Ideal Projective Measurements Have Infinite Resource Costs
Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
Published: | 2020-01-13, volume 4, page 222 |
Eprint: | arXiv:1805.11899v3 |
Doi: | https://doi.org/10.22331/q-2020-01-13-222 |
Citation: | Quantum 4, 222 (2020). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
We show that it is impossible to perform ideal projective measurements on quantum systems using finite resources. We identify three fundamental features of ideal projective measurements and show that when limited by finite resources only one of these features can be salvaged. Our framework is general enough to accommodate any system and measuring device (pointer) models, but for illustration we use an explicit model of an $N$-particle pointer. For a pointer that perfectly reproduces the statistics of the system, we provide tight analytic expressions for the energy cost of performing the measurement. This cost may be broken down into two parts. First, the cost of preparing the pointer in a suitable state, and second, the cost of a global interaction between the system and pointer in order to correlate them. Our results show that, even under the assumption that the interaction can be controlled perfectly, achieving perfect correlation is infinitely expensive. We provide protocols for achieving optimal correlation given finite resources for the most general system and pointer Hamiltonians, phrasing our results as fundamental bounds in terms of the dimensions of these systems.

Popular summary
Here, we investigate the structure and resource costs of non-ideal measurements and identify three fundamental properties that all ideal measurements possess. We argue that when limited by finite resources the three properties cannot hold simultaneously – one must choose which one of the properties to keep. Under the assumption that at least one property holds, we then derive expressions for the energy cost of performing such an imperfect measurement.
► BibTeX data
► References
[1] Sai Vinjanampathy and Janet Anders, Quantum thermodynamics, Contemp. Phys. 57, 545 (2016), arXiv:1508.06099.
https://doi.org/10.1080/00107514.2016.1201896
arXiv:arXiv:1508.06099
[2] James Millen and André Xuereb, Perspective on quantum thermodynamics, New J. Phys. 18, 011002 (2016), arXiv:1509.01086.
https://doi.org/10.1088/1367-2630/18/1/011002
arXiv:arXiv:1509.01086
[3] John Goold, Marcus Huber, Arnau Riera, Lídia del Rio, and Paul Skrzypczyk, The role of quantum information in thermodynamics — a topical review, J. Phys. A: Math. Theor. 49, 143001 (2016), arXiv:1505.07835.
https://doi.org/10.1088/1751-8113/49/14/143001
arXiv:arXiv:1505.07835
[4] Massimiliano Esposito and Christian Van den Broeck, Second law and landauer principle far from equilibrium, Europhys. Lett. 95, 40004 (2011), arXiv:1104.5165.
https://doi.org/10.1209/0295-5075/95/40004
arXiv:arXiv:1104.5165
[5] Kurt Jacobs, Quantum measurement and the first law of thermodynamics: the energy cost of measurement is the work value of the acquired information, Phys. Rev. E 86, 040106(R) (2012), arXiv:1208.1561.
https://doi.org/10.1103/PhysRevE.86.040106
arXiv:arXiv:1208.1561
[6] Fernando G. S. L. Brandão, Michał Horodecki, Nelly Huei Ying Ng, Jonathan Oppenheim, and Stephanie Wehner, The second laws of quantum thermodynamics, Proc. Natl. Acad. Sci. U.S.A. 11, 3275 (2015), arXiv:1305.5278.
https://doi.org/10.1073/pnas.1411728112
arXiv:arXiv:1305.5278
[7] Matteo Lostaglio, David Jennings, and Terry Rudolph, Description of quantum coherence in thermodynamic processes requires constraints beyond free energy, Nat. Commun. 6, 6383 (2015), arXiv:1405.2188.
https://doi.org/10.1038/ncomms7383
arXiv:arXiv:1405.2188
[8] Piotr Ć wikliński, Michał Studziński, Michał Horodecki, and Jonathan Oppenheim, Limitations on the Evolution of Quantum Coherences: Towards Fully Quantum Second Laws of Thermodynamics, Phys. Rev. Lett. 115, 210403 (2015), arXiv:1405.5029.
https://doi.org/10.1103/PhysRevLett.115.210403
arXiv:arXiv:1405.5029
[9] Álvaro M. Alhambra, Lluis Masanes, Jonathan Oppenheim, and Christopher Perry, Fluctuating Work: From Quantum Thermodynamical Identities to a Second Law Equality, Phys. Rev. X 6, 041017 (2016), arXiv:1601.05799.
https://doi.org/10.1103/PhysRevX.6.041017
arXiv:arXiv:1601.05799
[10] Henrik Wilming, Rodrigo Gallego, and Jens Eisert, Second law of thermodynamics under control restrictions, Phys. Rev. E 93, 042126 (2016), arXiv:1411.3754.
https://doi.org/10.1103/PhysRevE.93.042126
arXiv:arXiv:1411.3754
[11] Jakob Scharlau and Markus P. Müller, Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics, Quantum 2, 54 (2018), arXiv:1605.06092.
https://doi.org/10.22331/q-2018-02-22-54
arXiv:arXiv:1605.06092
[12] Lluis Masanes and Jonathan Oppenheim, A general derivation and quantification of the third law of thermodynamics, Nat. Commun. 8, 14538 (2017), arXiv:1412.3828.
https://doi.org/10.1038/ncomms14538
arXiv:arXiv:1412.3828
[13] Manabendra Nath Bera, Arnau Riera, Maciej Lewenstein, and Andreas Winter, Generalized Laws of Thermodynamics in the Presence of Correlations, Nat. Commun. 8, 2180 (2017), arXiv:1612.04779.
https://doi.org/10.1038/s41467-017-02370-x
arXiv:arXiv:1612.04779
[14] Leonard J. Schulman, Tal Mor, and Yossi Weinstein, Physical Limits of Heat-Bath Algorithmic Cooling, Phys. Rev. Lett. 94, 120501 (2005).
https://doi.org/10.1103/PhysRevLett.94.120501
[15] Henrik Wilming and Rodrigo Gallego, Third Law of Thermodynamics as a Single Inequality, Phys. Rev. X 7, 041033 (2017), arXiv:1701.07478.
https://doi.org/10.1103/PhysRevX.7.041033
arXiv:arXiv:1701.07478
[16] Fabien Clivaz, Ralph Silva, Géraldine Haack, Jonatan Bohr Brask, Nicolas Brunner, and Marcus Huber, Unifying paradigms of quantum refrigeration: fundamental limits of cooling and associated work costs, Phys. Rev. E 100, 042130 (2019a), arXiv:1710.11624.
https://doi.org/10.1103/PhysRevE.100.042130
arXiv:arXiv:1710.11624
[17] Fabien Clivaz, Ralph Silva, Géraldine Haack, Jonatan Bohr Brask, Nicolas Brunner, and Marcus Huber, Unifying Paradigms of Quantum Refrigeration: A Universal and Attainable Bound on Cooling, Phys. Rev. Lett. 123, 170605 (2019b), arXiv:1903.04970.
https://doi.org/10.1103/PhysRevLett.123.170605
arXiv:arXiv:1903.04970
[18] Tien D. Kieu, Principle of Unattainability of absolute zero temperature, the Third Law of Thermodynamics, and projective quantum measurements, Phys Lett A 383, 125848 (2019), arXiv:1804.04182.
https://doi.org/10.1016/j.physleta.2019.125848
arXiv:arXiv:1804.04182
[19] Jarosław K. Korbicz, Edgar A. Aguilar, Piotr Ć wikliński, and Paweł Horodecki, Generic appearance of objective results in quantum measurements, Phys. Rev. A 96, 032124 (2017), arXiv:1604.02011.
https://doi.org/10.1103/PhysRevA.96.032124
arXiv:arXiv:1604.02011
[20] Wojciech Hubert Zurek, Quantum Darwinism, Nat. Phys. 5, 181 (2009), arXiv:0903.5082.
https://doi.org/10.1038/nphys1202
arXiv:arXiv:0903.5082
[21] Takahiro Sagawa and Masahito Ueda, Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure, Phys. Rev. Lett. 102, 250602 (2009), arXiv:0809.4098.
https://doi.org/10.1103/PhysRevLett.102.250602
arXiv:arXiv:0809.4098
[22] Cyril Elouard, David Herrera-Martí, Benjamin Huard, and Alexia Auffèves, Extracting work from quantum measurement in Maxwell demon engines, Phys. Rev. Lett. 118, 260603 (2017), arXiv:1702.01917.
https://doi.org/10.1103/PhysRevLett.118.260603
arXiv:arXiv:1702.01917
[23] Patryk Lipka-Bartosik and Rafal Demkowicz-Dobrzanski, Thermodynamic work cost of quantum estimation protocols, J. Phys. A: Math. Theor. 51, 474001 (2018), arXiv:1805.01477.
https://doi.org/10.1088/1751-8121/aae664
arXiv:arXiv:1805.01477
[24] Cyril Elouard and Andrew N. Jordan, Efficient Quantum Measurement Engine, Phys. Rev. Lett. 120, 260601 (2018), arXiv:1801.03979.
https://doi.org/10.1103/PhysRevLett.120.260601
arXiv:arXiv:1801.03979
[25] David Reeb and Michael M. Wolf, An improved Landauer Principle with finite-size corrections, New J. Phys. 16, 103011 (2014), arXiv:1306.4352.
https://doi.org/10.1088/1367-2630/16/10/103011
arXiv:arXiv:1306.4352
[26] Kais Abdelkhalek, Yoshifumi Nakata, and David Reeb, Fundamental energy cost for quantum measurement, (2016), arXiv:1609.06981.
arXiv:arXiv:1609.06981
[27] Armen E. Allahverdyan, Karen V. Hovhannisyan, Dominik Janzing, and Guenter Mahler, Thermodynamic limits of dynamic cooling, Phys. Rev. E 84, 041109 (2011), arXiv:1107.1044.
https://doi.org/10.1103/PhysRevE.84.041109
arXiv:arXiv:1107.1044
[28] Gavin E. Crooks, The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences, Phys. Rev. E 60, 2721 (1999), arXiv:cond-mat/9901352.
https://doi.org/10.1103/PhysRevE.60.2721
arXiv:arXiv:cond-mat/9901352
[29] Hal Tasaki, Jarzynski Relations for Quantum Systems and Some Applications, (2000), arXiv:cond-mat/0009244.
arXiv:arXiv:cond-mat/0009244
[30] Peter Talkner, Eric Lutz, and Peter Hänggi, Fluctuation theorems: Work is not an observable, Phys. Rev. E 75, 050102(R) (2007), arXiv:cond-mat/0703189.
https://doi.org/10.1103/PhysRevE.75.050102
arXiv:arXiv:cond-mat/0703189
[31] Tiago Debarba, Gonzalo Manzano, Yelena Guryanova, Marcus Huber, and Nicolai Friis, Work estimation and work fluctuations in the presence of non-ideal measurements, New J. Phys. 21, 113002 (2019), arXiv:1902.08568.
https://doi.org/10.1088/1367-2630/ab4d9d
arXiv:arXiv:1902.08568
[32] Mihai D. Vidrighin, Oscar Dahlsten, Marco Barbieri, M. S. Kim, Vlatko Vedral, and Ian A. Walmsley, Photonic Maxwell's Demon, Phys. Rev. Lett. 116, 050401 (2016), arXiv:1510.02164.
https://doi.org/10.1103/PhysRevLett.116.050401
arXiv:arXiv:1510.02164
[33] Alhun Aydin, Altug Sisman, and Ronnie Kosloff, Landauer's Principle in a Quantum Szilard Engine Without Maxwell's Demon, (2019), arXiv:1908.04400.
arXiv:arXiv:1908.04400
[34] M. Hamed Mohammady and Janet Anders, A quantum Szilard engine without heat from a thermal reservoir, New J. Phys. 19, 113026 (2017), arXiv:1706.00938.
https://doi.org/10.1088/1367-2630/aa8ba1
arXiv:arXiv:1706.00938
[35] Michał Oszmaniec, Leonardo Guerini, Peter Wittek, and Antonio Acín, Simulating Positive-Operator-Valued Measures with Projective Measurements, Phys. Rev. Lett. 119, 190501 (2017), arXiv:1609.06139.
https://doi.org/10.1103/PhysRevLett.119.190501
arXiv:arXiv:1609.06139
[36] David E. Bruschi, Martí Perarnau-Llobet, Nicolai Friis, Karen V. Hovhannisyan, and Marcus Huber, The thermodynamics of creating correlations: Limitations and optimal protocols, Phys. Rev. E 91, 032118 (2015), arXiv:1409.4647.
https://doi.org/10.1103/PhysRevE.91.032118
arXiv:arXiv:1409.4647
[37] Marcus Huber, Martí Perarnau-Llobet, Karen V. Hovhannisyan, Paul Skrzypczyk, Claude Klöckl, Nicolas Brunner, and Antonio Ac$\acute{\i}$n, Thermodynamic cost of creating correlations, New J. Phys. 17, 065008 (2015), arXiv:1404.2169.
https://doi.org/10.1088/1367-2630/17/6/065008
arXiv:arXiv:1404.2169
[38] Giuseppe Vitagliano, Claude Klöckl, Marcus Huber, and Nicolai Friis, Trade-off between work and correlations in quantum thermodynamics, in Thermodynamics in the Quantum Regime, edited by Felix Binder, Luis A. Correa, Christian Gogolin, Janet Anders, and Gerardo Adesso (Springer, 2019) Chap. 30, pp. 731–750, arXiv:1803.06884.
https://doi.org/10.1007/978-3-319-99046-0_30
arXiv:arXiv:1803.06884
[39] Faraj Bakhshinezhad, Fabien Clivaz, Giuseppe Vitagliano, Paul Erker, Ali T. Rezakhani, Marcus Huber, and Nicolai Friis, Thermodynamically optimal creation of correlations, J. Phys. A: Math. Theor. 52, 465303 (2019), arXiv:1904.07942.
https://doi.org/10.1088/1751-8121/ab3932
arXiv:arXiv:1904.07942
[40] Matteo G. A. Paris, The modern tools of quantum mechanics, Eur. Phys. J. S. T. 203, 61 (2012), arXiv:1110.6815.
https://doi.org/10.1140/epjst/e2012-01535-1
arXiv:arXiv:1110.6815
Cited by
[1] Avijit Misra, Tomáš Opatrný, and Gershon Kurizki, "Work extraction from single-mode thermal noise by measurements: How important is information?", Physical Review E 106 5, 054131 (2022).
[2] M Hamed Mohammady, "Thermodynamically free quantum measurements", Journal of Physics A: Mathematical and Theoretical 55 50, 505304 (2022).
[3] Timo Kerremans, Peter Samuelsson, and Patrick Potts, "Probabilistically violating the first law of thermodynamics in a quantum heat engine", SciPost Physics 12 5, 168 (2022).
[4] Michael P. Frank and Karpur Shukla, "Quantum Foundations of Classical Reversible Computing", Entropy 23 6, 701 (2021).
[5] Gabriel T. Landi and Mauro Paternostro, "Irreversible entropy production: From classical to quantum", Reviews of Modern Physics 93 3, 035008 (2021).
[6] Juha-Pekka Pellonpää, Sébastien Designolle, and Roope Uola, "Naimark dilations of qubit POVMs and joint measurements", Journal of Physics A: Mathematical and Theoretical 56 15, 155303 (2023).
[7] Tom Purves and Anthony J. Short, "Channels, measurements, and postselection in quantum thermodynamics", Physical Review E 104 1, 014111 (2021).
[8] Philip Taranto, Faraj Bakhshinezhad, Andreas Bluhm, Ralph Silva, Nicolai Friis, Maximilian P.E. Lock, Giuseppe Vitagliano, Felix C. Binder, Tiago Debarba, Emanuel Schwarzhans, Fabien Clivaz, and Marcus Huber, "Landauer Versus Nernst: What is the True Cost of Cooling a Quantum System?", PRX Quantum 4 1, 010332 (2023).
[9] Tianfeng Feng and Vlatko Vedral, "Amplification of gravitationally induced entanglement", Physical Review D 106 6, 066013 (2022).
[10] Alexia Auffèves, "Quantum Technologies Need a Quantum Energy Initiative", PRX Quantum 3 2, 020101 (2022).
[11] Knud Thomsen, "Timelessness Strictly inside the Quantum Realm", Entropy 23 6, 772 (2021).
[12] Tom Bullock and Teiko Heinosaari, "Quantum state discrimination via repeated measurements and the rule of three", Quantum Studies: Mathematics and Foundations 8 1, 137 (2021).
[13] Michael J. Kewming and Sally Shrapnel, "Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature", Quantum 6, 685 (2022).
[14] M. Hamed Mohammady and Takayuki Miyadera, "Quantum measurements constrained by the third law of thermodynamics", Physical Review A 107 2, 022406 (2023).
[15] Dominik Šafránek, Dario Rosa, and Felix C. Binder, "Work Extraction from Unknown Quantum Sources", Physical Review Letters 130 21, 210401 (2023).
[16] M. Hamed Mohammady, "Self-consistency of the two-point energy measurement protocol", Physical Review A 103 4, 042214 (2021).
[17] M. Hamed Mohammady, "Classicality of the heat produced by quantum measurements", Physical Review A 104 6, 062202 (2021).
[18] Arindam Mitra, "Quantifying Unsharpness of Observables in an Outcome-Independent way", International Journal of Theoretical Physics 61 9, 236 (2022).
[19] Francesco Campaioli, Chang-shui Yu, Felix A Pollock, and Kavan Modi, "Resource speed limits: maximal rate of resource variation", New Journal of Physics 24 6, 065001 (2022).
[20] Gonzalo Manzano and Roberta Zambrini, "Quantum thermodynamics under continuous monitoring: A general framework", AVS Quantum Science 4 2, 025302 (2022).
[21] Samuel P. Loomis and James P. Crutchfield, "Thermal Efficiency of Quantum Memory Compression", Physical Review Letters 125 2, 020601 (2020).
[22] Mathias R. Jørgensen, Patrick P. Potts, Matteo G. A. Paris, and Jonatan B. Brask, "Tight bound on finite-resolution quantum thermometry at low temperatures", Physical Review Research 2 3, 033394 (2020).
[23] S. Gherardini, G. Giachetti, S. Ruffo, and A. Trombettoni, "Thermalization processes induced by quantum monitoring in multilevel systems", Physical Review E 104 3, 034114 (2021).
[24] Paolo Abiuso, Harry J. D. Miller, Martí Perarnau-Llobet, and Matteo Scandi, "Geometric Optimisation of Quantum Thermodynamic Processes", Entropy 22 10, 1076 (2020).
[25] Emanuel Schwarzhans, Maximilian P. E. Lock, Paul Erker, Nicolai Friis, and Marcus Huber, "Autonomous Temporal Probability Concentration: Clockworks and the Second Law of Thermodynamics", Physical Review X 11 1, 011046 (2021).
[26] Lorenzo Buffoni, Stefano Gherardini, Emmanuel Zambrini Cruzeiro, and Yasser Omar, "Third Law of Thermodynamics and the Scaling of Quantum Computers", Physical Review Letters 129 15, 150602 (2022).
[27] X. L. Huang, A. N. Yang, H. W. Zhang, S. Q. Zhao, and S. L. Wu, "Two particles in measurement-based quantum heat engine without feedback control", Quantum Information Processing 19 8, 242 (2020).
[28] Léa Bresque, Patrice A. Camati, Spencer Rogers, Kater Murch, Andrew N. Jordan, and Alexia Auffèves, "Two-Qubit Engine Fueled by Entanglement and Local Measurements", Physical Review Letters 126 12, 120605 (2021).
[29] Stefano Gherardini, Francesco Campaioli, Filippo Caruso, and Felix C. Binder, "Stabilizing open quantum batteries by sequential measurements", Physical Review Research 2 1, 013095 (2020).
[30] A. N. Pearson, Y. Guryanova, P. Erker, E. A. Laird, G. A. D. Briggs, M. Huber, and N. Ares, "Measuring the Thermodynamic Cost of Timekeeping", Physical Review X 11 2, 021029 (2021).
[31] Philipp Strasberg, Kavan Modi, and Michalis Skotiniotis, "How long does it take to implement a projective measurement?", European Journal of Physics 43 3, 035404 (2022).
[32] Xiayu Linpeng, Léa Bresque, Maria Maffei, Andrew N. Jordan, Alexia Auffèves, and Kater W. Murch, "Energetic Cost of Measurements Using Quantum, Coherent, and Thermal Light", Physical Review Letters 128 22, 220506 (2022).
[33] Mark T. Mitchison, John Goold, and Javier Prior, "Charging a quantum battery with linear feedback control", Quantum 5, 500 (2021).
[34] Roie Dann and Ronnie Kosloff, "Unification of the first law of quantum thermodynamics", New Journal of Physics 25 4, 043019 (2023).
[35] Tamal Guha, Mir Alimuddin, and Preeti Parashar, "Thermodynamic advancement in the causally inseparable occurrence of thermal maps", Physical Review A 102 3, 032215 (2020).
[36] Satoya Imai, Otfried Gühne, and Stefan Nimmrichter, "Work fluctuations and entanglement in quantum batteries", Physical Review A 107 2, 022215 (2023).
[37] Konstantin Beyer, Roope Uola, Kimmo Luoma, and Walter T. Strunz, "Joint measurability in nonequilibrium quantum thermodynamics", Physical Review E 106 2, L022101 (2022).
[38] Roie Dann, Ronnie Kosloff, and Peter Salamon, "Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine", Entropy 22 11, 1255 (2020).
[39] Philip Taranto, Faraj Bakhshinezhad, Philipp Schüttelkopf, Fabien Clivaz, and Marcus Huber, "Exponential Improvement for Quantum Cooling through Finite-Memory Effects", Physical Review Applied 14 5, 054005 (2020).
[40] J. Stevens, D. Szombati, M. Maffei, C. Elouard, R. Assouly, N. Cottet, R. Dassonneville, Q. Ficheux, S. Zeppetzauer, A. Bienfait, A. N. Jordan, A. Auffèves, and B. Huard, "Energetics of a Single Qubit Gate", Physical Review Letters 129 11, 110601 (2022).
[41] Lorenzo Buffoni, Andrea Solfanelli, Paola Verrucchi, Alessandro Cuccoli, and Michele Campisi, "Quantum Measurement Cooling", Physical Review Letters 122 7, 070603 (2019).
[42] Mark T. Mitchison, "Quantum thermal absorption machines: refrigerators, engines and clocks", Contemporary Physics 60 2, 164 (2019).
[43] Fabien Clivaz, Ralph Silva, Géraldine Haack, Jonatan Bohr Brask, Nicolas Brunner, and Marcus Huber, "Unifying Paradigms of Quantum Refrigeration: A Universal and Attainable Bound on Cooling", Physical Review Letters 123 17, 170605 (2019).
[44] Giuseppe Vitagliano, Claude Klöckl, Marcus Huber, and Nicolai Friis, "Trade-Off Between Work and Correlations in Quantum Thermodynamics", Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions 195, 731 (2018).
[45] Faraj Bakhshinezhad, Fabien Clivaz, Giuseppe Vitagliano, Paul Erker, Ali Rezakhani, Marcus Huber, and Nicolai Friis, "Thermodynamically optimal creation of correlations", Journal of Physics A Mathematical General 52 46, 465303 (2019).
[46] M. Hamed Mohammady and Alessandro Romito, "Conditional work statistics of quantum measurements", Quantum 3, 175 (2019).
[47] Francesco Albarelli, Matteo G. A. Paris, Bassano Vacchini, and Andrea Smirne, "Invasiveness of non-equilibrium quantum thermometry", arXiv:2305.03436, (2023).
[48] Fabien Clivaz, Ralph Silva, Géraldine Haack, Jonatan Bohr Brask, Nicolas Brunner, and Marcus Huber, "Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling", arXiv:1903.04970, (2019).
[49] Faraj Bakhshinezhad, Beniamin R. Jablonski, Felix C. Binder, and Nicolai Friis, "Trade-offs between precision and fluctuations in charging finite-dimensional quantum systems", arXiv:2303.16676, (2023).
[50] 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, (2019).
[51] Tien D. Kieu, "Principle of Unattainability of absolute zero temperature, the Third Law of Thermodynamics, and projective quantum measurements", Physics Letters A 383, 125848 (2019).
[52] Fabien Clivaz, "Optimal Manipulation Of Correlations And Temperature In Quantum Thermodynamics", arXiv:2012.04321, (2020).
[53] M. Hamed Mohammady and Alessandro Romito, "Conditional work statistics of quantum measurements", arXiv:1809.09010, (2018).
[54] Esteban Calzetta, "The importance of being measurement", arXiv:1909.13178, (2019).
The above citations are from Crossref's cited-by service (last updated successfully 2023-09-28 07:06:35) and SAO/NASA ADS (last updated successfully 2023-09-28 07:06:36). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.