Prof. dr hab. Antoni Wójcik
 Tel: +48 61 829 5004
 Loc: wing E, second floor, room 206
 Email: antwoj@amu.edu.pl
 URL: http://antwoj.home.amu.edu.pl/#/home
Scientific degrees
Title of professor – 2013
Habilitation – 2003
PhD in physics – 1992
Research interests
keywords: quantum information, quantum walk
Our research concentrates on:
1. Protocols of portbased teleportation
2. Thermodynamics of small quantum systems (heat engines and solar cells)
3. Topological effects in quantum walks
4. Relation between trapping of particles and Maxwell demon
4. Quantum error correction
Publications
2023 

4.  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. 
3.  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. 
2022 

2.  Andrzej Grudka, Antoni Wójcik Comment on 'Quantum principle of relativity' New J. Phys., 24 (9), pp. 098001, 2022. @article{Grudka2022, title = {Comment on 'Quantum principle of relativity'}, author = { Andrzej Grudka and Antoni Wójcik }, url = {https://iopscience.iop.org/article/10.1088/13672630/ac924e/meta}, doi = {10.1088/13672630/ac924e}, year = {2022}, date = {20221003}, journal = {New J. Phys.}, volume = {24}, number = {9}, pages = {098001}, abstract = {Recently Dragan and Ekert (2020 New. J. Phys. 22 033038) presented arguments that probabilistic dynamics inherent in the realm of quantum physics is related to the propagation of superluminal particles. Moreover they argue that existence of such particles is a natural consequence of the principle of relativity. We show that the proposed extension of the Lorentz transformation can be interpreted in a natural way without invoking superluminal phenomena.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Recently Dragan and Ekert (2020 New. J. Phys. 22 033038) presented arguments that probabilistic dynamics inherent in the realm of quantum physics is related to the propagation of superluminal particles. Moreover they argue that existence of such particles is a natural consequence of the principle of relativity. We show that the proposed extension of the Lorentz transformation can be interpreted in a natural way without invoking superluminal phenomena. 
2021 

1.  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. 