arXiv subjects

Jan Wojcik

Publications and source records attributed to Jan Wojcik.

4 recordsLinked to original sources

arXiv2026

Scalable Test of Genuine Multipartite Entanglement via Partially Randomized Measurements

Certifying genuine multipartite entanglement in quantum systems can require a number of measurements that grows exponentially with the system size. Here we introduce a criterion based on correlation-tensor subsector lengths restricted to local measurement planes and show that it can be evaluated using partially randomized measurements without an explicit exponential dependence on the number of qubits. We derive the corresponding bounds for $k$-separable states and illustrate the criterion using representative families of multipartite entangled states. Finally, we demonstrate the practical applicability of the method on an ion-trap quantum computer by certifying genuine five-partite entanglement.

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arXiv2026

Permutation asymmetry unlocks emergent advantage in randomized Bell tests

All maximally entangled two-qubit states violate local realism with the same probability under uniformly random projective measurements, yet they need not behave identically in randomized Bell tests. We show that when measurement settings are exchanged between the parties in sequential Bell experiments, permutation symmetry of the shared state determines the statistical relation between the two realizations. Permutationally invariant states yield identical nonlocality outcomes in both experiments, whereas asymmetric states can violate local realism in one realization but not in the other. This distinction leads to two operational consequences. First, it enables the detection of correlations between the measurement choices of Alice and Bob through the joint violation statistics. Second, in Bell tests with finite measurement pools, asymmetric maximally entangled states can significantly increase the probability of observing nonlocality without requiring additional resources. Our results identify permutation asymmetry as a useful feature in randomized Bell experiments and highlight a new role of symmetry in quantum nonlocality.

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arXiv2022

Relative homotopy approach to topological phases in quantum walks

Discrete-time quantum walks (DTQWs) provide a convenient platform for a realisation 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 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 new topological invariant corresponding to this concept. This invariant indicates the number of edge states at the interface between two distinct phases.

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arXiv2022

Complementarity in quantum walks

We study discrete-time quantum walks 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 $d$ there exists a strong complementarity property between the eigenvectors of two quantum walk evolution operators that act in the $2d$-dimensional Hilbert space. Namely, if $d$ is prime the corresponding eigenvectors of the evolution operators obey $|\langle v_q|v'_{q'} \rangle| \leq 1/\sqrt{d}$ for $q\neq q'$ and for all $|v_q\rangle$ and $|v'_{q'}\rangle$. We also discuss dynamical consequences of this complementarity. Finally, we show that the complementarity is still present in the continuous version of this model, which corresponds to a one-dimensional Dirac particle.

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