Dr hab. Paweł Kurzyński, prof. UAM
 Tel: +48 61 829 5055
 Loc: wing E, second floor, room 216
 Email: pawel.kurzynski@amu.edu.pl
Scientific degrees
Habilitation in Physics – 2015
PhD in Physics – 2007
MSc in Physics – 2005
Research interests
keywords: foundations of quantum theory, quantum dynamics
Foundations of quantum theory: contextuality and nonlocality, Bell inequalities, negative “probabilities”, entanglement, identical particles
Quantum dynamics: discrete quantum dynamics, quantum cellular automata, nonlinear quantum dynamics, quantum chaos, quantum synchronisa7on, dynamics of composite quantum objects
Interview with Prof. Kurzyński on Youtube.
Scientific achievements
(2016 – present) Visiting Senior Research Fellow (Centre for Quantum Technologies, Singapore)
(2015 – 2017) Scholarship for Talented Young Researchers (Ministry of Science and Higher Educa7on, Poland)
(2013 – present) Member of the Foundational Questions Institute (FQxI, USA)
(2010 – 2015) PostDoc (Centre for Quantum Technologies, Singapore)
Publications
2023 

6.  Andrzej Grudka, Paweł Kurzyński, Tomasz P Polak, Adam S Sajna, Jan Wójcik, Antoni Wójcik Complementarity in quantum walks Journal of Physics A, 56 , pp. 275303, 2023. @article{grudka232, title = {Complementarity in quantum walks}, author = {Andrzej Grudka and Paweł Kurzyński and Tomasz P Polak and Adam S Sajna and Jan Wójcik and Antoni Wójcik}, doi = {10.1088/17518121/acdcd0}, year = {2023}, date = {20230619}, journal = {Journal of Physics A}, volume = {56}, pages = {275303}, abstract = {The eigenbases of two quantum observables, {ai⟩}Di=1 and {bj⟩}Dj=1, form mutually unbiased bases (MUB) if ⟨ai bj⟩ = 1/ √D for all i and j. In realistic situations MUB are hard to obtain and one looks for approximate MUB (AMUB), in which case the corresponding eigenbases obey ⟨ai bj⟩ ⩽ c/√D, where c is some positive constant independent of D. In majority of cases observables corresponding to MUB and AMUB do not have clear physical interpretation. Here we study discretetime quantum walks (QWs) on dcycles with a position and coindependent phaseshift. Such a model simulates a dynamics of a quantum particle moving on a ring with an artificial gauge field. In our case the amplitude of the phaseshift is governed by a single discrete parameter q. We solve the model analytically and observe that for prime d the eigenvectors of two QW evolution operators form AMUB. Namely, if d is prime the corresponding eigenvectors of the evolution operators, that act in the Ddimensional Hilbert space (D = 2d), obey ⟨vqv ′q ′ ⟩ ⩽√2/√D for q ̸= q ′ and for all vq⟩ and v ′q ′ ⟩. Finally, we show that the analogous AMUB relation still holds in the continuous version of this model, which corresponds to a onedimensional Dirac particle.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The eigenbases of two quantum observables, {ai⟩}Di=1 and {bj⟩}Dj=1, form mutually unbiased bases (MUB) if ⟨ai bj⟩ = 1/ √D for all i and j. In realistic situations MUB are hard to obtain and one looks for approximate MUB (AMUB), in which case the corresponding eigenbases obey ⟨ai bj⟩ ⩽ c/√D, where c is some positive constant independent of D. In majority of cases observables corresponding to MUB and AMUB do not have clear physical interpretation. Here we study discretetime quantum walks (QWs) on dcycles with a position and coindependent phaseshift. Such a model simulates a dynamics of a quantum particle moving on a ring with an artificial gauge field. In our case the amplitude of the phaseshift is governed by a single discrete parameter q. We solve the model analytically and observe that for prime d the eigenvectors of two QW evolution operators form AMUB. Namely, if d is prime the corresponding eigenvectors of the evolution operators, that act in the Ddimensional Hilbert space (D = 2d), obey ⟨vqv ′q ′ ⟩ ⩽√2/√D for q ̸= q ′ and for all vq⟩ and v ′q ′ ⟩. Finally, we show that the analogous AMUB relation still holds in the continuous version of this model, which corresponds to a onedimensional Dirac particle. 
5.  Andrzej Grudka, Marcin Karczewski, Paweł Kurzyński, Jan Wójcik, Antoni Wójcik Topological invariants in quantum walks Physical Review A, 107 , pp. 032201, 2023. @article{grudka23, title = {Topological invariants in quantum walks}, author = {Andrzej Grudka and Marcin Karczewski and Paweł Kurzyński and Jan Wójcik and Antoni Wójcik}, doi = {10.1103/PhysRevA.107.032201}, year = {2023}, date = {20230301}, journal = {Physical Review A}, volume = {107}, pages = {032201}, abstract = {Discretetime quantum walks (DTQWs) provide a convenient platform for a realization of many topological phases in noninteracting systems. They often offer more possibilities than systems with a static Hamiltonian. Nevertheless, researchers are still looking for DTQW symmetries protecting topological phases and for definitions of appropriate topological invariants. Although the majority of DTQW studies on this topic focus on the socalled splitstep quantum walk, two distinct topological phases can be observed in more basic models. Here we infer topological properties of the basic DTQWs directly from the mapping of the Brillouin zone to the Bloch Hamiltonian. We show that for translationsymmetric systems they can be characterized by a homotopy relative to special points. We also propose a topological invariant corresponding to this concept. This invariant indicates the number of edge states at the interface between two distinct phases.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Discretetime quantum walks (DTQWs) provide a convenient platform for a realization of many topological phases in noninteracting systems. They often offer more possibilities than systems with a static Hamiltonian. Nevertheless, researchers are still looking for DTQW symmetries protecting topological phases and for definitions of appropriate topological invariants. Although the majority of DTQW studies on this topic focus on the socalled splitstep quantum walk, two distinct topological phases can be observed in more basic models. Here we infer topological properties of the basic DTQWs directly from the mapping of the Brillouin zone to the Bloch Hamiltonian. We show that for translationsymmetric systems they can be characterized by a homotopy relative to special points. We also propose a topological invariant corresponding to this concept. This invariant indicates the number of edge states at the interface between two distinct phases. 
2021 

4.  Andrzej Grudka, Paweł Kurzyński, Antoni Wójcik Quantum semipermeable barriers: Investigating Maxwell's demon toolbox Physical Review E, 104 , pp. 064114, 2021. @article{Grudka2021, title = {Quantum semipermeable barriers: Investigating Maxwell's demon toolbox}, author = {Andrzej Grudka and Paweł Kurzyński and Antoni Wójcik}, url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.064114}, doi = {10.1103/PhysRevE.104.064114}, year = {2021}, date = {20211210}, journal = {Physical Review E}, volume = {104}, pages = {064114}, abstract = {We study quantum Maxwell's demon in a discrete spacetime setup. We consider a collection of particles hopping on a onedimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is a formulation of a local unitary dynamics describing the action of this barrier. Such dynamics utilizes an auxiliary system A and we study how properties of A influence the behavior of particles. An immediate consequence of unitarity is the fact that particles cannot be trapped on one side of the barrier forever, unless A is infinite. In addition, coherent superpositions and quantum correlations are affected once particles enter the confinement region. Finally, we show that initial superposition of A allows the barrier to act as a beam splitter.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study quantum Maxwell's demon in a discrete spacetime setup. We consider a collection of particles hopping on a onedimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is a formulation of a local unitary dynamics describing the action of this barrier. Such dynamics utilizes an auxiliary system A and we study how properties of A influence the behavior of particles. An immediate consequence of unitarity is the fact that particles cannot be trapped on one side of the barrier forever, unless A is infinite. In addition, coherent superpositions and quantum correlations are affected once particles enter the confinement region. Finally, we show that initial superposition of A allows the barrier to act as a beam splitter. 
3.  Paweł Kurzyński Weighted Bures length uncovers quantum state sensitivity Physical Review E, 104 , pp. L052202, 2021. @article{Kurzyński2021, title = {Weighted Bures length uncovers quantum state sensitivity}, author = {Paweł Kurzyński}, url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.L052202}, doi = {10.1103/PhysRevE.104.L052202}, year = {2021}, date = {20211118}, journal = {Physical Review E}, volume = {104}, pages = {L052202}, abstract = {The unitarity of quantum evolutions implies that an overlap between two initial states does not change in time. This property is commonly believed to explain the apparent lack of state sensitivity in quantum theory, a feature that is prevailing in classical chaotic systems. However, classical state sensitivity is based on a distance between two trajectories in phase space which is a completely different mathematical concept than an overlap between two vectors in Hilbert space. It is possible that state sensitivity in quantum theory can be detected with the help of some special metric. Here we show that the recently introduced Weighted Bures length achieves this task. We numerically investigate a unitary cellular automaton of N interacting qubits and analyze how a singlequbit perturbation affects the evolution of WBL between the unperturbed and perturbed states. We observe a linear growth of WBL if the qubits are arranged into a cyclic graph and an exponential growth if they are arranged into a random bipartite graph.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The unitarity of quantum evolutions implies that an overlap between two initial states does not change in time. This property is commonly believed to explain the apparent lack of state sensitivity in quantum theory, a feature that is prevailing in classical chaotic systems. However, classical state sensitivity is based on a distance between two trajectories in phase space which is a completely different mathematical concept than an overlap between two vectors in Hilbert space. It is possible that state sensitivity in quantum theory can be detected with the help of some special metric. Here we show that the recently introduced Weighted Bures length achieves this task. We numerically investigate a unitary cellular automaton of N interacting qubits and analyze how a singlequbit perturbation affects the evolution of WBL between the unperturbed and perturbed states. We observe a linear growth of WBL if the qubits are arranged into a cyclic graph and an exponential growth if they are arranged into a random bipartite graph. 
2.  Marcin Markiewicz, Marcin Karczewski, Paweł Kurzyński Borromean states in discretetime quantum walks Quantum, 5 , pp. 523, 2021. @article{Markiewicz2021, title = {Borromean states in discretetime quantum walks}, author = {Marcin Markiewicz and Marcin Karczewski and Paweł Kurzyński}, url = {https://quantumjournal.org/papers/q20210816523/}, doi = {10.22331/q20210816523}, year = {2021}, date = {20210816}, journal = {Quantum}, volume = {5}, pages = {523}, abstract = {In the right conditions, removing one particle from a multipartite bound state can make it fall apart. This feature, known as the "Borromean property", has been recently demonstrated experimentally in Efimov states. One could expect that such peculiar behavior should be linked with the presence of strong interparticle correlations. However, any exploration of this connection is hindered by the complexity of the physical systems exhibiting the Borromean property. To overcome this problem, we introduce a simple dynamical toy model based on a discretetime quantum walk of many interacting particles. We show that the particles described by it need to exhibit the GreenbergerHorneZeillinger (GHZ) entanglement to form Borromean bound states. As this type of entanglement is very prone to particle losses, our work demonstrates an intuitive link between correlations and Borromean properties of the system. Moreover, we discuss our findings in the context of the formation of composite particles.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In the right conditions, removing one particle from a multipartite bound state can make it fall apart. This feature, known as the "Borromean property", has been recently demonstrated experimentally in Efimov states. One could expect that such peculiar behavior should be linked with the presence of strong interparticle correlations. However, any exploration of this connection is hindered by the complexity of the physical systems exhibiting the Borromean property. To overcome this problem, we introduce a simple dynamical toy model based on a discretetime quantum walk of many interacting particles. We show that the particles described by it need to exhibit the GreenbergerHorneZeillinger (GHZ) entanglement to form Borromean bound states. As this type of entanglement is very prone to particle losses, our work demonstrates an intuitive link between correlations and Borromean properties of the system. Moreover, we discuss our findings in the context of the formation of composite particles. 
1.  XiaoXiao Chen, Zhe Meng, Jian Li, JiaZhi Yang, AnNing Zhang, Tomasz Kopyciuk, Paweł Kurzyński Nonclassical oscillations in pre and postselected quantum walks Phys. Rev. A, 104 , pp. 012220, 2021. @article{PhysRevA.104.012220, title = {Nonclassical oscillations in pre and postselected quantum walks}, author = {XiaoXiao Chen and Zhe Meng and Jian Li and JiaZhi Yang and AnNing Zhang and Tomasz Kopyciuk and Paweł Kurzyński}, url = {https://link.aps.org/doi/10.1103/PhysRevA.104.012220}, doi = {10.1103/PhysRevA.104.012220}, year = {2021}, date = {20210728}, journal = {Phys. Rev. A}, volume = {104}, pages = {012220}, publisher = {American Physical Society}, abstract = {Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet, some of their properties can be emulated with classical light. This raises a question: which aspects of the model are truly nonclassical? We address it by carrying out a photonic experiment based on a pre and postselection paradox. The paradox implies that if somebody could choose to ask either if the particle is at position x = 0 at even time steps or at position x = d (d > 1) at odd time steps, the answer would be positive, no matter the question asked. Therefore, the particle seems to undergo long distance oscillations despite the fact that the model allows it to jump one position at a time. We translate this paradox into a Belllike inequality and then into a contextuality witness. Finally, we experimentally verify this witness up to eight standard deviations.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet, some of their properties can be emulated with classical light. This raises a question: which aspects of the model are truly nonclassical? We address it by carrying out a photonic experiment based on a pre and postselection paradox. The paradox implies that if somebody could choose to ask either if the particle is at position x = 0 at even time steps or at position x = d (d > 1) at odd time steps, the answer would be positive, no matter the question asked. Therefore, the particle seems to undergo long distance oscillations despite the fact that the model allows it to jump one position at a time. We translate this paradox into a Belllike inequality and then into a contextuality witness. Finally, we experimentally verify this witness up to eight standard deviations. 