##### Leader of the research group: Lukasz RudnickiPost-doc: Fattah Sakuldee, Stefano CusumanoPhD student: Tomasz Linowski, Otavio Augusto Dantas Molitor, Amrapali Sen

The aim of the group is to explore intersections of quantum optics, quantum thermodynamics and open system dynamics. The group’s research interests lay within standard quantum optics, currently, looked at from the perspective of open quantum systems and thermodynamics. We also extensively collaborate with experimental groups concerned with quantum technologies, with emphasis recently put on metrology.

## Activity

Open Quantum Systems and Quantum Optics

Among various topics of our interest there are: bosonic systems at a mesoscopic scale, open quantum evolution of Gaussian systems, limitations concerning quantum batteries, non-Markovian dynamics, interplays between work and coherence, as well as potential thermodynamic advantages of indefinite causal order.

Quantum Metrology

We coordinate the QuantERA project “Application-ready superresolution in space and frequency” (ApresSF), and take part in Horizon 2020, FET Open project “Spectral-Temporal Metrology with Tailored Quantum Measurements” (Stormytune). Both projects are devoted to superresolution in quantum metrology.

## Publications

### 2022

1. Łukasz Rudnicki. Geophysics and Stuart vortices on a sphere meet differential geometry. Communications on Pure and Applied Analysis, 21(7):2479-2493, 2022. acknowledgment to ICTQT IRAP project included
[BibTeX]
@article{1534-0392_2022_7_2479,
title = {Geophysics and Stuart vortices on a sphere meet differential geometry},
journal = {Communications on Pure and Applied Analysis},
volume = {21},
number = {7},
pages = {2479-2493},
year = {2022},
author = {Łukasz Rudnicki},
note = {acknowledgment to ICTQT IRAP project included}
}
2. Thais L. Silva, Łukasz Rudnicki, Daniel S. Tasca, and Stephen P. Walborn. Discretized continuous quantum-mechanical observables that are neither continuous nor discrete. Phys. Rev. Research, 4:013060, jan 2022. acknowledgment to ICTQT IRAP project included doi:10.1103/PhysRevResearch.4.013060
@article{PhysRevResearch.4.013060,
title = {Discretized continuous quantum-mechanical observables that are neither continuous nor discrete},
author = {Silva, Thais L. and Rudnicki, \L{}ukasz and Tasca, Daniel S. and Walborn, Stephen P.},
journal = {Phys. Rev. Research},
volume = {4},
issue = {1},
pages = {013060},
numpages = {9},
year = {2022},
month = jan,
publisher = {American Physical Society},
doi = {10.1103/PhysRevResearch.4.013060},
note = {acknowledgment to ICTQT IRAP project included}
}
3. Paweł Horodecki, Łukasz Rudnicki, and Karol ifmmode dotZelse Żfiyczkowski. Five Open Problems in Quantum Information Theory. PRX Quantum, 3:010101, mar 2022. acknowledgment to ICTQT IRAP project included doi:10.1103/PRXQuantum.3.010101
@article{PRXQuantum.3.010101,
title = {Five Open Problems in Quantum Information Theory},
author = {Horodecki, Pawe\l{} and Rudnicki, \L{}ukasz and \ifmmode \dot{Z}\else \.{Z}\fi{}yczkowski, Karol},
journal = {PRX Quantum},
volume = {3},
issue = {1},
pages = {010101},
numpages = {17},
year = {2022},
month = mar,
publisher = {American Physical Society},
doi = {10.1103/PRXQuantum.3.010101},
note = {acknowledgment to ICTQT IRAP project included}
}
4. Klaus Liegener and Łukasz Rudnicki. Quantum speed limit and stability of coherent states in quantum gravity. Classical and Quantum Gravity, 39(12):12LT01, may 2022. acknowledgment to ICTQT IRAP project included doi:10.1088/1361-6382/ac6faa

Utilizing the program of expectation values in coherent states and its recently developed algorithmic tools, this letter investigates the dynamical properties of cosmological coherent states for loop quantum gravity. To this end, the quantum speed limit (QSL) is adapted to quantum gravity, yielding necessary consistency checks for any proposal of stable families of states. To showcase the strength of the developed tools, they are applied to a prominent model: the Euclidean part of the quantum scalar constraint. We report the variance of this constraint evaluated on a family of coherent states showing that, for short times, this family passes the QSL test, allowing the transition from one coherent state to another one.

@article{Liegener_2022,
doi = {10.1088/1361-6382/ac6faa},
url = {https://doi.org/10.1088/1361-6382/ac6faa},
year = 2022,
month = may,
publisher = {{IOP} Publishing},
volume = {39},
number = {12},
pages = {12LT01},
author = {Klaus Liegener and {\L}ukasz Rudnicki},
title = {Quantum speed limit and stability of coherent states in quantum gravity},
journal = {Classical and Quantum Gravity},
abstract = {Utilizing the program of expectation values in coherent states and its recently developed algorithmic tools, this letter investigates the dynamical properties of cosmological coherent states for loop quantum gravity. To this end, the quantum speed limit (QSL) is adapted to quantum gravity, yielding necessary consistency checks for any proposal of stable families of states. To showcase the strength of the developed tools, they are applied to a prominent model: the Euclidean part of the quantum scalar constraint. We report the variance of this constraint evaluated on a family of coherent states showing that, for short times, this family passes the QSL test, allowing the transition from one coherent state to another one.},
note = {acknowledgment to ICTQT IRAP project included}
}
5. Fattah Sakuldee and Łukasz Cywi’nski. Statistics of projective measurement on a quantum probe as a witness of noncommutativity of algebra of a probed system. Quantum Information Processing, 21(7), jul 2022. acknowledgment to ICTQT IRAP project included doi:10.1007/s11128-022-03576-9
@article{Sakuldee2022a,
doi = {10.1007/s11128-022-03576-9},
url = {https://doi.org/10.1007/s11128-022-03576-9},
year = {2022},
month = jul,
publisher = {Springer Science and Business Media {LLC}},
volume = {21},
number = {7},
author = {Fattah Sakuldee and {\L}ukasz Cywi{\'{n}}ski},
title = {Statistics of projective measurement on a quantum probe as a witness of noncommutativity of algebra of a probed system},
journal = {Quantum Information Processing},
note = {acknowledgment to ICTQT IRAP project included}
}
6. Fattah Sakuldee, Philip Taranto, and Simon Milz. Connecting commutativity and classicality for multitime quantum processes. Physical Review A, 106(2), aug 2022. acknowledgment to ICTQT IRAP project included doi:10.1103/physreva.106.022416
@article{Sakuldee2022b,
doi = {10.1103/physreva.106.022416},
url = {https://doi.org/10.1103/physreva.106.022416},
year = {2022},
month = aug,
publisher = {American Physical Society ({APS})},
volume = {106},
number = {2},
author = {Fattah Sakuldee and Philip Taranto and Simon Milz},
title = {Connecting commutativity and classicality for multitime quantum processes},
journal = {Physical Review A},
note = {acknowledgment to ICTQT IRAP project included}
}

### 2021

1. Stefano Cusumano and Łukasz Rudnicki. Comment on “Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries”. Physical Review Letters, 127(2):028901, jul 2021. arXiv: 2102.05627 doi:10.1103/PhysRevLett.127.028901

In the abstract of\textasciitilde[Phys. Rev. Lett. \\textbackslashbf 125\, 040601 (2020)] one can read that: […]\\textbackslashit to have a nonzero rate of change of the extractable work, the state \$\textbackslashrho\_\textbackslashmathcal\W\\$ of the battery cannot be an eigenstate of a “free energy operator”, defined by \$\textbackslashmathcal\F\=H\_\textbackslashmathcal\W\+\textbackslashbeta\textasciicircum\-1\\textbackslashlog \textbackslashrho\_\textbackslashmathcal\W\\$, where \$H\_\textbackslashmathcal\W\\$ is the Hamiltonian of the battery and \$\textbackslashbeta\$ is the inverse temperature\ […]. Contrarily to what is presented below Eq.\textasciitilde(17) of the paper, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.

@Article{cusumano_comment_2021,
author   = {Cusumano, Stefano and Rudnicki, Łukasz},
journal  = {Physical {R}eview {L}etters},
title    = {Comment on "{Fluctuations} in {Extractable} {Work} {Bound} the {Charging} {Power} of {Quantum} {Batteries}"},
year     = {2021},
issn     = {0031-9007, 1079-7114},
month    = jul,
note     = {arXiv: 2102.05627},
number   = {2},
pages    = {028901},
volume   = {127},
abstract = {In the abstract of{\textasciitilde}[Phys. Rev. Lett. \{{\textbackslash}bf 125\}, 040601 (2020)] one can read that: [...]\{{\textbackslash}it to have a nonzero rate of change of the extractable work, the state \${\textbackslash}rho\_{\textbackslash}mathcal\{W\}\$ of the battery cannot be an eigenstate of a "free energy operator", defined by \${\textbackslash}mathcal\{F\}=H\_{\textbackslash}mathcal\{W\}+{\textbackslash}beta{\textasciicircum}\{-1\}{\textbackslash}log {\textbackslash}rho\_{\textbackslash}mathcal\{W\}\$, where \$H\_{\textbackslash}mathcal\{W\}\$ is the Hamiltonian of the battery and \${\textbackslash}beta\$ is the inverse temperature\} [...]. Contrarily to what is presented below Eq.{\textasciitilde}(17) of the paper, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.},
doi      = {10.1103/PhysRevLett.127.028901},
keywords = {Quantum Physics},
url      = {http://arxiv.org/abs/2102.05627},
urldate  = {2021-07-28},
note = {acknowledgment to ICTQT IRAP project included}
}
2. Stefano Cusumano and Łukasz Rudnicki. Thermodynamics of Reduced State of the Field. Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 23(9):Paper No. 1198, 2021. acknowledgment to ICTQT IRAP project included doi:10.3390/e23091198
@Article{Cusumano2021,
author   = {Cusumano, Stefano and Rudnicki, Łukasz},
journal  = {Entropy. {A}n {I}nternational and {I}nterdisciplinary {J}ournal of {E}ntropy and {I}nformation {S}tudies},
title    = {Thermodynamics of {R}educed {S}tate of the {F}ield},
year     = {2021},
number   = {9},
pages    = {Paper No. 1198},
volume   = {23},
doi      = {10.3390/e23091198},
keywords = {81},
mrnumber = {4320432},
url      = {https://www.mdpi.com/1099-4300/23/9/1198/pdf},
note = {acknowledgment to ICTQT IRAP project included}
}
3. Łukasz Rudnicki. Quantum speed limit and geometric measure of entanglement. Physical Review A, 104(3):032417, sep 2021. acknowledgment to ICTQT IRAP project included doi:10.1103/PhysRevA.104.032417

Using the approach offered by quantum speed limit, we show that geometric measure of multipartite entanglement for pure states [T.-C. Wei and P. M. Goldbart, Phys. Rev. A 68, 042307 (2003), 10.1103/PhysRevA.68.042307] can be interpreted as the minimal time necessary to unitarily evolve a given quantum state to a separable one.

@Article{Rudnicki2021,
author        = {Rudnicki, Łukasz},
journal       = {Physical {R}eview {A}},
title         = {Quantum speed limit and geometric measure of entanglement},
year          = {2021},
month         = sep,
number        = {3},
pages         = {032417},
volume        = {104},
abstract      = {Using the approach offered by quantum speed limit, we show that         geometric measure of multipartite entanglement for pure states         [T.-C. Wei and P. M. Goldbart, Phys. Rev. A 68, 042307 (2003),         10.1103/PhysRevA.68.042307] can be interpreted as the minimal         time necessary to unitarily evolve a given quantum state to a         separable one.},
archiveprefix = {arXiv},
doi           = {10.1103/PhysRevA.104.032417},
eid           = {032417},
eprint        = {2107.11877},
groups        = {Rudnicki},
keywords      = {Quantum Physics},
primaryclass  = {quant-ph},
note = {acknowledgment to ICTQT IRAP project included}
}
4. Klaus Liegener and Łukasz Rudnicki. Algorithmic approach to cosmological coherent state expectation values in loop quantum gravity. Classical and Quantum Gravity, 38(20):Paper No. 205001, 39, 2021. acknowledgment to ICTQT IRAP project included doi:10.1088/1361-6382/ac226f
@Article{Liegener2021,
author   = {Liegener, Klaus and Rudnicki, Łukasz},
journal  = {Classical and {Q}uantum {G}ravity},
title    = {Algorithmic approach to cosmological coherent state expectation values in loop quantum gravity},
year     = {2021},
issn     = {0264-9381},
number   = {20},
pages    = {Paper No. 205001, 39},
volume   = {38},
doi      = {10.1088/1361-6382/ac226f},
keywords = {83C45 (83C27)},
mrnumber = {4318548},
url      = {https://iopscience.iop.org/article/10.1088/1361-6382/ac226f/pdf},
note = {acknowledgment to ICTQT IRAP project included}
}
5. Łukasz Rudnicki and Stephen P. Walborn. Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resembling their discrete counterparts. Physical Review A, 104(4):Paper No. 042210, 2021. acknowledgment to ICTQT IRAP project included doi:10.1103/physreva.104.042210
@Article{Rudnicki2021a,
author   = {Rudnicki, Łukasz and Walborn, Stephen P.},
journal  = {Physical {R}eview {A}},
title    = {Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resembling their discrete counterparts},
year     = {2021},
issn     = {2469-9926},
number   = {4},
pages    = {Paper No. 042210},
volume   = {104},
doi      = {10.1103/physreva.104.042210},
keywords = {81S07},
mrnumber = {4339485},
url      = {https://journals.aps.org/pra/pdf/10.1103/PhysRevA.104.042210},
note = {acknowledgment to ICTQT IRAP project included}
}

### 2020

1. Tomasz Linowski, Grzegorz Rajchel-Mieldzioć, and Karol Życzkowski. Entangling power of multipartite unitary gates. Journal of Physics A: Mathematical and Theoretical, 53(12):125303, mar 2020. doi:10.1088/1751-8121/ab749a
@Article{linowski_entangling_2020,
author  = {Linowski, Tomasz and Rajchel-Mieldzioć, Grzegorz and Życzkowski, Karol},
journal = {Journal of {P}hysics {A}: {M}athematical and {T}heoretical},
title   = {Entangling power of multipartite unitary gates},
year    = {2020},
issn    = {1751-8113, 1751-8121},
month   = mar,
number  = {12},
pages   = {125303},
volume  = {53},
doi     = {10.1088/1751-8121/ab749a},
url     = {https://iopscience.iop.org/article/10.1088/1751-8121/ab749a},
urldate = {2020-04-22},
}
2. Simon Milz, Fattah Sakuldee, Felix A. Pollock, and Kavan Modi. Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories. Quantum, 4:255, apr 2020. doi:10.22331/q-2020-04-20-255

In classical physics, the Kolmogorov extension theorem lays the foundation for the theory of stochastic processes. It has been known for a long time that, in its original form, this theorem does not hold in quantum mechanics. More generally, it does not hold in any theory of stochastic processes — classical, quantum or beyond — that does not just describe passive observations, but allows for active interventions. Such processes form the basis of the study of causal modelling across the sciences, including in the quantum domain. To date, these frameworks have lacked a conceptual underpinning similar to that provided by Kolmogorov’s theorem for classical stochastic processes. We prove a generalized extension theorem that applies to all theories of stochastic processes, putting them on equally firm mathematical ground as their classical counterpart. Additionally, we show that quantum causal modelling and quantum stochastic processes are equivalent. This provides the correct framework for the description of experiments involving continuous control, which play a crucial role in the development of quantum technologies. Furthermore, we show that the original extension theorem follows from the generalized one in the correct limit, and elucidate how a comprehensive understanding of general stochastic processes allows one to unambiguously define the distinction between those that are classical and those that are quantum.

@Article{milz_kolmogorov_2020,
author   = {Milz, Simon and Sakuldee, Fattah and Pollock, Felix A. and Modi, Kavan},
journal  = {Quantum},
title    = {Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories},
year     = {2020},
issn     = {2521-327X},
month    = apr,
pages    = {255},
volume   = {4},
abstract = {In classical physics, the Kolmogorov extension theorem lays the foundation for the theory of stochastic processes. It has been known for a long time that, in its original form, this theorem does not hold in quantum mechanics. More generally, it does not hold in any theory of stochastic processes -- classical, quantum or beyond -- that does not just describe passive observations, but allows for active interventions. Such processes form the basis of the study of causal modelling across the sciences, including in the quantum domain. To date, these frameworks have lacked a conceptual underpinning similar to that provided by Kolmogorov’s theorem for classical stochastic processes. We prove a generalized extension theorem that applies to all theories of stochastic processes, putting them on equally firm mathematical ground as their classical counterpart. Additionally, we show that quantum causal modelling and quantum stochastic processes are equivalent. This provides the correct framework for the description of experiments involving continuous control, which play a crucial role in the development of quantum technologies. Furthermore, we show that the original extension theorem follows from the generalized one in the correct limit, and elucidate how a comprehensive understanding of general stochastic processes allows one to unambiguously define the distinction between those that are classical and those that are quantum.},
doi      = {10.22331/q-2020-04-20-255},
language = {en},
url      = {https://quantum-journal.org/papers/q-2020-04-20-255/},
urldate  = {2020-04-22},
}
3. Ł. Rudnicki, L. L. Sánchez-Soto, G. Leuchs, and R. W. Boyd. Fundamental quantum limits in ellipsometry. Optics Letters, 45(16):4607, aug 2020. acknowledgment to ICTQT IRAP project included doi:10.1364/OL.392955
@Article{rudnicki_fundamental_2020,
author   = {Rudnicki, Ł. and Sánchez-Soto, L. L. and Leuchs, G. and Boyd, R. W.},
journal  = {Optics {L}etters},
title    = {Fundamental quantum limits in ellipsometry},
year     = {2020},
issn     = {0146-9592, 1539-4794},
month    = aug,
number   = {16},
pages    = {4607},
volume   = {45},
doi      = {10.1364/OL.392955},
language = {en},
url      = {https://www.osapublishing.org/abstract.cfm?URI=ol-45-16-4607},
urldate  = {2021-05-10},
note = {acknowledgment to ICTQT IRAP project included}
}
4. Tomasz Linowski, Clemens Gneiting, and Łukasz Rudnicki. Stabilizing entanglement in two-mode Gaussian states. Physical Review A, 102(4):042405, oct 2020. acknowledgment to ICTQT IRAP project included doi:10.1103/PhysRevA.102.042405
@Article{linowski_stabilizing_2020,
author   = {Linowski, Tomasz and Gneiting, Clemens and Rudnicki, Łukasz},
journal  = {Physical {R}eview {A}},
title    = {Stabilizing entanglement in two-mode {Gaussian} states},
year     = {2020},
issn     = {2469-9926, 2469-9934},
month    = oct,
number   = {4},
pages    = {042405},
volume   = {102},
doi      = {10.1103/PhysRevA.102.042405},
language = {en},
urldate  = {2021-05-10},
note = {acknowledgment to ICTQT IRAP project included}
}

### 2019

1. Alejandro Pozas-Kerstjens, Rafael Rabelo, Łukasz Rudnicki, Rafael Chaves, Daniel Cavalcanti, Miguel Navascués, and Antonio Acín. Bounding the sets of classical and quantum correlations in networks. Physical Review Letters, 123(14):140503, oct 2019. acknowledgment to ICTQT IRAP project included doi:10.1103/PhysRevLett.123.140503
@Article{pozas-kerstjens_bounding_2019,
author   = {Pozas-Kerstjens, Alejandro and Rabelo, Rafael and Rudnicki, Łukasz and Chaves, Rafael and Cavalcanti, Daniel and Navascués, Miguel and Acín, Antonio},
journal  = {Physical {R}eview {L}etters},
title    = {Bounding the sets of classical and quantum correlations in networks},
year     = {2019},
issn     = {0031-9007, 1079-7114},
month    = oct,
number   = {14},
pages    = {140503},
volume   = {123},
doi      = {10.1103/PhysRevLett.123.140503},
groups   = {Rudnicki},
language = {en},
urldate  = {2020-04-22},
note = {acknowledgment to ICTQT IRAP project included}
}

## arXiv preprints

### 2022

1. Łukasz Rudnicki, Waldemar Kłobus, Otavio A. D. Molitor, and Wiesław Laskowski. Salient signatures of entanglement in the surrounding environment. 2022. doi:10.48550/ARXIV.2209.05197
@misc{https://doi.org/10.48550/arxiv.2209.05197,
doi = {10.48550/ARXIV.2209.05197},
url = {https://arxiv.org/abs/2209.05197},
author = {Rudnicki, Łukasz and Kłobus, Waldemar and Molitor, Otavio A. D. and Laskowski, Wiesław},
keywords = {Quantum Physics (quant-ph), FOS: Physical sciences, FOS: Physical sciences},
title = {Salient signatures of entanglement in the surrounding environment},
publisher = {arXiv},
year = {2022},
}
2. Fattah Sakuldee and Łukasz Rudnicki. When does an entanglement breaking channel break entanglement?. , 2022.
[BibTeX]
@article{https://doi.org/10.48550/arxiv.2209.08689,
author = {Sakuldee, Fattah and Rudnicki, Łukasz},
title = {When does an entanglement breaking channel break entanglement?},
publisher = {arXiv},
year = {2022}
}
3. Tomasz Linowski, Alexander Teretenkov, and Łukasz Rudnicki. Dissipative evolution of quantum Gaussian states. arXiv e-prints, pages arXiv:2105.12644, 2022.

The covariance matrix contains the complete information about the second-order expectation values of the mode quadratures (position and momentum operators) of the system. Due to its prominence in studies of continuous variable systems, most significantly Gaussian states, special emphasis is put on time evolution models that result in self-contained equations for the covariance matrix. So far, despite not being explicitly implied by this requirement, virtually all such models assume a so- called quadratic, or second-order case, in which the generator of the evolution is at most second-order in the mode quadratures. Here, we provide an explicit model of covariance matrix evolution of infinite order. Furthermore, we derive the solution, including stationary states, for a large subclass of proposed evolutions. Our findings challenge the contemporary understanding of covariance matrix dynamics and may give rise to new methods and improvements in quantum technologies employing continuous variable systems.

@Article{Linowski2021a,
author        =  {Linowski, Tomasz and Teretenkov, Alexander and Rudnicki, Łukasz},
journal       = {arXiv e-prints},
title         = {Dissipative evolution of quantum Gaussian states},
year          = {2022},
pages         = {arXiv:2105.12644},
abstract      = {The covariance matrix contains the complete information about the         second-order expectation values of the mode quadratures         (position and momentum operators) of the system. Due to its         prominence in studies of continuous variable systems, most         significantly Gaussian states, special emphasis is put on time         evolution models that result in self-contained equations for the         covariance matrix. So far, despite not being explicitly implied         by this requirement, virtually all such models assume a so-         called quadratic, or second-order case, in which the generator         of the evolution is at most second-order in the mode         quadratures. Here, we provide an explicit model of covariance         matrix evolution of infinite order. Furthermore, we derive the         solution, including stationary states, for a large subclass of         proposed evolutions. Our findings challenge the contemporary         understanding of covariance matrix dynamics and may give rise to         new methods and improvements in quantum technologies employing         continuous variable systems.},
archiveprefix = {arXiv},
eid           = {arXiv:2105.12644},
eprint        = {2105.12644},
keywords      = {Quantum {P}hysics},
primaryclass  = {quant-ph},
}
4. Tomasz Linowski, Konrad Schlichtholz, and Łukasz Rudnicki. A formal relation between Pegg-Barnett and Paul quantum phase frameworks. arXiv e-prints, pages arXiv.2205.09481, may 2022.

The problem of defining a Hermitian quantum phase operator is nearly as old as quantum mechanics itself. Throughout the years, a number of solutions was proposed, ranging from abstract operator formalisms to phase-space methods. In this work, we connect two of the most prominent approaches: Pegg-Barnett and Paul formalisms, by proving that the Paul formalism is equivalent to the Pegg-Barnett formalism applied to an infinitely amplified state. Our findings fill in a conceptual gap in the understanding of the quantum phase problem.

@Article{Linowski2022,
author        = {Linowski, Tomasz and Schlichtholz, Konrad and Rudnicki, Łukasz},
journal       = {arXiv e-prints},
title         = {A formal relation between Pegg-Barnett and Paul quantum phase frameworks},
year          = {2022},
month         = may,
pages         = {arXiv.2205.09481},
abstract      = {The problem of defining a Hermitian quantum phase operator is nearly as old as quantum mechanics itself. Throughout the years, a number of solutions was proposed, ranging from abstract operator formalisms to phase-space methods. In this work, we connect two of the most prominent approaches: Pegg-Barnett and Paul formalisms, by proving that the Paul formalism is equivalent to the Pegg-Barnett formalism applied to an infinitely amplified state. Our findings fill in a conceptual gap in the understanding of the quantum phase problem.},
archiveprefix = {arXiv},
eid           = {arXiv.2205.09481},
eprint        = {2205.09481},
keywords      = {Quantum Physics, Physical sciences},
primaryclass  = {quant-ph},
url           = {https://arxiv.org/abs/2205.09481},
}

### 2021

1. Lucas Chibebe Céleri and Łukasz Rudnicki. Gauge invariant quantum thermodynamics: consequences for the first law. arXiv e-prints, pages arXiv:2104.10153, apr 2021.

Universality of classical thermodynamics rests on the central limit theorem, due to which, measurements of thermal fluctuations are unable to reveal detailed information regarding the microscopic structure of a macroscopic body. When small systems are considered and fluctuations become important, thermodynamic quantities can be understood in the context of classical stochastic mechanics. A fundamental assumption behind thermodynamics is therefore that of coarse-graning, which stems from a substantial lack of control over all degrees of freedom. However, when quantum systems are concerned, one claims a high level of control. As a consequence, information theory plays a major role in the identification of thermodynamic functions. Here, drawing from the concept of gauge symmetry, essential in all modern physical theories, we put forward a new possible, intermediate route. Working within the realm of quantum thermodynamics we explicitly construct physically motivated gauge transformations which encode a gentle variant of coarse- graining behind thermodynamics. As a consequence, we reinterpret quantum work and heat, as well as the role of quantum coherence.

@Article{ChibebeCeleri2021,
author        = {Chibebe Céleri, Lucas and Rudnicki, Łukasz},
journal       = {arXiv e-prints},
title         = {Gauge invariant quantum thermodynamics: consequences for the first law},
year          = {2021},
month         = apr,
pages         = {arXiv:2104.10153},
abstract      = {Universality of classical thermodynamics rests on the central limit         theorem, due to which, measurements of thermal fluctuations are         unable to reveal detailed information regarding the microscopic         structure of a macroscopic body. When small systems are         considered and fluctuations become important, thermodynamic         quantities can be understood in the context of classical         stochastic mechanics. A fundamental assumption behind         thermodynamics is therefore that of coarse-graning, which stems         from a substantial lack of control over all degrees of freedom.         However, when quantum systems are concerned, one claims a high         level of control. As a consequence, information theory plays a         major role in the identification of thermodynamic functions.         Here, drawing from the concept of gauge symmetry, essential in         all modern physical theories, we put forward a new possible,         intermediate route. Working within the realm of quantum         thermodynamics we explicitly construct physically motivated         gauge transformations which encode a gentle variant of coarse-         graining behind thermodynamics. As a consequence, we reinterpret         quantum work and heat, as well as the role of quantum coherence.},
archiveprefix = {arXiv},
eid           = {arXiv:2104.10153},
eprint        = {2104.10153},
keywords      = {Quantum Physics},
primaryclass  = {quant-ph},
}
2. Tomasz Linowski and Łukasz Rudnicki. Reduced state of the field and classicality of quantum Gaussian evolution. arXiv e-prints, pages arXiv:2107.03196, jul 2021.

We discuss compatibility between various quantum aspects of bosonic fields, relevant for quantum optics and quantum thermodynamics, and the mesoscopic formalism of reduced state of the field (RSF). In particular, we derive exact conditions under which Gaussian and Bogoliubov-type evolutions can be cast into the RSF framework. In that regard, special emphasis is put on Gaussian thermal operations. To strengthen the link between the RSF formalism and the notion of classicality for bosonic quantum fields, we prove that RSF contains no information about entanglement in two-mode Gaussian states. For the same purpose, we show that the entropic characterisation of RSF by means of the von Neumann entropy is qualitatively the same as its description based on the Wehrl entropy. Our findings help bridge the conceptual gap between quantum and classical mechanics.

@Article{Linowski2021,
author        = {Linowski, Tomasz and Rudnicki, Łukasz},
journal       = {arXiv e-prints},
title         = {Reduced state of the field and classicality of quantum Gaussian evolution},
year          = {2021},
month         = jul,
pages         = {arXiv:2107.03196},
abstract      = {We discuss compatibility between various quantum aspects of bosonic         fields, relevant for quantum optics and quantum thermodynamics,         and the mesoscopic formalism of reduced state of the field         (RSF). In particular, we derive exact conditions under which         Gaussian and Bogoliubov-type evolutions can be cast into the RSF         framework. In that regard, special emphasis is put on Gaussian         thermal operations. To strengthen the link between the RSF         formalism and the notion of classicality for bosonic quantum         fields, we prove that RSF contains no information about         entanglement in two-mode Gaussian states. For the same purpose,         we show that the entropic characterisation of RSF by means of         the von Neumann entropy is qualitatively the same as its         description based on the Wehrl entropy. Our findings help bridge         the conceptual gap between quantum and classical mechanics.},
archiveprefix = {arXiv},
eid           = {arXiv:2107.03196},
eprint        = {2107.03196},
keywords      = {Quantum Physics},
primaryclass  = {quant-ph},
}

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Keywords: open system dynamics, quantum optics, indefinite causal order, quantum metrology.