Dr hab. Karol Bartkiewicz, prof. UAM
- Tel: +48 61 829 ...
- Loc: wing G, second floor, room 288
- Email: bark@amu.edu.pl
- URL: https://bark.home.amu.edu.pl/
Scientific degrees
- Habilitation – 2019
- PhD in physics – 2012
- MSc in physics – 2008
K. Bartkiewicz earned PhD in physics in 2012 at Adam Mickiewicz University in Poznań (AMU), Poland. As of 2019, he is an associate professor at the Faculty of Physics at AMU. For ten years he has been working as a researcher (applied physics) at Palacký University in the Czech Republic. He has co-authored more than 60 publications on quantum optics, quantum information processing and quantum information, two of which on secure quantum communication protocols have been commented on in specialized (e.g. Nature Physics) and popular media (e.g. New Scientist, Science Daily, TVN 24). For the past six years, he has been working on quantum machine learning as one of the most promising applications of quantum computing.
Research interests
The scope of my scientific interests includes quantum physics and optics, more specifically:
- quantum cloning,
- quantum teleportation,
- quantum cryptography,
- quantum correlations,
- machine learning,
- optical methods of quantum information processing,
- mathematical and computational methods of physics,
- foudations of physics,
- photonics and quantum optics.
Awards
- Award of the Minister of Science for teaching activities 2024
Projects
2. | Karol Bartkiewicz Quantum Excellence Centre for Quantum-Enhanced Applications (QEC4QEA) 2025 - 2029, (European Quantum Excellence Centres (QECs) in applications for science and industry (HORIZON-EUROHPC-JU-2023-QEC-05), budget: 462 250€ [AMU]). @misc{BartkiewiczHE, title = {Quantum Excellence Centre for Quantum-Enhanced Applications (QEC4QEA)}, author = {Karol Bartkiewicz}, url = {https://eurohpc-ju.europa.eu/european-quantum-excellence-centres-qecs-applications-science-and-industry_en}, year = {2029}, date = {2029-01-01}, urldate = {2024-11-25}, abstract = {Quantum computing has the potential to revolutionize science and technology, offering breakthroughs in optimization, cryptography, machine learning, materials science, and drug discovery. However, challenges including the lack of standardized tools, specialized training, infrastructure access, and limited industrial collaboration hinder its impactful progress or adoption. The QEC4QEA project seeks to overcome these obstacles by building a unified platform to accelerate the development and integration of quantum-enhanced applications across various scientific and industrial fields. QEC4QEA will provide a suite of resources, including a hardware-agnostic application library, benchmarking tools, compilers, APIs, and curated access to high-performance computing and quantum computing infrastructures. The project will refine its capabilities through agile development while promoting cross-disciplinary collaboration. A training program and help desk will support scientists and developers, enabling them to build and integrate quantum-enhanced solutions. By focusing on applications such as complex multi-objective optimization, advanced cryptography, quantum-enhanced machine learning, accelerated materials discovery, financial crash prediction, image analysis, graph classification and routing, QEC4QEA aims to demonstrate quantum computing's practical potential. Leveraging the collective expertise of its consortium and engaging industries like finance, pharmaceuticals, and supply chain management, QEC4QEA will deliver impactful solutions for real-world needs. This outreach strategy will foster collaboration between academia and industry, translating scientific breakthroughs into commercial applications. QEC4QEA will eliminate the barriers to adoption and catalyse a rapid shift from theoretical potential to practical deployment. These deployments might then enable new pathways for quantum computing applications with accelerated societal and economic benefits.}, howpublished = {2025}, note = {European Quantum Excellence Centres (QECs) in applications for science and industry (HORIZON-EUROHPC-JU-2023-QEC-05), budget: 462 250€ [AMU]}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Quantum computing has the potential to revolutionize science and technology, offering breakthroughs in optimization, cryptography, machine learning, materials science, and drug discovery. However, challenges including the lack of standardized tools, specialized training, infrastructure access, and limited industrial collaboration hinder its impactful progress or adoption. The QEC4QEA project seeks to overcome these obstacles by building a unified platform to accelerate the development and integration of quantum-enhanced applications across various scientific and industrial fields. QEC4QEA will provide a suite of resources, including a hardware-agnostic application library, benchmarking tools, compilers, APIs, and curated access to high-performance computing and quantum computing infrastructures. The project will refine its capabilities through agile development while promoting cross-disciplinary collaboration. A training program and help desk will support scientists and developers, enabling them to build and integrate quantum-enhanced solutions. By focusing on applications such as complex multi-objective optimization, advanced cryptography, quantum-enhanced machine learning, accelerated materials discovery, financial crash prediction, image analysis, graph classification and routing, QEC4QEA aims to demonstrate quantum computing's practical potential. Leveraging the collective expertise of its consortium and engaging industries like finance, pharmaceuticals, and supply chain management, QEC4QEA will deliver impactful solutions for real-world needs. This outreach strategy will foster collaboration between academia and industry, translating scientific breakthroughs into commercial applications. QEC4QEA will eliminate the barriers to adoption and catalyse a rapid shift from theoretical potential to practical deployment. These deployments might then enable new pathways for quantum computing applications with accelerated societal and economic benefits. |
1. | Karol Bartkiewicz Kernel based quantum machine learning in optical circuits 2019 - 2021, (Czech Science Foundation (at Palacy University in Olomouc), budget: 4 875 000 CZK (~ 850 000 PLN)). @misc{Bartkiewicz2021, title = {Kernel based quantum machine learning in optical circuits}, author = {Karol Bartkiewicz}, year = {2021}, date = {2021-12-01}, abstract = {This project focuses on theoretical and experimental research on kernel-based quantum machine learning (QML) using linear optics and individual photons as information carriers. QML is crucial for future development of quantum artificial neural networks and other quantum-enhanced technologies. QML can exponentially improve machine learning (ML) vastly applied in many industries. Here, we focus on three research objectives.First task is to design quantum optical circuits and implementing assorted kernels for QML. We plan on implementing these kernels to verify the benefits of this approach to QML over other solutions described in the literature.Second part of the project is to apply QML to classification or clustering, i.e., typical supervised and unsupervised ML problems. We plan to apply QML to learning properties of a quantum system. We will be developing a fremework for explaining parameters of QML system in terms directly relevant to the investigated problem. In the third stage we plan on applying QML to generative models (creating new data based on the training data). Three research objectives will be investigated both theoretically and experimentally: (i) quantum optical circuits for QML kernel implementation, (ii) applications and explainability of QML with kernels for supervised and unsupervised learning problems, (iii) quantum generative models.}, howpublished = {2019}, note = {Czech Science Foundation (at Palacy University in Olomouc), budget: 4 875 000 CZK (~ 850 000 PLN)}, keywords = {}, pubstate = {published}, tppubtype = {misc} } This project focuses on theoretical and experimental research on kernel-based quantum machine learning (QML) using linear optics and individual photons as information carriers. QML is crucial for future development of quantum artificial neural networks and other quantum-enhanced technologies. QML can exponentially improve machine learning (ML) vastly applied in many industries. Here, we focus on three research objectives.First task is to design quantum optical circuits and implementing assorted kernels for QML. We plan on implementing these kernels to verify the benefits of this approach to QML over other solutions described in the literature.Second part of the project is to apply QML to classification or clustering, i.e., typical supervised and unsupervised ML problems. We plan to apply QML to learning properties of a quantum system. We will be developing a fremework for explaining parameters of QML system in terms directly relevant to the investigated problem. In the third stage we plan on applying QML to generative models (creating new data based on the training data). Three research objectives will be investigated both theoretically and experimentally: (i) quantum optical circuits for QML kernel implementation, (ii) applications and explainability of QML with kernels for supervised and unsupervised learning problems, (iii) quantum generative models. |
Publications
2024 |
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11. | Josef Kadlec, Karol Bartkiewicz, Antonín Černoch, Karel Lemr, Adam Miranowicz Experimental relative entanglement potentials of single-photon states Phys. Rev. A, 110 , pp. 023720, 2024. @article{PhysRevA.110.023720, title = {Experimental relative entanglement potentials of single-photon states}, author = {Josef Kadlec and Karol Bartkiewicz and Antonín Černoch and Karel Lemr and Adam Miranowicz}, url = {https://link.aps.org/doi/10.1103/PhysRevA.110.023720}, doi = {10.1103/PhysRevA.110.023720}, year = {2024}, date = {2024-08-01}, journal = {Phys. Rev. A}, volume = {110}, pages = {023720}, publisher = {American Physical Society}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
10. | Vojtiěch Trávníček, Jan Roik, Karol Bartkiewicz, Antonín Černoch, Paweł Horodecki, Karel Lemr Sensitivity versus selectivity in entanglement detection via collective witnesses Phys. Rev. Res., 6 , pp. 033056, 2024. @article{PhysRevResearch.6.033056, title = {Sensitivity versus selectivity in entanglement detection via collective witnesses}, author = {Vojtiěch Trávníček and Jan Roik and Karol Bartkiewicz and Antonín Černoch and Paweł Horodecki and Karel Lemr}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.6.033056}, doi = {10.1103/PhysRevResearch.6.033056}, year = {2024}, date = {2024-07-01}, journal = {Phys. Rev. Res.}, volume = {6}, pages = {033056}, publisher = {American Physical Society}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
9. | Anna Jelec, Karol Bartkiewicz, Katarzyna Stachowiak-Szymczak, Joanna Ziobro-Strzępek Why not(es)? Automatic analysis of notes for consecutive interpreting training Biernacka Agnieszka, Figiel Wojciech (Ed.): 18 (12), pp. 245-268, Peter Lang Verlag, Berlin, Bruxelles, Chennai, Lausanne, New York, Oxford, 2024, ISBN: 9783631907122. @inbook{UAM3e12f04642694835a7c486a6658d9b64, title = {Why not(es)? Automatic analysis of notes for consecutive interpreting training}, author = {Anna Jelec and Karol Bartkiewicz and Katarzyna Stachowiak-Szymczak and Joanna Ziobro-Strzępek}, editor = {Biernacka Agnieszka, Figiel Wojciech}, url = {https://www.peterlang.com/document/1370692}, doi = {10.3726/b21104}, isbn = {9783631907122}, year = {2024}, date = {2024-07-01}, journal = {Phys. Rev. Res.}, volume = {18}, number = {12}, pages = {245-268}, publisher = {Peter Lang Verlag}, address = {Berlin, Bruxelles, Chennai, Lausanne, New York, Oxford}, series = {Studies in Language, Culture and Society: New Insights into Interpreting Studies}, abstract = {This volume is a collective work of eighteen eminent researchers representing various sub-fields of Interpreting Studies who contribute with fourteen chapters. The topics include various areas and approaches: interpreting from a philosophical, sociological and historical perspective, ethics of interpreters, court interpreting, public service interpreting, signed language interpreting, interpreting for minors and for refugees and asylum seekers, note-taking in consecutive interpreting, accessibility, as well as technology in interpreting and interpreter training. The multiplicity of themes and the multifaceted nature of the research prove that Interpreting Studies is nowadays a field that combines different disciplines and methodologies.}, type = {book}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } This volume is a collective work of eighteen eminent researchers representing various sub-fields of Interpreting Studies who contribute with fourteen chapters. The topics include various areas and approaches: interpreting from a philosophical, sociological and historical perspective, ethics of interpreters, court interpreting, public service interpreting, signed language interpreting, interpreting for minors and for refugees and asylum seekers, note-taking in consecutive interpreting, accessibility, as well as technology in interpreting and interpreter training. The multiplicity of themes and the multifaceted nature of the research prove that Interpreting Studies is nowadays a field that combines different disciplines and methodologies. |
8. | Josef Kadlec, Karol Bartkiewicz, Antonín Černoch, Karel Lemr, Adam Miranowicz Opt. Express, 32 (2), pp. 2333–2346, 2024. @article{Kadlec:24, title = {Experimental hierarchy of the nonclassicality of single-qubit states via potentials for entanglement, steering, and Bell nonlocality}, author = {Josef Kadlec and Karol Bartkiewicz and Antonín Černoch and Karel Lemr and Adam Miranowicz}, url = {https://opg.optica.org/oe/abstract.cfm?URI=oe-32-2-2333}, doi = {10.1364/OE.506169}, year = {2024}, date = {2024-01-01}, journal = {Opt. Express}, volume = {32}, number = {2}, pages = {2333--2346}, publisher = {Optica Publishing Group}, abstract = {Entanglement potentials are a promising way to quantify the nonclassicality of single-mode states. They are defined by the amount of entanglement (expressed by, e.g., the Wootters concurrence) obtained after mixing the examined single-mode state with a purely classical state; such as the vacuum or a coherent state. We generalize the idea of entanglement potentials to other quantum correlations: the EPR steering and Bell nonlocality, thus enabling us to study mutual hierarchies of these nonclassicality potentials. Instead of the usual vacuum and one-photon superposition states, we experimentally test this concept using specially tailored polarization-encoded single-photon states. One polarization encodes a given nonclassical single-mode state, while the other serves as the vacuum place-holder. This technique proves to be experimentally more convenient in comparison to the vacuum and a one-photon superposition as it does not require the vacuum detection.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Entanglement potentials are a promising way to quantify the nonclassicality of single-mode states. They are defined by the amount of entanglement (expressed by, e.g., the Wootters concurrence) obtained after mixing the examined single-mode state with a purely classical state; such as the vacuum or a coherent state. We generalize the idea of entanglement potentials to other quantum correlations: the EPR steering and Bell nonlocality, thus enabling us to study mutual hierarchies of these nonclassicality potentials. Instead of the usual vacuum and one-photon superposition states, we experimentally test this concept using specially tailored polarization-encoded single-photon states. One polarization encodes a given nonclassical single-mode state, while the other serves as the vacuum place-holder. This technique proves to be experimentally more convenient in comparison to the vacuum and a one-photon superposition as it does not require the vacuum detection. |
7. | Jan Roik, Karol Bartkiewicz, Antonín Černoch, Karel Lemr Routing in quantum communication networks using reinforcement machine learning Quantum Information Processing, 23 (3), 2024, ISSN: 1573-1332. @article{Roik2024, title = {Routing in quantum communication networks using reinforcement machine learning}, author = {Jan Roik and Karol Bartkiewicz and Antonín Černoch and Karel Lemr}, url = {http://dx.doi.org/10.1007/s11128-024-04287-z}, doi = {10.1007/s11128-024-04287-z}, issn = {1573-1332}, year = {2024}, date = {2024-01-01}, journal = {Quantum Information Processing}, volume = {23}, number = {3}, publisher = {Springer Science and Business Media LLC}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
2023 |
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6. | Karol Bartkiewicz, Patrycja Tulewicz, Jan Roik, Karel Lemr Synergic quantum generative machine learning Scientific Reports, 13 (1), pp. 12893, 2023, ISSN: 2045-2322. @article{bartkiewicz_synergic_2023, title = {Synergic quantum generative machine learning}, author = {Karol Bartkiewicz and Patrycja Tulewicz and Jan Roik and Karel Lemr}, url = {https://www.nature.com/articles/s41598-023-40137-1}, doi = {10.1038/s41598-023-40137-1}, issn = {2045-2322}, year = {2023}, date = {2023-08-09}, urldate = {2023-10-18}, journal = {Scientific Reports}, volume = {13}, number = {1}, pages = {12893}, abstract = {We introduce a new approach towards generative quantum machine learning significantly reducing the number of hyperparameters and report on a proof-of-principle experiment demonstrating our approach. Our proposal depends on collaboration between the generators and discriminator, thus, we call it quantum synergic generative learning. We present numerical evidence that the synergic approach, in some cases, compares favorably to recently proposed quantum generative adversarial learning. In addition to the results obtained with quantum simulators, we also present experimental results obtained with an actual programmable quantum computer. We investigate how a quantum computer implementing generative learning algorithm could learn the concept of a maximally-entangled state. After completing the learning process, the network is able both to recognize and to generate an entangled state. Our approach can be treated as one possible preliminary step to understanding how the concept of quantum entanglement can be learned and demonstrated by a quantum computer.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We introduce a new approach towards generative quantum machine learning significantly reducing the number of hyperparameters and report on a proof-of-principle experiment demonstrating our approach. Our proposal depends on collaboration between the generators and discriminator, thus, we call it quantum synergic generative learning. We present numerical evidence that the synergic approach, in some cases, compares favorably to recently proposed quantum generative adversarial learning. In addition to the results obtained with quantum simulators, we also present experimental results obtained with an actual programmable quantum computer. We investigate how a quantum computer implementing generative learning algorithm could learn the concept of a maximally-entangled state. After completing the learning process, the network is able both to recognize and to generate an entangled state. Our approach can be treated as one possible preliminary step to understanding how the concept of quantum entanglement can be learned and demonstrated by a quantum computer. |
5. | Shilan Abo, Jan Soubusta, Kateřina Jiráková, Karol Bartkiewicz, Antonín Černoch, Karel Lemr, Adam Miranowicz Experimental hierarchy of two-qubit quantum correlations without state tomography Scientific Reports, 13 (1), pp. 8564, 2023, ISSN: 2045-2322. @article{abo_experimental_2023, title = {Experimental hierarchy of two-qubit quantum correlations without state tomography}, author = {Shilan Abo and Jan Soubusta and Kateřina Jiráková and Karol Bartkiewicz and Antonín Černoch and Karel Lemr and Adam Miranowicz}, url = {https://www.nature.com/articles/s41598-023-35015-9}, doi = {10.1038/s41598-023-35015-9}, issn = {2045-2322}, year = {2023}, date = {2023-05-26}, urldate = {2023-10-18}, journal = {Scientific Reports}, volume = {13}, number = {1}, pages = {8564}, abstract = {A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise. |
4. | Grzegorz Chimczak, Anna Kowalewska‑Kudłaszyk, Ewelina Lange, Karol Bartkiewicz, Jan Peřina Jr. The effect of thermal photons on exceptional points in coupled resonators. Scientific Reports, 13 , pp. 5859, 2023. @article{Chimczak2023, title = {The effect of thermal photons on exceptional points in coupled resonators.}, author = {Grzegorz Chimczak and Anna Kowalewska‑Kudłaszyk and Ewelina Lange and Karol Bartkiewicz and Jan Peřina Jr.}, url = {https://www.nature.com/articles/s41598-023-32864-2}, doi = {https://doi.org/10.1038/s41598-023-32864-2}, year = {2023}, date = {2023-04-11}, journal = {Scientific Reports}, volume = {13}, pages = {5859}, abstract = {We analyse two quantum systems with hidden parity-time ( PT ) symmetry: one is an optical device, whereas another is a superconducting microwave-frequency device. To investigate their symmetry, we introduce a damping frame (DF), in which loss and gain terms for a given Hamiltonian are balanced. We show that the non-Hermitian Hamiltonians of both systems can be tuned to reach an exceptional point (EP), i.e., the point in parameter space at which a transition from broken to unbroken hidden PT symmetry takes place. We calculate a degeneracy of a Liouvillian superoperator, which is called the Liouvillian exceptional point (LEP), and show that, in the optical domain, LEP is equivalent to EP obtained from the non-Hermitian Hamiltonian (HEP). We also report breaking the equivalence between LEP and HEP by a non-zero number of thermal photons for the microwave-frequency system.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We analyse two quantum systems with hidden parity-time ( PT ) symmetry: one is an optical device, whereas another is a superconducting microwave-frequency device. To investigate their symmetry, we introduce a damping frame (DF), in which loss and gain terms for a given Hamiltonian are balanced. We show that the non-Hermitian Hamiltonians of both systems can be tuned to reach an exceptional point (EP), i.e., the point in parameter space at which a transition from broken to unbroken hidden PT symmetry takes place. We calculate a degeneracy of a Liouvillian superoperator, which is called the Liouvillian exceptional point (LEP), and show that, in the optical domain, LEP is equivalent to EP obtained from the non-Hermitian Hamiltonian (HEP). We also report breaking the equivalence between LEP and HEP by a non-zero number of thermal photons for the microwave-frequency system. |
2022 |
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3. | Jan Roik, Karol Bartkiewicz, Antonín Černoch, Karel Lemr Entanglement quantification from collective measurements processed by machine learning Physics Letters A, 446 , pp. 128270, 2022, ISSN: 0375-9601. @article{ROIK2022128270b, title = {Entanglement quantification from collective measurements processed by machine learning}, author = {Jan Roik and Karol Bartkiewicz and Antonín Černoch and Karel Lemr}, url = {https://www.sciencedirect.com/science/article/pii/S0375960122003528}, doi = {https://doi.org/10.1016/j.physleta.2022.128270}, issn = {0375-9601}, year = {2022}, date = {2022-09-15}, journal = {Physics Letters A}, volume = {446}, pages = {128270}, abstract = {This paper investigates how to reduce the number of measurement configurations needed for sufficiently precise entanglement quantification. Instead of analytical formulae, we employ artificial neural networks to predict the amount of entanglement in a quantum state based on results of collective measurements (simultaneous measurements on multiple instances of the investigated state). We consider collective measurement limited to two copies of the investigated state. This approach allows us to explore the precision of entanglement quantification as a function of measurement configurations in a relevant scenario for practical quantum communications. For the purpose of our research, we consider general two-qubit states and their negativity as entanglement quantifier. We outline the benefits of this approach in future quantum communication networks.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper investigates how to reduce the number of measurement configurations needed for sufficiently precise entanglement quantification. Instead of analytical formulae, we employ artificial neural networks to predict the amount of entanglement in a quantum state based on results of collective measurements (simultaneous measurements on multiple instances of the investigated state). We consider collective measurement limited to two copies of the investigated state. This approach allows us to explore the precision of entanglement quantification as a function of measurement configurations in a relevant scenario for practical quantum communications. For the purpose of our research, we consider general two-qubit states and their negativity as entanglement quantifier. We outline the benefits of this approach in future quantum communication networks. |
2021 |
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2. | Kateřina Jirákov á, Antonín Č, Karel Lemr, Karol Bartkiewicz, Adam Miranowicz Physical Review A, 104 (6), pp. 062436, 2021. @article{Jirakova2021b, title = {Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise}, author = {Kate{ř}ina Jirákov á and Antonín Č and Karel Lemr and Karol Bartkiewicz and Adam Miranowicz}, url = {https://doi.org/10.1103/physreva.104.062436}, doi = {10.1103/physreva.104.062436}, year = {2021}, date = {2021-12-21}, journal = {Physical Review A}, volume = {104}, number = {6}, pages = {062436}, publisher = {American Physical Society (APS)}, abstract = {We demonstrate a hierarchy of various classes of quantum correlations on experimentally prepared two-qubit Werner-like states with controllable white noise. Werner states, which are white-noise-affected Bell states, are prototypal examples for studying such a hierarchy as a function of the amount of white noise. We experimentally generate Werner states and their generalizations, i.e., partially entangled pure states affected by white noise. These states enable us to study the hierarchy of the following classes of correlations: separability, entanglement, steering in three- and two-measurement scenarios, and Bell nonlocality. We show that the generalized Werner states (GWSs) reveal fundamentally different aspects of the hierarchy compared to the Werner states. In particular, we find five different parameter regimes of the GWSs, including those steerable in a two-measurement scenario but not violating Bell inequalities. This regime cannot be observed for the usual Werner states. Moreover, we find threshold curves separating different regimes of the quantum correlations and find the optimal states which allow for the largest amount of white noise which does not destroy their specific quantum correlations (e.g., unsteerable entanglement). Thus, we could identify the optimal Bell-nondiagonal GWSs which are, for this specific meaning, more robust against the white noise compared to the Bell-diagonal GWSs (i.e., Werner states).}, keywords = {}, pubstate = {published}, tppubtype = {article} } We demonstrate a hierarchy of various classes of quantum correlations on experimentally prepared two-qubit Werner-like states with controllable white noise. Werner states, which are white-noise-affected Bell states, are prototypal examples for studying such a hierarchy as a function of the amount of white noise. We experimentally generate Werner states and their generalizations, i.e., partially entangled pure states affected by white noise. These states enable us to study the hierarchy of the following classes of correlations: separability, entanglement, steering in three- and two-measurement scenarios, and Bell nonlocality. We show that the generalized Werner states (GWSs) reveal fundamentally different aspects of the hierarchy compared to the Werner states. In particular, we find five different parameter regimes of the GWSs, including those steerable in a two-measurement scenario but not violating Bell inequalities. This regime cannot be observed for the usual Werner states. Moreover, we find threshold curves separating different regimes of the quantum correlations and find the optimal states which allow for the largest amount of white noise which does not destroy their specific quantum correlations (e.g., unsteerable entanglement). Thus, we could identify the optimal Bell-nondiagonal GWSs which are, for this specific meaning, more robust against the white noise compared to the Bell-diagonal GWSs (i.e., Werner states). |
1. | Jan Roik, Karol Bartkiewicz, Antonín Černoch, Karel Lemr Phys. Rev. Applied, 15 , pp. 054006, 2021. @article{Bartkiewicz2021b, title = {Accuracy of Entanglement Detection via Artificial Neural Networks and Human-Designed Entanglement Witnesses}, author = {Jan Roik and Karol Bartkiewicz and Antonín Černoch and Karel Lemr}, url = {https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.15.054006}, doi = {https://doi.org/10.1103/PhysRevApplied.15.054006}, year = {2021}, date = {2021-05-04}, journal = {Phys. Rev. Applied}, volume = {15}, pages = {054006}, abstract = {The detection of entangled states is essential in both fundamental and applied quantum physics. However, this task proves to be challenging, especially for general quantum states. One can execute full state tomography but this method is time demanding, especially in complex systems. Other approaches use entanglement witnesses: these methods tend to be less demanding but lack reliability. Here, we demonstrate that artificial neural networks (ANNs) provide a balance between the two approaches. In this paper, we make a comparison of ANN performance with witness-based methods for random general two-qubit quantum states without any prior information on the states. Furthermore, we apply our approach to a real experimental data set.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The detection of entangled states is essential in both fundamental and applied quantum physics. However, this task proves to be challenging, especially for general quantum states. One can execute full state tomography but this method is time demanding, especially in complex systems. Other approaches use entanglement witnesses: these methods tend to be less demanding but lack reliability. Here, we demonstrate that artificial neural networks (ANNs) provide a balance between the two approaches. In this paper, we make a comparison of ANN performance with witness-based methods for random general two-qubit quantum states without any prior information on the states. Furthermore, we apply our approach to a real experimental data set. |