Precision and Work Fluctuations in Gaussian Battery Charging

Nicolai Friis1,2 and Marcus Huber1

1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
2Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria

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One of the most fundamental tasks in quantum thermodynamics is extracting energy from one system and subsequently storing this energy in an appropriate battery. Both of these steps, work extraction and charging, can be viewed as cyclic Hamiltonian processes acting on individual quantum systems. Interestingly, so-called passive states exist, whose energy cannot be lowered by unitary operations, but it is safe to assume that the energy of any not fully charged battery may be increased unitarily. However, unitaries raising the average energy by the same amount may differ in qualities such as their precision, fluctuations, and charging power. Moreover, some unitaries may be extremely difficult to realize in practice. It is hence of crucial importance to understand the qualities that can be expected from practically implementable transformations. Here, we consider the limitations on charging batteries when restricting to the feasibly realizable family of Gaussian unitaries. We derive optimal protocols for general unitary operations as well as for the restriction to easier implementable Gaussian unitaries. We find that practical Gaussian battery charging, while performing significantly less well than is possible in principle, still offers asymptotically vanishing relative charge variances and fluctuations.

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[1] J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics — a topical review, J. Phys. A: Math. Theor. 49, 143001 (2016) [arXiv:1505.07835].

[2] J. Millen and A. Xuereb, Perspective on quantum thermodynamics, New J. Phys. 18, 011002 (2016) [arXiv:1509.01086].

[3] S. Vinjanampathy and J. Anders, Quantum Thermodynamics, Contemp. Phys. 57, 1 (2016) [arXiv:1508.06099].

[4] F. G. S. L. Brandão, M. Horodecki, N. H. Y. Ng, J. Oppenheim, and S. Wehner, The second laws of quantum thermodynamics, Proc. Natl. Acad. Sci. U.S.A. 112, 3275 (2015) [arXiv:1305.5278].

[5] F. G. S. L. Brandão, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, The Resource Theory of Quantum States Out of Thermal Equilibrium, Phys. Rev. Lett. 111, 250404 (2013) [arXiv:1111.3882].

[6] M. P. Müller, Correlating thermal machines and the second law at the nanoscale, e-print arXiv:1707.03451 [quant-ph] (2017).

[7] C. Gogolin and J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys. 79, 056001 (2016) [arXiv:1503.07538].

[8] W. Pusz and S. L. Woronowicz, Passive states and KMS states for general quantum systems, Commun. Math. Phys. 58, 273 (1978).

[9] M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, J. Tura, and A. Acín, Most energetic passive states, Phys. Rev. E 92, 042147 (2015) [arXiv:1502.07311].

[10] E. G. Brown, N. Friis, and M. Huber, Passivity and practical work extraction using Gaussian operations, New J. Phys. 18, 113028 (2016) [arXiv:1608.04977].

[11] C. Perry, P. Ć wikliński, J. Anders, M. Horodecki, and J. Oppenheim, A sufficient set of experimentally implementable thermal operations, e-print arXiv:1511.06553 [quant-ph] (2017).

[12] M. Lostaglio, Á. M. Alhambra, and C. Perry, Elementary Thermal Operations, Quantum 2, 52 (2018) [arXiv:1607.00394].

[13] P. Mazurek and M. Horodecki, Decomposability and Convex Structure of Thermal Processes, e-print arXiv:1707.06869 [quant-ph] (2017).

[14] F. Clivaz, R. Silva, G. Haack, J. Bohr Brask, N. Brunner, and M. Huber, Unifying paradigms of quantum refrigeration: resource-dependent limits, e-print arXiv:1710.11624 [quant-ph] (2017).

[15] M. Horodecki and J. Oppenheim, Fundamental limitations for quantum and nanoscale thermodynamics, Nat. Commun. 4, 2059 (2013) [arXiv:1111.3834].

[16] G. Gour, M. P. Müller, V. Narasimhachar, R. W. Spekkens, and N. Yunger Halpern, The resource theory of informational nonequilibrium in thermodynamics, Phys. Rep. 583, 1-58 (2015) [arXiv:1309.6586].

[17] J. Åberg, Catalytic Coherence, Phys. Rev. Lett. 113, 150402 (2014), [arXiv:1304.1060].

[18] A. S. L. Malabarba, A. J. Short, and P. Kammerlander, Clock-Driven Quantum Thermal Engines, New J. Phys. 17, 045027 (2015) [arXiv:1412.1338].

[19] P. Skrzypczyk, A. J. Short, and S. Popescu, Extracting work from quantum systems, e-print arXiv:1302.2811 [quant-ph] (2013).

[20] P. Skrzypczyk, A. J. Short, and S. Popescu, Work extraction and thermodynamics for individual quantum systems, Nat. Commun. 5, 4185 (2014) [arXiv:1307.1558].

[21] F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantacell: Powerful charging of quantum batteries, New J. Phys. 17, 075015 (2015) [arXiv:1503.07005].

[22] F. Campaioli, F. A. Pollock, F. C. Binder, L. C. Céleri, J. Goold, S. Vinjanampathy, and K. Modi, Enhancing the charging power of quantum batteries, Phys. Rev. Lett. 118, 150601 (2017) [arXiv:1612.04991].

[23] D. Ferraro, M. Campisi, G. M. Andolina, V. Pellegrini, and M. Polini, High-Power Collective Charging of a Solid-State Quantum Battery, Phys. Rev. Lett. 120, 117702 (2018) [arXiv:1707.04930].

[24] P. P. Hofer, J.-R. Souquet, and A. A. Clerk, Quantum heat engine based on photon-assisted Cooper pair tunneling, Phys. Rev. B 93, 041418 (2016) [arXiv:1512.02165].

[25] P. P. Hofer, M. Perarnau-Llobet, J. Bohr Brask, R. Silva, M. Huber, and N. Brunner, Autonomous Quantum Refrigerator in a Circuit-QED Architecture Based on a Josephson Junction, Phys. Rev. B 94, 235420 (2016) [arXiv:1607.05218].

[26] M. T. Mitchison, M. Huber, J. Prior, M. P. Woods, and M. B. Plenio, Realising a quantum absorption refrigerator with an atom-cavity system, Quantum Sci. Technol. 1, 015001 (2016) [arXiv:1603.02082].

[27] G. Maslennikov, S. Ding, R. Hablutzel, J. Gan, A. Roulet, S. Nimmrichter, J. Dai, V. Scarani, and D. Matsukevich, Quantum absorption refrigerator with trapped ions, e-print arXiv:1702.08672 [quant-ph] (2017).

[28] J. Roßnagel, S. T. Dawkins, K. N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, and K. Singer, A single-atom heat engine, Science 352, 325 (2016) [arXiv:1510.03681].

[29] C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621 (2012) [arXiv:1110.3234].

[30] M. Campisi, P. Hänggi, and P. Talkner, Colloquium. Quantum Fluctuation Relations: Foundations and Applications, Rev. Mod. Phys. 83, 771 (2011); Erratum: Rev. Mod. Phys. 83, 1653 (2011) [arXiv:1012.2268].

[31] Á. M. Alhambra, L. Masanes, J. Oppenheim, and C. Perry, The second law of quantum thermodynamics as an equality, Phys. Rev. X 6, 041017 (2016) [arXiv:1601.05799].

[32] J. G. Richens and L. Masanes, From single-shot to general work extraction with bounded fluctuations in work, Nat. Commun. 7, 13511 (2016) [arXiv:1603.02417].

[33] M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys. 81, 1665 (2009) [arXiv:0811.3717].

[34] S. Olivares, Quantum optics in the phase space - A tutorial on Gaussian states, Eur. Phys. J. 203, 3 (2012) [arXiv:1111.0786].

[35] S. L. Braunstein, Squeezing as an irreducible resource, Phys. Rev. A 71, 055801 (2005) [arXiv:quant-ph/​9904002].

[36] S. Lloyd and S. L. Braunstein, Quantum computation over continuous variables, Phys. Rev. Lett. 82, 1784 (1999) [arXiv:quant-ph/​9810082].

[37] D. E. Bruschi, M. Perarnau-Llobet, N. Friis, K. V. Hovhannisyan, and M. Huber, The thermodynamics of creating correlations: Limitations and optimal protocols, Phys. Rev. E 91, 032118 (2015) [arXiv:1409.4647].

[38] D. E. Bruschi, N. Friis, I. Fuentes, and S. Weinfurtner, On the robustness of entanglement in analogue gravity systems, New J. Phys. 15, 113016 (2013) [arXiv:1305.3867].

[39] M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, and A. Acín, Extractable work from correlations, Phys. Rev. X 5, 041011 (2015) [arXiv:1407.7765].

[40] M. Huber, M. Perarnau-Llobet, K. V. Hovhannisyan, P. Skrzypczyk, C. Klöckl, N. Brunner, and A. Acín, Thermodynamic cost of creating correlations, New J. Phys. 17, 065008 (2015) [arXiv:1404.2169].

[41] N. Friis, M. Huber, and M. Perarnau-Llobet, Energetics of correlations in interacting systems, Phys. Rev. E 93, 042135 (2016) [arXiv:1511.08654].

[42] M. Brunelli, M. G. Genoni, M. Barbieri, and M. Paternostro, Detecting Gaussian entanglement via extractable work, Phys. Rev. A 96, 062311 (2017) [arXiv:1702.05110].

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[2] A Crescente, M Carrega, M Sassetti, and D Ferraro, "Charging and energy fluctuations of a driven quantum battery", New Journal of Physics 22 6, 063057 (2020).

[3] Dario Ferraro, Michele Campisi, Gian Marcello Andolina, Vittorio Pellegrini, Marco Polini, and E. Puppin, "Quantum resources for energy storage", EPJ Web of Conferences 230, 00003 (2020).

[4] Sergi Julià-Farré, Tymoteusz Salamon, Arnau Riera, Manabendra N. Bera, and Maciej Lewenstein, "Bounds on the capacity and power of quantum batteries", Physical Review Research 2 2, 023113 (2020).

[5] Francesco Campaioli, Felix A. Pollock, and Sai Vinjanampathy, Fundamental Theories of Physics 195, 207 (2018) ISBN:978-3-319-99045-3.

[6] Francesco Caravelli, Ghislaine Coulter-De Wit, Luis Pedro García-Pintos, and Alioscia Hamma, "Random quantum batteries", Physical Review Research 2 2, 023095 (2020).

[7] Luis Pedro García-Pintos, Alioscia Hamma, and Adolfo del Campo, "Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries", Physical Review Letters 125 4, 040601 (2020).

[8] Mir Alimuddin, Tamal Guha, and Preeti Parashar, "Structure of passive states and its implication in charging quantum batteries", Physical Review E 102 2, 022106 (2020).

[9] Stefano Gherardini, Francesco Campaioli, Filippo Caruso, and Felix C. Binder, "Stabilizing open quantum batteries by sequential measurements", Physical Review Research 2 1, 013095 (2020).

[10] A. Serafini, M. Lostaglio, S. Longden, U. Shackerley-Bennett, C.-Y. Hsieh, and G. Adesso, "Gaussian Thermal Operations and The Limits of Algorithmic Cooling", Physical Review Letters 124 1, 010602 (2020).

[11] Elisa Bäumer, Martí Perarnau-Llobet, Philipp Kammerlander, Henrik Wilming, and Renato Renner, "Imperfect Thermalizations Allow for Optimal Thermodynamic Processes", Quantum 3, 153 (2019).

[12] Tiago Debarba, Gonzalo Manzano, Yelena Guryanova, Marcus Huber, and Nicolai Friis, "Work estimation and work fluctuations in the presence of non-ideal measurements", arXiv:1902.08568, New Journal of Physics 21 11, 113002 (2019).

[13] Yu-Yu Zhang, Tian-Ran Yang, Libin Fu, and Xiaoguang Wang, "Powerful harmonic charging in a quantum battery", Physical Review E 99 5, 052106 (2019).

[14] Jie Chen, Liyao Zhan, Lei Shao, Xingyu Zhang, Yuyu Zhang, and Xiaoguang Wang, "Charging Quantum Batteries with a General Harmonic Driving Field", Annalen der Physik 532 4, 1900487 (2020).

[15] Emma McKay, Nayeli A. Rodríguez-Briones, and Eduardo Martín-Martínez, "Fluctuations of work cost in optimal generation of correlations", Physical Review E 98 3, 032132 (2018).

[16] Ludovico Lami, Bartosz Regula, Xin Wang, Rosanna Nichols, Andreas Winter, and Gerardo Adesso, "Gaussian quantum resource theories", Physical Review A 98 2, 022335 (2018).

[17] Alan C. Santos, Barış Çakmak, Steve Campbell, and Nikolaj T. Zinner, "Stable adiabatic quantum batteries", Physical Review E 100 3, 032107 (2019).

[18] Domingos S. P. Salazar and Gabriel T. Landi, "Nonlinear Onsager relations for Gaussian quantum maps", Physical Review Research 2 3, 033090 (2020).

[19] Niels Lörch, Christoph Bruder, Nicolas Brunner, and Patrick P Hofer, "Optimal work extraction from quantum states by photo-assisted Cooper pair tunneling", Quantum Science and Technology 3 3, 035014 (2018).

[20] Raffaele Salvia and Vittorio Giovannetti, "Energy upper bound for structurally stable N-passive states", Quantum 4, 274 (2020).

[21] Srijon Ghosh, Titas Chanda, and Aditi Sen(De), "Enhancement in the performance of a quantum battery by ordered and disordered interactions", Physical Review A 101 3, 032115 (2020).

[22] Fu-Quan Dou, Yuan-Jin Wang, and Jian-An Sun, "Closed-loop three-level charged quantum battery", EPL (Europhysics Letters) 131 4, 43001 (2020).

[23] Dario Ferraro, Gian Marcello Andolina, Michele Campisi, Vittorio Pellegrini, and Marco Polini, "Quantum supercapacitors", Physical Review B 100 7, 075433 (2019).

[24] Giuseppe Vitagliano, Claude Klöckl, Marcus Huber, and Nicolai Friis, Fundamental Theories of Physics 195, 731 (2018) ISBN:978-3-319-99045-3.

[25] Arnab Ghosh, Wolfgang Niedenzu, Victor Mukherjee, and Gershon Kurizki, Fundamental Theories of Physics 195, 37 (2018) ISBN:978-3-319-99045-3.

[26] Thao P. Le, Jesper Levinsen, Kavan Modi, Meera M. Parish, and Felix A. Pollock, "Spin-chain model of a many-body quantum battery", Physical Review A 97 2, 022106 (2018).

[27] Francesco Campaioli, Felix A. Pollock, and Sai Vinjanampathy, "Quantum Batteries - Review Chapter", arXiv:1805.05507.

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