Marcus Huber
Independent Research Group Leader
Huber Group
Contact
Email: Marcus.Huber(at)oeaw.ac.at
Telephone: +43 (1) 51581 - 9560
Room: 1.09
Biographical sketch
Professional Status
2016- present: IQOQI Vienna, Group Leader (FWF-START)
2015 – 2016 University of Geneva, SNF-AMBIZIONE Grantee, applied physics group (GAP-Optique)
2014 – 2015 Universitat Autonoma de Barcelona , Juan de la Cierva Fellow, quantum information group (GIQ)
2013 –2016 Institute of Photonic Sciences (ICFO), visiting scientist, Acin group
2013 – 2014 Universitat Autonoma de Barcelona, Marie Curie Fellow, quantum information group (GIQ)
2012 – 2013 University of Bristol , Marie Curie Fellow, department of applied mathematics
2012 University of Bristol, ERC funded research associate, department of applied mathematics
2010 – 2012 University of Vienna, FWF funded post-doctoral researcher, particle physics group
2008 University of Vienna, research assistant, particle physics group
Education
2010: Dr. rer. nat. (PhD equivalent) University of Vienna
2008: Mag. rer. nat. (MSc equivalent) University of Vienna
Teaching
Publications
Journal Publication (75)
- Kanitschar, Florian; Bergmayr-Mann, Alexandra; Pivoluska, Matej; Huber, Marcus (2024) Harnessing high-dimensional temporal entanglement using limited interferometric setups. PHYS REV APPL, Bd. 22 (5), S. ARTN 054054.
- Guzmán, José Antonio Marín; Erker, Paul; Gasparinetti, Simone; Huber, Marcus; Halpern, Nicole Yunger (2024) Key Issues Review: Useful autonomous quantum machines. Rep. Prog. Phys., Bd. 87 (12), S. 122001.
- Bittermann, Julius; Bulla, Lukas; Ecker, Sebastian; Neumann, Sebastian P.; Fink, Matthias et al. [..] (2024) Photonic entanglement during a zero-g flight. Quantum, Bd. 8, S. 1256.
- Liu, Shuheng; Fadel, Matteo; He, Qiongyi; Huber, Marcus; Vitagliano, Giuseppe (2024) Bounding entanglement dimensionality from the covariance matrix. Quantum, Bd. 8, S. 1236.
- Morelli, Simon; Eltschka, Christopher; Huber, Marcus; Siewert, Jens (2024) Correlation constraints and the Bloch geometry of two qubits. PHYS REV A, Bd. 109 (1), S. ARTN 012423.
- Meier, Florian; Schwarzhans, Emanuel; Erker, Paul; Huber, Marcus (2023) Fundamental Accuracy-Resolution Trade-Off for Timekeeping Devices. Physical Review Letters, Bd. 131 (22), S. 220201.
- Morelli, Simon; Huber, Marcus; Tavakoli, Armin (2023) Resource-Efficient High-Dimensional Entanglement Detection via Symmetric Projections. Physical Review Letters, Bd. 131 (17).
- Xuereb, Jake; Erker, Paul; Meier, Florian; Mitchison, Mark T.; Huber, Marcus (2023) Impact of Imperfect Timekeeping on Quantum Control. Physical Review Letters, Bd. 131 (16), S. 160204.
- Gao, Xiaoqin; Appel, Paul; Friis, Nicolai; Ringbauer, Martin; Huber, Marcus (2023) On the role of entanglement in qudit-based circuit compression. QUANTUM, Bd. 7.
- Araújo, Mateus; Huber, Marcus; Navascués, Miguel; Pivoluska, Matej; Tavakoli, Armin (2023) Quantum key distribution rates from semidefinite programming. QUANTUM-AUSTRIA, Bd. 7, S. 1019.
- Liu, Shuheng; He, Qiongyi; Huber, Marcus; Guhne, Otfried; Vitagliano, Giuseppe (2023) Characterizing Entanglement Dimensionality from Randomized Measurements. PRX QUANTUM, Bd. 4 (2), S. ARTN 020324.
- Achatz, Lukas; Bulla, Lukas; Ecker, Sebastian; Ortega, Evelyn A.; Bartokos, Michael et al. [..] (2023) Simultaneous transmission of hyper-entanglement in three degrees of freedom through a multicore fiber. NPJ QUANTUM INFORMATION, Bd. 9 (1), S. ARTN 45.
- Hrmo, Pavel; Wilhelm, Benjamin; Gerster, Lukas; van Mourik, Martin W.; Huber, Marcus et al. [..] (2023) Native qudit entanglement in a trapped ion quantum processor. NATURE COMMUNICATIONS, Bd. 14 (1), S. 2242.
- Bulla, Lukas; Pivoluska, Matej; Hjorth, Kristian; Kohout, Oskar; Lang, Jan et al. [..] (2023) Nonlocal Temporal Interferometry for Highly Resilient Free-Space Quantum Communication. Phys. Rev. X, Bd. 13 (2).
- Taranto, Philip; Bakhshinezhad, Faraj; Bluhm, Andreas; Silva, Ralph; Friis, Nicolai et al. [..] (2023) Landauer Versus Nernst: What is the True Cost of Cooling a Quantum System?. PRX QUANTUM, Bd. 4 (1), S. ARTN 010332.
- Morelli, Simon; Yamasaki, Hayata; Huber, Marcus; Tavakoli, Armin (2022) Entanglement Detection with Imprecise Measurements. Phys. Rev. Lett., Bd. 128 (25), S. ARTN 250501.
- Appel, Paul; Heilman, Alexander J.; Wertz, Ezekiel W.; Lyons, David W.; Huber, Marcus et al. [..] (2022) Finite-Function-Encoding Quantum States. Quantum, Bd. 6, S. ARTN 708.
- Yamasaki, Hayata; Morelli, Simon; Miethlinger, Markus; Bavaresco, Jessica; Friis, Nicolai et al. [..] (2022) Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation. Quantum Journal, Bd. 6, S. 695.
- Chen, Yuanyuan; Ecker, Sebastian; Chen, Lixiang; Steinlechner, Fabian; Huber, Marcus et al. [..] (2021) Temporal distinguishability in Hong-Ou-Mandel interference for harnessing high-dimensional frequency entanglement. npj quantum information, Bd. 7 (1), S. ARTN 167 <'https://www.nature.com/articles/s41534-021-00504-0'>.
- Usui, Ayaka; Niedenzu, Wolfgang; Huber, Marcus (2021) Simplifying the design of multilevel thermal machines using virtual qubits. Phys. Rev. A, Bd. 104 (4), S. ARTN 042224.
- Hu, Xiao-Min; Zhang, Chao; Guo, Yu; Wang, Fang-Xiang; Xing, Wen-Bo et al. [..] (2021) Pathways for Entanglement-Based Quantum Communication in the Face of High Noise. Phys. Rev. Lett., Bd. 127 (11), S. ARTN 110505.
- Ecker, Sebastian; Sohr, Philipp; Bulla, Lukas; Huber, Marcus; Bohmann, Martin et al. [..] (2021) Experimental Single-Copy Entanglement Distillation. Physical Review Letters, Bd. 127 (4), S. 040506.
- Gluza, Marek; Sabino, Joao; Ng, Nelly H. Y.; Vitagliano, Giuseppe; Pezzutto, Marco et al. [..] (2021) Quantum Field Thermal Machines. PRX QUANTUM, Bd. 2 (3), S. ARTN 030310.
- Fadel, Matteo; Usui, Ayaka; Huber, Marcus; Friis, Nicolai; Vitagliano, Giuseppe (2021) Entanglement Quantification in Atomic Ensembles. Phys. Rev. Lett., Bd. 127 (1), S. ARTN 010401.
- Eltschka, Christopher; Huber, Marcus; Morelli, Simon; Siewert, Jens (2021) The shape of higher-dimensional state space: Bloch-ball analog for a qutrit. Quantum, Bd. 5, S. 485.
- Kraft, Tristan; Designolle, Sebastien; Ritz, Christina; Brunner, Nicolas; Guehne, Otfried et al. [..] (2021) Quantum entanglement in the triangle network. Phys. Rev. A, Bd. 103 (6), S. ARTN L060401.
- Chen, Xiaojiong; Deng, Yaohao; Liu, Shuheng; Pramanik, Tanumoy; Mao, Jun et al. [..] (2021) A generalized multipath delayed-choice experiment on a large-scale quantum nanophotonic chip. Nat. Commun., Bd. 12 (1), S. ARTN 2712.
- Pearson, A. N.; Guryanova, Y.; Erker, P.; Laird, E. A.; Briggs, G. A. D. et al. [..] (2021) Measuring the Thermodynamic Cost of Timekeeping. Phys. Rev. X, Bd. 11 (2), S. ARTN 021029.
- Schwarzhans, Emanuel; Lock, Maximilian P. E.; Erker, Paul; Friis, Nicolai; Huber, Marcus (2021) Autonomous Temporal Probability Concentration: Clockworks and the Second Law of Thermodynamics. Physical Review X, Bd. 11, S. 011046.
- Doda, Mirdit; Huber, Marcus; Murta, Glaucia; Pivoluska, Matej; Plesch, Martin et al. [..] (2021) Quantum Key Distribution Overcoming Extreme Noise: Simultaneous Subspace Coding Using High-Dimensional Entanglement. Phys. Rev. Appl., Bd. 15 (3), S. ARTN 034003.
- Herrera Valencia, N.; Srivastav, V.; Pivoluska, M.; Huber, M.; Friis, N. et al. [..] (2020) High-Dimensional Pixel Entanglement: Efficient Generation and Certification. Quantum, Bd. 4, S. 376.
- Taranto, P.; Bakhshinezhad, F.; Schüttelkopf, P.; Clivaz, F.; Huber, M. (2020) Exponential Improvement for Quantum Cooling through Finite-Memory Effects. Physical Review Applied, Bd. 14, S. 054005.
- Hu, X.-M.; Xing, W.-B.; Zhang, C.; Liu, B.-H.; Pivoluska, M. et al. [..] (2020) Experimental creation of multi-photon high-dimensional layered quantum states. npj Quantum Information, Bd. 6, S. 88.
- Hu, Xiao-Min; Xing, Wen-Bo; Liu, Bi-Heng; Huang, Yun-Feng; Li, Chuan-Feng et al. [..] (2020) Efficient Generation of High-Dimensional Entanglement through Multipath Down-Conversion. Physical Review Letters, Bd. 125 (9), S. 090503.
- Chen, Yuanyuan; Ecker, Sebastian; Bavaresco, Jessica; Scheidl, Thomas; Chen, Lixiang et al. [..] (2020) Verification of high-dimensional entanglement generated in quantum interference. Physical Review A, Bd. 101 (3), S. 032302.
- Brandt, Forian; Hiekkamaeki, Markus; Bouchard, Frederic; Huber, Marcus; Fickler, Robert (2020) High-dimensional quantum gates using full-field spatial modes of photons. Optica, Bd. 7 (2), S. 98-107.
- Appel, Paul; Huber, Marcus; Klockl, Claude (2020) Monogamy of correlations and entropy inequalities in the Bloch picture. Journal of Physics Communications, Bd. 4 (2), S. 025009.
- Guryanova, Yelena; Friis, Nicolai; Huber, Marcus (2020) Ideal Projective Measurements Have Infinite Resource Costs. Quantum, Bd. 4, S. 222.
- Morelli, Simon; Kloeckl, Claude; Eltschka, Christopher; Siewert, Jens; Huber, Marcus (2020) Dimensionally sharp inequalities for the linear entropy. Linear Alg. Appl., Bd. 584, S. 294-325.
- Daniel Llewellyn, Yunhong Ding, Imad I. Faruque, Stefano Paesani, Davide Bacco, Raffaele Santagati, Yan-Jun Qian, Yan Li, Yun-Feng Xiao, Marcus Huber, Mehul Malik, Gary F. Sinclair, Xiaoqi Zhou, Karsten Rottwitt, Jeremy L. O’Brien, John G. Rarity, Qihuang Gong, Leif K. Oxenlowe, Jianwei Wang & Mark G. Thompson (2019) Chip-to-chip quantum teleportation and multi-photon entanglement in silicon. nature physics, Bd. Letters, S. 1-7.
- Ecker, Sebastian; Bouchard, Frederic; Bulla, Lukas; Brandt, Florian; Kohout, Oskar et al. [..] (2019) Overcoming Noise in Entanglement Distribution. Physical Review X, Bd. 9, S. 041042.
- Debarba, Tiago; Manzano, Gonzalo; Guryanova, Yelena; Huber, Marcus; Friis, Nicolai (2019) Work estimation and work fluctuations in the presence of non-ideal measurements. New Journal of Physics, Bd. 21, S. 113002.
- Clivaz, Fabien; Silva, Ralph; Haack, Geraldine; Brask, Jonatan Bohr; Brunner, Nicolas et al. [..] (2019) Unifying Paradigms of Quantum Refrigeration: A Universal and Attainable Bound on Cooling. Physical Revieew Letters, Bd. 123 (17), S. 170605.
- Clivaz, Fabien; Silva, Ralph; Haack, Geraldine; Brask, Jonatan Bohr; Brunner, Nicolas et al. [..] (2019) Unifying paradigms of quantum refrigeration: Fundamental limits of cooling and associated work costs. Physical Review E, Bd. 100 (4), S. 042130.
- Bakhshinezhad, Faraj; Clivaz, Fabien; Vitagliano, Giuseppe; Erker, Paul; Rezakhani, Ali et al. [..] (2019) Thermodynamically optimal creation of correlations. Journal of Physics A, Bd. 52, S. 46.
- Niedenzu, Wolfgang; Huber, Marcus; Boukobza, Erez (2019) Concepts of work in autonomous quantum heat engines. QUANTUM, Bd. 3, S. 195.
- Friis, N.; Vitagliano, G.; Malik, M.; Huber, M. (2019) Entanglement certification from theory to experiment. Nature Reviews Physics, Bd. 1, S. 72-87.
- Bouchard, Frederic; Valencia, Natalia Herrera; Brandt, Florian; Fickler, Robert; Huber, Marcus et al. [..] (2018) Measuring azimuthal and radial modes of photons. Opt. Express, Bd. 26 (24), S. 31925-31941.
- Huber, Marcus; Lami, Ludovico; Lancien, Cecilia; Mueller-Hermes, Alexander (2018) High-Dimensional Entanglement in States with Positive Partial Transposition. Physical Review Letters, Bd. 121 (20), S. 200503.
- Bavaresco, Jessica; Valencia, Natalia Herrera; Kloeckl, Claude; Pivoluska, Matej; Erker, Paul et al. [..] (2018) Measurements in two bases are sufficient for certifying high-dimensional entanglement. Nature Physics, Bd. 14 (10), S. 1032-1037.
- Bohr Brask, Jonatan; Brunner, Nicolas; Huber, Marcus; Haack, Géraldine; Tavakoli, Armin (2018) Heralded generation of maximal entanglement in any dimension via incoherent coupling to thermal baths. Quantum, Bd. 2, S. 73.
- Friis, Nicolai; Huber, Marcus (2018) Precision and Work Fluctuations in Gaussian Battery Charging. QUANTUM, Bd. 2, S. 61.
- Anza, Fabio; Gogolin, Christian; Huber, Marcus (2018) Eigenstate Thermalization for Degenerate Observables. Physical Review Letters, Bd. 120 (15), S. 150603.
- Pivoluska, Matej; Huber, Marcus; Malik, Mehul (2018) Layered quantum key distribution. Physical Review A, Bd. 97 (3), S. 032312.
- Kraft, Tristan; Ritz, Christina; Brunner, Nicolas; Huber, Marcus; Guehne, Otfried (2018) Characterizing Genuine Multilevel Entanglement. Physical Review Letters, Bd. 120 (6), S. 060502.
- Tiranov, Alexey; Designolle, Sebastien; Cruzeiro, Emmanuel Zambrini; Lavoie, Jonathan; Brunner, Nicolas et al. [..] (2017) Quantification of multidimensional entanglement stored in a crystal. Physical Review A, Bd. 96 (4), S. 040303.
- Clivaz, F.; Huber, M.; Lami, L.; Murta, G. (2017) Genuine-multipartite entanglement criteria based on positive maps. Journal of Mathematical Physics, Bd. 58 (8), S. 082201.
- Erker, P.; Mitchison, M. T.; Silva, R.; Woods, M. P.; Brunner, N. et al. [..] (2017) Autonomous Quantum Clocks: Does Thermodynamics Limit Our Ability to Measure Time?. Physical Review X, Bd. 7 (3), S. 031022.
- Erker, P.; Krenn, M.; Huber, M. (2017) Quantifying high dimensional entanglement with two mutually unbiased bases. Quantum, Bd. 1, S. 22.
- Steinlechner, F.; Ecker, S.; Fink, M.; Liu, B.; Bavaresco, J. et al. [..] (2017) Distribution of high-dimensional entanglement via an intra-city free-space link. Nature Communications, Bd. 8, S. 15971.
- Lahiri, Mayukh; Hochrainer, Armin; Lapkiewicz, Radek; Barreto Lemos, Gabriela; Zeilinger, Anton (2017) Partial Polarization by Quantum Distinguishability. Physical Review A, Bd. 95, S. 033816.
- Martin, A.; Guerreiro, T.; Tiranov, A.; Designolle, S.; Frowis, F. et al. [..] (2017) Quantifying Photonic High-Dimensional Entanglement. Physical Review Letters, Bd. 118 (11), S. 110501.
- Perarnau-Llobet, Marti; Baumer, Elisa; Hovhannisyan, Karen V.; Huber, Marcus; Acin, Antonio (2017) No-Go Theorem for the Characterization of Work Fluctuations in Coherent Quantum Systems. Physical Review Letters, Bd. 118 (7), S. 070601.
- Hofer, Patrick P.; Perarnau-Llobet, Marti; Brask, Jonatan Bohr; Silva, Ralph; Huber, Marcus et al. [..] (2016) Autonomous quantum refrigerator in a circuit QED architecture based on a Josephson junction. Physical Review B, Bd. 94 (23), S. 235420.
- Tiranov, Alexey; Strassmann, Peter C.; Lavoie, Jonathan; Brunner, Nicolas; Huber, Marcus et al. [..] (2016) Temporal Multimode Storage of Entangled Photon Pairs. Physical Review Letters, Bd. 117 (24), S. 240506.
- Brown, Eric G.; Friis, Nicolai; Huber, Marcus (2016) Passivity and practical work extraction using Gaussian operations. New Journal of Physics, Bd. 18, S. 113028.
- Sentis, Gael; Eltschka, Christopher; Guehne, Otfried; Huber, Marcus; Siewert, Jens (2016) Quantifying Entanglement of Maximal Dimension in Bipartite Mixed States. Physical Review Letters, Bd. 117 (9), S. 190502.
- Lami, Ludovico; Huber, Marcus (2016) Bipartite depolarizing maps. Journal of Mathematical Physics, Bd. 57 (9), S. 092201.
- Lancien, Cecilia; Di Martino, Sara; Huber, Marcus; Piani, Marco; Adesso, Gerardo et al. [..] (2016) Should Entanglement Measures be Monogamous or Faithful?. Physical Review Letters, Bd. 117 (6), S. 060501.
- Asadian, Ali; Erker, Paul; Huber, Marcus; Klockl, Claude (2016) Heisenberg-Weyl Observables: Bloch vectors in phase space. Physical Review A, Bd. 94 (1), S. 010301.
- Moroder, Tobias; Gittsovich, Oleg; Huber, Marcus; Uola, Roope; Guehne, Otfried (2016) Steering Maps and Their Application to Dimension-Bounded Steering. Physical Review Letters, Bd. 116 (9), S. 090403.
- Malik, Mehul; Erhard, Manuel; Huber, Marcus; Krenn, Mario; Fickler, Robert et al. [..] (2016) Multi-photon entanglement in high dimensions. Nature Photonics, Bd. 10, S. 248-252.
- Kloeckl, C.; Huber, M. (2015) Characterizing multipartite entanglement without shared reference frames. Phys. Rev. A, Bd. 91 (4), S. 042339.
- Krenn, Mario; Huber, Marcus; Fickler, Robert; Lapkiewicz, Radek; Ramelow, Sven et al. [..] (2014) Generation and confirmation of a (100 × 100)-dimensional entangled quantum system. Proceedings of the National Academy of Sciences, Bd. 111 (17), S. 6243-6247.
- Krenn, Mario; Fickler, Robert; Huber, Marcus; Lapkiewicz, Radek; Plick, William et al. [..] (2013) Entangled singularity patterns of photons in Ince-Gauss modes. Physical Review A, Bd. 87 (1), S. 012326.
Other Publication (16)
- Lib, Ohad; Liu, Shuheng; Shekel, Ronen; He, Qiongyi; Huber, Marcus et al. [..] (2024) Experimental certification of high-dimensional entanglement with randomized measurements. arXiv:quant-ph, Bd. 2412.04643 [quant-ph].
- Xuereb, Jake; Junior, A. de Oliveira; Clivaz, Fabien; Bakhshinezhad, Pharnam; Huber, Marcus (2024) What resources do agents need to acquire knowledge in Quantum Thermodynamics?. arXiv:quant-ph, Bd. 2410.18167 [quant-ph].
- Mehboudi, Mohammad; Meier, Florian; Huber, Marcus; Miller, Harry J. D. (2024) Optimal limits of continuously monitored thermometers and their Hamiltonian structure. arXiv:quant-ph, Bd. 2408.01313 [quant-ph].
- Liu, Zhi-Feng; Ren, Zhi-Cheng; Wan, Pei; Zhu, Wen-Zheng; Cheng, Zi-Mo et al. [..] (2024) Heralded High-Dimensional Photon-Photon Quantum Gate. arXiv:quant-ph, Bd. 2407.16356 [quant-ph].
- Meier, Florian; Minoguchi, Yuri; Sundelin, Simon; Apollaro, Tony J. G.; Erker, Paul et al. [..] (2024) Precision is not limited by the second law of thermodynamics. arXiv:quant-ph, Bd. 2407.07948 [quant-ph].
- Kanitschar, Florian; Huber, Marcus (2024) A practical framework for analyzing high-dimensional QKD setups. arXiv:quant-ph, Bd. 2406.08544 [quant-ph].
- Li, Nicky Kai Hong; Huber, Marcus; Friis, Nicolai (2024) High-dimensional entanglement witnessed by correlations in arbitrary bases. arXiv:quant-ph, Bd. 2406.04395 [quant-ph].
- Meier, Florian; Rivlin, Tom; Debarba, Tiago; Xuereb, Jake; Huber, Marcus et al. [..] (2024) Emergence of a second law of thermodynamics in isolated quantum systems. arXiv:quant-ph, Bd. 2406.01677 [quant-ph].
- Liu, Shuheng; He, Qiongyi; Huber, Marcus; Vitagliano, Giuseppe (2024) A nonlinear criterion for characterizing high-dimensional multipartite entanglement. arXiv:quant-ph, Bd. 2405.03261 [quant-ph].
- White, Simon J. U.; Polino, Emanuele; Ghafari, Farzad; Joch, Dominick J.; Villegas-Aguilar, Luis et al. [..] (2024) A robust approach for time-bin encoded photonic quantum information protocols. arXiv:quant-ph, Bd. 2404.16106 [quant-ph].
- Taranto, Philip; Lipka-Bartosik, Patryk; Rodríguez-Briones, Nayeli A.; Perarnau-Llobet, Martí; Friis, Nicolai et al. [..] (2024) Efficiently Cooling Quantum Systems with Finite Resources: Insights from Thermodynamic Geometry. arXiv:quant-ph, Bd. 2404.06649 [quant-ph].
- Debarba, Tiago; Huber, Marcus; Friis, Nicolai (2024) Broadcasting Quantum Information using Finite Resources. arXiv:quant-ph, Bd. 2403.07660 [quant-ph].
- Meier, Florian; Huber, Marcus; Erker, Paul; Xuereb, Jake (2024) Autonomous Quantum Processing Unit: What does it take to construct a self-contained model for quantum computation?. arXiv:quant-ph, Bd. 2402.00111 [quant-ph].
- Xuereb, Jake; Debarba, Tiago; Huber, Marcus; Erker, Paul (2023) Quantum Coding with Finite Thermodynamic Resources. arXiv:quant-ph, Bd. 2311.14561 [quant-ph].
- Chang, Kai-Chi; Sarihan, Murat Can; Cheng, Xiang; Erker, Paul; Mueller, Andrew et al. [..] (2023) Experimental high-dimensional entanglement certification and quantum steering with time-energy measurements. arXiv:quant-ph, Bd. 2310.20694 [quant-ph].
- Guzmán, José Antonio Marín; Erker, Paul; Gasparinetti, Simone; Huber, Marcus; Halpern, Nicole Yunger (2023) DiVincenzo-like criteria for autonomous quantum machines. arXiv:quant-ph, Bd. 2307.08739 [quant-ph].