arXiv subjects

Paweł Kurzyński

Publications and source records attributed to Paweł Kurzyński.

15 recordsLinked to original sources

arXiv2026

Unitary Realizations of Synchronizing Automata in Quantum Systems

We introduce a quantum analogue of a classical synchronizing automaton. In classical case the state of a system evolves according to a set of rules forming an alphabet, and sequences of these rules, called words, govern its evolution. Certain special words, known as synchronizing words, drive the automaton into a predetermined state regardless of its initial configuration. Although such an apparently irreversible process seems incompatible with the unitarity of quantum mechanics, we present a resetting protocol based on quantum synchronizing words by incorporating auxiliary qubits whose states encode the rules of the automaton's alphabet. These qubits interact with the quantum automaton, whose state is encoded in a qudit, via a global unitary operation. When the qubit register is initially prepared in a state corresponding to a synchronizing word, the automaton evolves into a predetermined pure state independent of its initial state, while the qubit register is transformed into a complex, often entangled, state that encodes information about the automaton's original configuration. The resulting entanglement depends on both the rule set and the automaton's initial state, and we show how specific entangled states can be generated within this framework.

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arXiv2025

Rabi transport and the other finite-size effects in one-dimensional discrete-time topological quantum walk

This paper investigates Rabi transport and finite-size effects in one-dimensional discrete-time topological quantum walks. We demonstrate the emergence of localized states at boundaries between topologically distinct phases and analyze how finite system sizes influence quantum walk dynamics. For finite lattices, we show that topology induces localized and bilocalized states, leading to Rabi-like transport as a result of degeneracy breaking due to finite-size effects. The study bridges the gap between topological protection and size-dependent dynamics, revealing transitions from ballistic motion to localized or oscillatory behavior based on the system's topological properties. Analytical and numerical methods are employed to explore the spectra and dynamics of quantum walks, highlighting the robustness of Rabi transport against disorder. The findings provide insights into controlled quantum transport and potential applications in quantum information processing.

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arXiv2025

Genuine monogamy relations in no-signaling theories - a geometric approach

Quantum correlations are subject to certain distribution rules represented by so-called monogamy relations. Derivation of monogamy relations for multipartite systems is a non-trivial problem, as the multipartite correlations reveal their behaviors in a way different from bipartite systems. We here show that simple geometric properties of probabilistic spaces, in conjunction with no-signaling principle, lead to genuine monogamy relations for a large class of Bell type inequalities for many qubits. The term of 'genuine' implies that only one out of $N$ Bell inequalities exhibits a quantum violation. We also generalize our method to qudits. Using the similar geometric approach with a quasi-distance employed, we derive Svetlichny-Zohren-Gill type Bell inequalities for $d$-dimensional tripartite systems, and show their monogamous nature.

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arXiv2025

Bi-Contextuality: A Novel Non-Classical Phenomenon in Bipartite Quantum Systems

We present and experimentally demonstrate a novel non-classical phenomenon, bi-contextuality, observed in quantum systems prepared by two independent sources. This discovery plays a key role in the developing framework of network nonlocality, offering a new method for confirming the quantum nature of measurements within a single network node. Bi-contextuality acts as a reversed Bell scenario: while Bell scenarios involve splitting a system for independent measurements, our approach combines systems from separate independent sources for joint measurements. The outcomes defy classical models that assume independence and non-contextuality. The simplest Bell scenario can be seen as a subset of the Peres-Mermin (PM) square, and our phenomenon represents another important subset of this framework. Moreover, bi-contextuality has notable consequences related to the Pusey-Barrett-Rudolph (PBR) theorem, suggesting that classical psi-ontic models must account for contextuality or the dependence of preparations, challenging established assumptions.

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arXiv2025

Quantum Resetting Protocols Based on Synchronizing Words

Resetting a system's state plays a fundamental role in physics, engineering, computer science, and many other fields. Here we focus on a method originally proposed in automata theory. The state of an automaton evolves according to a set of rules. These rules form an alphabet, and one can apply these rules one after another. Such a sequence of rules is known as a word. Some particular words, known as synchronizing words, enable a system to evolve into a predetermined state regardless of its initial configuration. This process, which is inherently irreversible, appears at first glance to be incompatible with the unitarity of quantum mechanics. Unitary evolution preserves information, hence forbids such classical resetting to a predetermined state. In this work, we introduce a novel resetting protocol based on quantum-synchronizing words by incorporating auxiliary qubits whose states encode rules of the automaton's alphabet. We further propose a quantum circuit that realizes this protocol and can be implemented on a quantum computer. Additionally, we establish a connection between this approach and Kraus channels, showing that quantum synchronizing words can be achieved without explicit reference to the states of ancillary qubits. Our results bridge classical and quantum notions of synchronizing words, shedding light on the interplay between quantum information processing and non-unitary dynamics.

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arXiv2025

Quantum Synchronizing Words: Resetting and Preparing Qutrit States

Synchronizing words in classical automata theory provide a mechanism to reset any state of a deterministic automaton to a specific target state via a carefully chosen finite sequence of transition rules. In this work, we extend the concept of synchronizing words to quantum information theory. Specifically, we show that with only two quantum channels, it is possible to bring an arbitrary qutrit state close to a designated target state. Furthermore, we demonstrate that following this reset, any pure real qutrit state can be closely approximated using the same two channels. These findings establish a quantum analogue of synchronizing words, highlighting their potential applications in constructing minimal sets of universal quantum gates capable of both resetting and preparing arbitrary states.

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arXiv2024

Exploring Many-body Interactions Through Quantum Fisher Information

The investigation of many-body interactions holds significant importance in both quantum foundations and information. Hamiltonians coupling multiple particles at once, beyond others, can lead to a faster entanglement generation, multiqubit gate implementation and improved error correction. As an increasing number of quantum platforms enable the realization of such physical settings, it becomes interesting to study the verification of many-body interaction resources. In this work, we explore the possibility of higher-order couplings detection through the quantum Fisher information. For a family of symmetric and translationally invariant $k$-body Ising-like Hamiltonians, we derive the bounds on the quantum Fisher information in product states. Due to its ordering with respect to the order of interaction, we demonstrate the possibility of detecting many-body couplings for a given Hamiltonian from the discussed family by observing violations of an appropriate bound. As a possible extension to these observations, we further analyse an example concerning the three-body interaction detection in the XY model.

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arXiv2023

The fastest generation of multipartite entanglement with natural interactions

Natural interactions among multiple quantum objects are fundamentally composed of two-body terms only. In contradistinction, single global unitaries that generate highly entangled states typically arise from Hamiltonians that couple multiple individual subsystems simultaneously. Here, we study the time to produce strongly nonclassical multipartite correlations with a single unitary generated by the natural interactions. We restrict the symmetry of two-body interactions to match the symmetry of the target states and focus on the fastest generation of multipartite entangled Greenberger-Horne-Zeilinger (GHZ), W, Dicke and absolutely maximally entangled (AME) states for up to seven qubits. These results are obtained by constraining the energy in the system and accordingly can be seen as state-dependent quantum speed limits for symmetry-adjusted natural interactions. They give rise to a counter-intuitive effect where the creation of particular entangled states with an increasing number of particles does not require more time. The methods used rely on extensive numerical simulations and analytical estimations.

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arXiv2023

Exposing Hypersensitivity in Quantum Chaotic Dynamics

We demonstrate that the unitary dynamics of a multi-qubit system can display hypersensitivity to initial state perturbation. This contradicts the common belief that the classical approach based on the exponential divergence of initially neighboring trajectories cannot be applied to identify chaos in quantum systems. To observe hypersensitivity we use quantum state-metric, introduced by Girolami and Anza in [Phys. Rev. Lett. 126 (2021) 170502], which can be interpreted as a quantum Hamming distance. As an example of a quantum system, we take the multi-qubit implementation of the quantum kicked top, a paradigmatic system known to exhibit quantum chaotic behavior. Our findings confirm that the observed hypersensitivity corresponds to commonly used signatures of quantum chaos. Furthermore, we demonstrate that the proposed metric can detect quantum chaos in the same regime and under analogous initial conditions as in the corresponding classical case.

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arXiv2021

Transition from order to chaos in reduced quantum dynamics

We study a damped kicked top dynamics of a large number of qubits ($N \rightarrow \infty$) and focus on an evolution of a reduced single-qubit subsystem. Each subsystem is subjected to the amplitude damping channel controlled by the damping constant $r\in [0,1]$, which plays the role of the single control parameter. In the parameter range for which the classical dynamics is chaotic, while varying $r$ we find the universal period-doubling behavior characteristic to one-dimensional maps: period-two dynamics starts at $r_1 \approx 0.3181$, while the next bifurcation occurs at $ r_2 \approx 0.5387$. In parallel with period-four oscillations observed for $r \leq r_3 \approx 0.5672$, we identify a secondary bifurcation diagram around $r\approx 0.544$, responsible for a small-scale chaotic dynamics inside the attractor. The doubling of the principal bifurcation tree continues until $r \leq r_{\infty} \sim 0.578$, which marks the onset of the full scale chaos interrupted by the windows of the oscillatory dynamics corresponding to the Sharkovsky order.

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arXiv2018

Genuine multipartite indistinguishability and its detection via generalized Hong-Ou-Mandel effect

The question whether two indistinguishable particles are bosons or fermions can be answered by observing the Hong-Ou-Mandel effect on a beam splitter. However, already for three particles one can consider symmetries that are neither bosonic nor fermionic. In this work, we describe a simple method of identifying them experimentally and propose a measure of a genuine multipartite indistinguishability.

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arXiv2015

Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons

Quantum walk (QW) provides a versatile tool to study fundamental physics and also to make a variety of practical applications. We here start with the recent idea of {\it nonlinear} QW and show that introducing {\it nonlinearity} to QW can lead to a wealth of remarkable possibilities, e.g., simulating nonlinear quantum dynamics thus enhancing the applicability of QW above the existing level for a universal quantum simulator. As an illustration, we show that the dynamics of a nonlinear Dirac particle can be simulated on an optical nonlinear QW platform implemented with a measurement-based-feedforward scheme. The nonlinear evolution induced by the feed-forward introduces a self-coupling mechanism to (otherwise linear) Dirac particles, which accordingly behave as a \emph{soliton}. We particularly consider two kinds of nonlinear Dirac equations, one with a scalar-type self-coupling (Gross-Neveu model) and the other with a vector-type one (Thirring model), respectively. Using their known stationary solutions, we confirm that our nonlinear QW framework is capable of exhibiting characteristic features of a soliton. Furthermore, we show that the nonlinear QW enables us to observe and control an enhancement and suppression of the ballistic diffusion.

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arXiv2015

Heisenberg's error-disturbance relations: a joint measurement-based experimental test

The Heisenberg's error-disturbance relation is a cornerstone of quantum physics. It was recently shown to be not universally valid and two different approaches to reformulate it were proposed.The first one focuses on how error and disturbance of two observables, A and B, depend on a particular quantum state. The second one asks how a joint measurement of A and B affects their eigenstates. Previous experiments focused on the first approach. Here, we focus on the second one. Firstly, we propose and implement an extendible method for quantum walk-based joint measurements of noisy Pauli operators to test the error-disturbance relation for qubits. Then, we formulate and experimentally test a new universally valid relation for the three mutually unbiased observables. We therefore establish a fundamentally new method of testing error-disturbance relations.

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arXiv2015

Quantum leap: how to complete a quantum walk in a single step

Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and measurements of non-classical multi-particle correlations is likely to reveal the quantum nature. The number of elements $O(n)$ in a setup realizing walks grows with their length or spread $n$. We introduce the concept of a quantum leap, a process which can be achieved with fewer or complementary resources and which in a single step simulates another long process. The process and its leap are described by the same Hamiltonian but, the latter parametrizes the evolution with a tunable parameter of a setup. In the case of walks, a leap immediately gives a probability distribution which results only after many steps. This may be appealing for simulation of processes which are lengthy or require dynamical control. We discuss a leap based on the multi-particle Hong--Ou--Mandel interference, an inherently quantum phenomenon. It reproduces a quantum walk enabling perfect state transfer through spin chains. It requires a beam splitter, two detectors and $n$ particles to mimic a walk on a chain of size $O(n)$, for time fixed by beam-splitter's reflectivity. Our results apply to a broad class of systems where the HOM-like effects can be observed, and may constitute a new approach to simulation of complex Hamiltonians with passive interferometers.

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arXiv2015

Probing quantum-classical boundary with compression software

We experimentally demonstrate that it is impossible to simulate quantum bipartite correlations with a deterministic universal Turing machine. Our approach is based on the Normalized Information Distance (NID) that allows the comparison of two pieces of data without detailed knowledge about their origin. Using NID, we derive an inequality for output of two local deterministic universal Turing machines with correlated inputs. This inequality is violated by correlations generated by a maximally entangled polarization state of two photons. The violation is shown using a freely available lossless compression program. The presented technique may allow to complement the common statistical interpretation of quantum physics by an algorithmic one.

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