## Scientific output

# Papers

# Presentations

Robustness of Noether's principle: Maximal disconnects between conservation laws and symmetries in quantum theory

01.

Cristina Cirstoiu, Kamil Korzekwa, David Jennings

Spin-orbit implementation of Solovay-Kitaev decomposition of single-qubit channels

02.

M. H. M. Passos, A. de Oliveira Junior, M. C. de Oliveira, A. Z. Khoury, J. A. O Huguenin

Optimal allocation of quantum resources

03.

Roberto Salazar, Tanmoy Biswas, Jakub Czartowski, Karol Życzkowski, Paweł Horodecki

Quantum advantage in simulating stochastic processes

04.

Kamil Korzekwa, Matteo Lostaglio

Work fluctuations due to partial thermalizations in two-level systems

05.

Maria Quadeer, Kamil Korzekwa, Marco Tomamichel

No-go theorem for device-independent security in relativistic causal theories

06.

R. Salazar, M. Kamoń, K. Horodecki, D. Goyeneche, D. Saha, R. Ramanathan, P. Horodecki

Universal structure of objective states in all fundamental causal theories

07.

Carlo Maria Scandolo, Roberto Salazar, Jarosław K. Korbicz, and Paweł Horodecki

Dephasing superchannels

08.

Zbigniew Puchała, Kamil Korzekwa, Roberto Salazar, Paweł Horodecki, Karol Życzkowski

Algebraic and geometric structures inside the Birkhoff polytope

09.

Grzegorz Rajchel-Mieldzioć, Kamil Korzekwa, Zbigniew Puchała, Karol Życzkowski

Machine classification for probe based quantum thermometry

10.

Fabricio S. Luiz, A. de Oliveira Junior, Felipe F. Fanchini, Gabriel T. Landi

Encoding classical information into quantum resources

11.

Kamil Korzekwa, Zbigniew Puchała, Marco Tomamichel, Karol Życzkowski

Fluctuation-dissipation relations for thermodynamic distillation processes

12.

Tanmoy Biswas, A. de Oliveira Junior, Michał Horodecki, Kamil Korzekwa

Unravelling the non-classicality role in Gaussian heat engines

13.

A. de Oliveira Junior, M.C de Oliveira

Fast estimation of outcome probabilities for quantum circuits

14.

Hakop Pashayan, Oliver Reardon-Smith, Kamil Korzekwa, Stephen D. Bartlett

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

15.

Matteo Lostaglio, Kamil Korzekwa

Resource theory of absolute negativity

17.

Roberto Salazar, Jakub Czartowski, A. de Oliveira Junior

The rank of contextuality

18.

K. Horodecki, J. Zhou, M. Stankiewicz, R. Salazar, P. Horodecki, R. Raussendorf, R. Horodecki, R. Ramanathan, E. Tyhurst

Geometric structure of thermal cones

19.

A. de Oliveira Junior, Jakub Czartowski, Karol Życzkowski, Kamil Korzekwa

Classical simulations of quantum circuits

01.

Hakop Pashayan, Oliver Reardon-Smith, __Kamil Korzekwa__, Stephen Bartlett

AGH University of Science and Technology, Kraków, Poland (Jan 2020)

Jagiellonian University, Kraków, Poland (Jan 2020)

University of Gdańsk, Gdańsk, Poland (Mar 2020)

Encoding classical information in quantum resources

02.

__Kamil Korzekwa__, Zbigniew Puchała, Marco Tomamichel, Karol Życzkowski

Jagiellonian University, Kraków, Poland (Apr 2020)

15th Conference on the Theory of Quantum Computation, Communication and Cryptography, Riga, Latvia (Jun 2020)

Beyond IID in Information Theory 8, Palo Alto, USA (Nov 2020)

CTP Quantum Information Days, Warsaw, Poland (Feb 2021)

Quantum advantage in simulating stochastic processes

03.

__Kamil Korzekwa__, Matteo Lostaglio

Nanyang Technological University, Singapore (Jul 2020)

Jagiellonian University, Kraków, Poland (Oct 2020)

Distinguished talk at the Annual Ingarden session on Quantum Information (Nov 2020)

Faster classical estimation of Born rule probabilities for Clifford + T circuits

04.

Hakop Pashayan, __Oliver Reardon-Smith__, Kamil Korzekwa, Stephen Bartlett

Center for Theoretical Physics of the Polish Academy of Sciences, Warsaw, Poland (Oct 2020)

AGH University of Science and Technology, Kraków, Poland (Mar 2021)

Fast estimation of outcome probabilities for quantum circuits

05.

__Hakop Pashayan__, __Oliver Reardon-Smith__, __Kamil Korzekwa__, Stephen Bartlett

24th Annual Conference on Quantum Information Processing, Munich, Germany (Feb 2021)

CTP Quantum Information Days, Warsaw, Poland (Feb 2021)

QuTech, Delft, Netherlands (Mar 2021)

Fluctuation-dissipation relations for thermodynamic distillation processes

06.

Tanmoy Biswas, __Alexssandre de Oliveira Junior__, Michał Horodecki, __Kamil Korzekwa__

Jagiellonian University, Kraków, Poland (Mar 2021)

Quantum Optics X, Toruń, Poland (Sep 2021)

25th Annual Conference on Quantum Information Processing, Pasadena, USA (Mar 2022)

Optimal allocation of quantum resources

07.

__Roberto Salazar__, Tanmoy Biswas, Jakub Czartowski, Karol Życzkowski, Paweł Horodecki

Jagiellonian University, Kraków, Poland (Apr 2021)

Machine classification for probe-based quantum thermometry

08.

Fabrício S. Luiz, __A. de Oliveira Junior__, Felipe F. Fanchini, Gabriel Landi

Quantum Thermodynamics Summer School, Les Diablerets, Switzerland (Aug 2021)

Allocation of quantum resources in optical networks

09.

__R. Salazar__, J. Czartowski, I. Vagniluca, D. Ribezzo, A. Zavatta, N. Farrugia, J. A. Briffa, A. Xuereb

Quantum Optics X, Toruń, Poland (Sep 2021)

Geometric structure of thermal cones

14.

__A. de Oliveira Junior__, Jakub Czartowski, Karol Życzkowski, Kamil Korzekwa

Entanglement in Action Conference, Benasque, Spain (May 2022)

Quantum Thermodynamics Conference 2022, Belfast, Ireland (June 2022)

DPG Meeting of the Condensed Matter Section, Regensburg, Germany (Sep 2022)

Finite-size effects in quantum thermodynamics

15.

__Kamil Korzekwa__

DPG Meeting of the Condensed Matter Section, Regensburg, Germany (Sep 2022)

## Ongoing research projects

# Classical simulation of quantum circuits

Team

Kamil Korzekwa

Oliver Reardon-Smith

Collaborators

Hakop Pashayan

(Freie Universität Berlin)

Stephen Bartlett

(University of Sydney)

Michał Oszmaniec (CFT PAN, Warszawa)

Project description

Started January 2020

Background: For the future development of quantum technologies, it is crucial for us to understand what components of the quantum theory are responsible for quantum supremacy, i.e. the potential ability of quantum computers to solve problems that cannot be solved efficiently on classical machines. One of the most promising ways to achieve this is to identify sub-theories of the quantum theory that can be efficiently simulated on classical computers. The first result of this kind was the celebrated Gottesman-Knill theorem, which states that the stabiliser sub-theory, where one is restricted to state preparation and measurements in the computational basis and evolution according to Clifford gates, can be simulated in such a way. Moreover, the addition of a single type of a pure “magic” (non-stabiliser) state allows one to promote this classically simulable sub-theory to universal quantum computing, making magic states a proper resource for quantum computation when Clifford gates are considered free (easy to implement experimentally).

Goals: We want to develop a unified scheme for classical simulation of universal quantum circuits based on a three-step algorithm: identifying a free sub-theory, gadgetizing all resources (i.e. replacing non-free quantum gates with resource states), sampling and propagating the free states taken from optimal decomposition of resource states into free states of the theory. This three-step algorithm should unify many known simulation schemes, thus deepening our understanding of the nature of quantum computing, but also will provide a clear way to develop novel simulation algorithms. First, we want to apply this approach to build a fast classical algorithm to simulate Clifford+T circuits. We then want to extend it to circuits built from Gaussian+non-Gaussian gates and matchgate circuits with a resource SWAP gate. Finally, we would like to design a fully universal treatment of the problem. Complementary to this, we aim at implementing our algorithms on classical computers and use the developed software to verify near-term intermediate scale quantum devices.

Output

Classical simulation of quantum circuits

Faster classical estimation of Born rule probabilities for Clifford + T circuits

Clifford-T-estimator

Fast estimation of outcome probabilities for quantum circuits

Resource theory based simulation of quantum circuits

# Resource theories and quantum communication

Team

Kamil Korzekwa

Roberto Salazar

Collaborators

Marco Tomamichel (NU Singapore)

Paweł Horodecki (ICTQT Gdańsk)

Zbigniew Puchała (IITiS PAN Gliwice)

Karol Życzkowski (JU Kraków)

Jakub Czartowski (JU Kraków)

Project description

Started May 2019

Background: Communication problems lie at the very heart of quantum information science, with protocols such as quantum teleportation and super-dense coding capturing the essence of quantum information processing. A typical communication scenario consists of encoding a message in a quantum system, sending it via a channel, and then decoding it on the other side. All three stages require a fine control over quantum systems and the ability to manipulate them efficiently. It is then very natural to ask: how would the communication be affected, if the control is not perfect or the state manipulation is constrained?

Goals: Our aim will be to describe constrained communication scenarios in the language of resource theories, and then apply its formalism to relate constrained communication rates to appropriate quantum resources. On a more technical side, we would like to develop physically relevant resource theories of channels, which would provide useful quantifiers for important information processing tasks such as error correction or entanglement sharing.

Output

Encoding classical information into quantum resources

IEEE Trans. Inf. Theory 68, 4518 (2022)

The rank of contextuality

Optimal allocation of quantum resources

No-go theorem for device-independent security in relativistic causal theories

Phys. Rev. Research 3, 033148 (2021)

Dephasing superchannels

Phys. Rev. A 104, 052611 (2021)

Allocation of quantum resources in optical networks

# Dissipation of quantum resources

Team

Kamil Korzekwa

Alexssandre de Oliveira Junior

Collaborators

Michał Horodecki (ICTQT Gdańsk)

Tanmoy Biswas (ICTQT Gdańsk)

Maria Quadeer (University of Sydney)

Marco Tomamichel (NU Singapore)

Matteo Lostaglio (PsiQuantum)

Jakub Czartowski (JU Kraków)

Project description

Started March 2020

Background: In principle, while processing quantum information, any initial state can be transformed into any final state. One could thus conclude that all quantum states are equally valuable or resourceful. In reality, however, some transformations are harder to implement than others, which results in a partial ordering of the set of quantum states, with the hardest to prepare at the top, and easiest at the bottom. Such a resource hierarchy arises naturally when we face any kind of restriction: from the locality constraint, through experimental difficulties in preparing particular superpositions, to fundamental constraints induced by physical laws like energy conservation. Moreover, these constraints on processing quantum information result in irreversibility, i.e. during the interconversion process some resource content is unavoidably lost. From both the fundamental and applied perspective it is then important to understand the nature and limits of the dissipation of quantum resources.

Goals: We would like to develop a general framework allowing one to quantitatively study resource dissipation for various resource theories (thermodynamics, entanglement, magic, etc.), and to characterise optimal state transformation protocols that minimise dissipation. We would also like to explore the phenomenon of resource resonance (leading to lossless interconversion) and design experimental setups employing it. Finally, we aim at employing our results to derive general fluctuation-dissipation relations for quantum resources, thus generalising the known thermodynamic phenomenon to a general resource-theoretic setting.

Output

Fluctuation-dissipation relations for thermodynamic distillation processes

Phys. Rev. E 105, 054127 (2022)

Work fluctuations due to partial thermalizations in two-level systems

Phys. Rev. E 103, 042141 (2021)

Geometric structure of thermal cones

Finite-size effects in quantum thermodynamics

# Quantum thermodynamics: advantages and applications

Team

Kamil Korzekwa

Fereshte Shahbeigi

Alexssandre de Oliveira Junior

Collaborators

Matteo Lostaglio (PsiQuantum)

Chris Chubb (ETH Zurich)

Ryszard Kukulski (IITiS PAN Gliwice)

Łukasz Pawela (IITiS PAN Gliwice)

Project description

Started June 2019

Background: Most of the resource-theoretic results concerning quantum thermodynamics have a very fundamental character, telling us whether a given transformation is possible in principle. The problem is that in many cases optimal transformation protocols require a very fine control over the transformed systems and their interactions with the environment. It is then important to extend this theory so that it does not only characterise fundamental constraints of physical processes, but also faithfully describes the limitations arising in realistic experimental scenarios. This way the predictions of resource theories could be tested experimentally, which is a necessary condition for a theory to play an active role in developing future quantum technologies. Moreover, in order for such technologies to be useful, we need to investigate possibilities for real quantum advantage within thermodynamics, analogous to quantum supremacy in the computational field, i.e., we need to identify thermodynamic protocols whose performance cannot be explained within classical theory.

Goals: On the applicational side, we would like to explore the capabilities of resource-theoretic formalism under the restrictions of limited control due to access only to transformations that could be implemented experimentally (e.g. local Hamiltonian control, partial thermalisations, or coarse-grained operations), and to assess and quantify the role of memory in performing optimal thermodynamic transformations. Concerning quantum advantages, we want to investigate the potential of coherence to act as a memory, both in thermodynamic and information-processing scenarios (e.g. enhanced cooling or exponential improvement in space-time cost of realising a given process). On a more mathematical side, we would like to characterise quantum embeddable stochastic processes, i.e. these processes that can be implemented quantumly without employing a memory. Finally, we will also try to employ the developed framework to bridge the gap between the resource theories and control theory.

Output

Fundamental constraints of quantum thermodynamics in the Markovian regime

Phys. Rev. A 106, 012426 (2022)

Phys. Rev. Lett. 129, 040602 (2022)

Algorithm for continuous thermomajorization

Unravelling the non-classicality role in Gaussian heat engines

Sci. Rep. 12, 10412 (2022)

Machine classification for probe based quantum thermometry

Phys. Rev. A 105, 022413 (2022)

Quantum advantage in simulating stochastic processes

Phys. Rev. X 11, 021019 (2021)

Spin-orbit implementation of Solovay-Kitaev decomposition of single-qubit channels

# Structural differences between classical and quantum randomness

Team

Kamil Korzekwa

Roberto Salazar

Alexssandre de Oliveira Junior

Collaborators

Zbigniew Puchała (IITiS PAN Gliwice)

Grzegorz Rajchel (CFT PAN, Warszawa)

Karol Życzkowski (JU Kraków)

Jakub Czartowski (JU Kraków)

Paweł Horodecki (ICTQT Gdańsk)

Project description

Started February 2020

Background: Random processes are ubiquitous in both classical and quantum physics. However, the nature of randomness in these two regimes differs significantly. On the one hand, classical random evolution is necessarily irreversible. On the other hand, quantum evolution may be completely deterministic (and thus reversible if no measurement is performed), but nevertheless lead to random measurement outcomes of observable A by transforming a system into a coherent superposition of eigenstates of A. When probing the dynamics of the system one can therefore observe the same random transitions, irrespectively of whether the evolution is coherent or incoherent. The questions then arise: to what extent an observed random transformation can be explained via the underlying deterministic and coherent process, and how much unavoidable classical randomness must be involved in it?

Goals: Our main goal will be to study what kind of transition matrices can be induced by reversible unitary dynamics, i.e. we wish to understand the structure of unistochastic matrices. These technical results will not only characterise random processes with a potentially deterministic cause, but could also be employed to the studies of quantum walks on graphs. More generally, we would like to investigate what structural aspects of quantum randomness, as compared to classical probability theory, may lead to enhanced processing of information.

Output

Algebraic and geometric structures inside the Birkhoff polytope

J. Math. Phys. 63, 012202 (2022)

Resource theory of absolute negativity

Universal structure of objective states in all fundamental causal theories