@article{Grudka2023,
title = {Superluminal observers do not explain quantum superpositions},
author = {Andrzej Grudka and Jȩdrzej Stempin and Jan Wójcik and Antoni Wójcik},
url = {https://www.sciencedirect.com/science/article/pii/S0375960123005078},
doi = {10.1016/j.physleta.2023.129127},
year = {2023},
date = {2023-11-05},
journal = {Physics Letters A},
volume = {487},
pages = {129127},
abstract = {The quantum description of reality is quite different from the classical one. Understanding this difference at a fundamental level is still an interesting topic. Recently, Dragan and Ekert (2020) postulated that considering so-called superluminal observers can be useful in this context. In particular, they claim that the full mathematical structure of the generalized Lorentz transformation may imply the emergence of multiple quantum mechanical trajectories. On the contrary, here we show that the generalized Lorentz transformation, when used in a consistent way, does not provide any correspondence between the classical concept of a definite path and the multiple paths of quantum mechanics.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{grudka23-2,
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 = {10.1088/1751-8121/acdcd0},
year = {2023},
date = {2023-06-19},
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 discrete-time quantum walks (QWs) on d-cycles with a position and coin-dependent phase-shift. 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 phase-shift 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 D-dimensional Hilbert space (D = 2d), obey |⟨vq|v ′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 one-dimensional Dirac particle.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@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 = {2023-03-01},
journal = {Physical Review A},
volume = {107},
pages = {032201},
abstract = {Discrete-time 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
so-called split-step 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 translation-symmetric 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}
}

@article{Grudka2022,
title = {Comment on 'Quantum principle of relativity'},
author = { Andrzej Grudka and Antoni Wójcik },
url = {https://iopscience.iop.org/article/10.1088/1367-2630/ac924e/meta},
doi = {10.1088/1367-2630/ac924e},
year = {2022},
date = {2022-10-03},
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}
}

@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 = {2021-12-10},
journal = {Physical Review E},
volume = {104},
pages = {064114},
abstract = {We study quantum Maxwell's demon in a discrete space-time setup. We consider a collection of particles hopping on a one-dimensional 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}
}