 2 or 3 neighbouring parties) is enough to guarantee nonlocality over the entire network. This shows that quantum network nonlocality can be extremely robust to changes in the network topology. Moreover, we demonstrate that applications of quantum nonlocality, such as the black-box certification of randomness and entanglement, are also possible in such a setting.

quant-ph↗

arXiv2024

Custom Bell inequalities from formal sums of squares

Bell inequalities play a key role in certifying quantum properties for device-independent quantum information protocols. It is still a major challenge, however, to devise Bell inequalities tailored for an arbitrary given quantum state. Existing approaches based on sums of squares provide results in this direction, but they are restricted by the necessity of first choosing measurement settings suited to the state. Here, we show how the sum of square property can be enforced for an arbitrary target state by making an appropriate choice of nullifiers, which is made possible by leaving freedom in the choice of measurement. Using our method, we construct simple Bell inequalities for several families of quantum states, including partially entangled multipartite GHZ states and qutrit states. In most cases we are able to prove that the constructed Bell inequalities achieve self-testing of the target state. We also use the freedom in the choice of measurement to self-test partially entangled two-qubit states with a family of settings with two parameters. Finally, we show that some statistics can be self-tested with distinct Bell inequalities, hence obtaining new insight on the shape of the set of quantum correlations.

quant-ph↗

arXiv2024

Towards a minimal example of quantum nonlocality without inputs

The network scenario offers interesting new perspectives on the phenomenon of quantum nonlocality. Notably, when considering networks with independent sources, it is possible to demonstrate quantum nonlocality without the need for measurements inputs, i.e. with all parties performing a fixed quantum measurement. Here we aim to find minimal examples of this effect. Focusing on the minimal case of the triangle network, we present examples involving output cardinalities of $3-3-3$ and $3-3-2$. Finally, we discuss the prospects of finding an example of quantum nonlocality in the triangle network with binary outputs, and point out a connection to the Lovasz local lemma.

quant-ph↗

arXiv2023

An exponentially-growing family of universal quantum circuits

Quantum machine learning has become an area of growing interest but has certain theoretical and hardware-specific limitations. Notably, the problem of vanishing gradients, or barren plateaus, renders the training impossible for circuits with high qubit counts, imposing a limit on the number of qubits that data scientists can use for solving problems. Independently, angle-embedded supervised quantum neural networks were shown to produce truncated Fourier series with a degree directly dependent on two factors: the depth of the encoding and the number of parallel qubits the encoding applied to. The degree of the Fourier series limits the model expressivity. This work introduces two new architectures whose Fourier degrees grow exponentially: the sequential and parallel exponential quantum machine learning architectures. This is done by efficiently using the available Hilbert space when encoding, increasing the expressivity of the quantum encoding. Therefore, the exponential growth allows staying at the low-qubit limit to create highly expressive circuits avoiding barren plateaus. Practically, parallel exponential architecture was shown to outperform the existing linear architectures by reducing their final mean square error value by up to 44.7% in a one-dimensional test problem. Furthermore, the feasibility of this technique was also shown on a trapped ion quantum processing unit.

quant-ph↗

arXiv2023

Improved DIQKD protocols with finite-size analysis

The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on noisy preprocessing, random key measurements, and modified CHSH inequalities. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of $9.33\%$, exceeding all previously known noise thresholds. We also develop a modification to random-key-measurement protocols, using a pre-shared seed followed by a "seed recovery" step, which yields substantially higher net key generation rates by essentially removing the sifting factor. Some of our results may also improve the keyrates of device-independent randomness expansion.

quant-ph↗

arXiv2023

Optimal distributed multiparameter estimation in noisy environments

We consider the task of multiple parameter estimation in the presence of strong correlated noise with a network of distributed sensors. We study how to find and improve noise-insensitive strategies. We show that sequentially probing GHZ states is optimal up to a factor of at most 4. This allows us to connect the problem to single parameter estimation, and to use techniques such as protection against correlated noise in a decoherence-free subspace, or read-out by local measurements.

quant-ph↗