Conditional work statistics of quantum measurements

M. Hamed Mohammady1,2 and Alessandro Romito1

1Department of Physics, Lancaster University, LA1 4YB, United Kingdom
2RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava 84511, Slovakia

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In this paper we introduce a definition for conditional energy changes due to general quantum measurements, as the change in the conditional energy evaluated before, and after, the measurement process. By imposing minimal physical requirements on these conditional energies, we show that the most general expression for the conditional energy after the measurement is simply the expected value of the Hamiltonian given the post-measurement state. Conversely, the conditional energy before the measurement process is shown to be given by the real component of the weak value of the Hamiltonian. Our definition generalises well-known notions of distributions of internal energy change, such as that given by stochastic thermodynamics. By determining the conditional energy change of both system and measurement apparatus, we obtain the full conditional work statistics of quantum measurements, and show that this vanishes for all measurement outcomes if the measurement process conserves the total energy. Additionally, by incorporating the measurement process within a cyclic heat engine, we quantify the non-recoverable work due to measurements. This is shown to always be non-negative, thus satisfying the second law, and will be independent of the apparatus specifics for two classes of projective measurements.

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[1] J. C. Maxwell, Theory of Heat (Cambridge University Press, Cambridge, 2011).

[2] L. Szilard, Z. Phys. 53, 840 (1929).

[3] R. Landauer, IBM J. Res. Dev. 5, 183 (1961).

[4] O. Penrose, Foundations of Statistical Mechanics (Elsevier, 1970).

[5] R. Landauer, Phys. Lett. A 217, 188 (1996).

[6] C. H. Bennett, Stud. Hist. Philos. Sci. A 34, 501 (2003).

[7] K. Maruyama, F. Nori, and V. Vedral, Rev. Mod. Phys. 81, 1 (2009).

[8] J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, J. Phys. A 49, 143001 (2016).

[9] S. Vinjanampathy and J. Anders, Contemp. Phys. 57, 545 (2016).

[10] J. Millen and A. Xuereb, New J. Phys. 18, 011002 (2016).

[11] M. Campisi, P. Hänggi, and P. Talkner, Rev. Mod. Phys. 83, 771 (2011).

[12] K. Funo, Y. Watanabe, and M. Ueda, Phys. Rev. E 88, 052121 (2013).

[13] A. E. Allahverdyan, Phys. Rev. E 90, 032137 (2014).

[14] H. J. D. Miller and J. Anders, New J. Phys. 19, 062001 (2017).

[15] J. Åberg, Phys. Rev. X 8, 011019 (2018).

[16] M. Perarnau-Llobet, E. Bäumer, K. V. Hovhannisyan, M. Huber, and A. Acin, Phys. Rev. Letters 118, 070601 (2017).

[17] M. Lostaglio, Phys. Rev. Letters 120, 040602 (2018).

[18] T. Sagawa and M. Ueda, Phys. Rev. Letters 106, 189901 (2011).

[19] K. Jacobs, Phys. Rev. E 86, 040106 (2012).

[20] M. Navascués and S. Popescu, Phys. Rev. Letters 112, 140502 (2014).

[21] K. Abdelkhalek, Y. Nakata, and D. Reeb, (2016), arXiv:1609.06981.

[22] Y. Guryanova, N. Friis, and M. Huber, (2018), arXiv:1805.11899.

[23] J. M. Horowitz, Phys. Rev. E 85, 031110 (2012).

[24] F. W. J. Hekking and J. P. Pekola, Phys. Rev. Letters 111, 093602 (2013).

[25] J. J. Alonso, E. Lutz, and A. Romito, Phys. Rev. Letters 116, 080403 (2016).

[26] C. Elouard, D. A. Herrera-Martí, M. Clusel, and A. Auffèves, npj Quantum Inf. 3, 9 (2017).

[27] M. Naghiloo, D. Tan, P. M. Harrington, J. J. Alonso, E. Lutz, A. Romito, and K. W. Murch, (2017), arXiv:1703.05885.

[28] M. Naghiloo, J. J. Alonso, A. Romito, E. Lutz, and K. W. Murch, Phys. Rev. Letters 121, 030604 (2018).

[29] C. Elouard and M. H. Mohammady, in Thermodynamics in the quantum regime: Fundamental Aspects and New Directions, Fundamental Theories of Physics, Vol. 195, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer International Publishing, Cham, 2018) pp. 363–393.

[30] Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Letters 60, 1351 (1988).

[31] E. Haapasalo, P. Lahti, and J. Schultz, Phys. Rev. A 84, 052107 (2011).

[32] A. Romito and Y. Gefen, Physica E 42, 343 (2010).

[33] J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Rev. Mod. Phys. 86, 307 (2014).

[34] K. V. Hovhannisyan and A. Imparato, New J. Phys. 21, 052001 (2019).

[35] P. Busch, M. Grabowski, and P. J. Lahti, Operational Quantum Physics, Lecture Notes in Physics Monographs, Vol. 31 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1995).

[36] P. Busch, P. J. Lahti, and Peter Mittelstaedt, The Quantum Theory of Measurement, Lecture Notes in Physics Monographs, Vol. 2 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1996).

[37] P. Busch, P. Lahti, J.-P. Pellonpää, and K. Ylinen, Quantum Measurement, Theoretical and Mathematical Physics (Springer International Publishing, Cham, 2016).

[38] T. Heinosaari and M. Ziman, The Mathematical language of Quantum Theory (Cambridge University Press, Cambridge, 2011).

[39] P. Mittelstaedt, The Interpretation of Quantum Mechanics and the Measurement Process (Cambridge University Press, Cambridge, 1997).

[40] J. Dressel and A. N. Jordan, Phys. Rev. A 85, 012107 (2012).

[41] A. Steinberg, Phys. Rev. Letters 74, 2405 (1995).

[42] A. Romito and Y. Gefen, Phys. Rev. B 90, 085417 (2014).

[43] J. Dressel, S. Agarwal, and A. N. Jordan, Phys. Rev. Lett. 104, 240401 (2010).

[44] E. P. Wigner, Z. Phys. 133, 101 (1952).

[45] H. Araki and M. M. Yanase, Phys. Rev. 120, 622 (1960).

[46] L. Loveridge and P. Busch, The Eur. Phys. J. D 62, 297 (2011).

[47] M. H. Mohammady and J. Anders, New J. Phys. 19, 113026 (2017).

[48] J. Anders and V. Giovannetti, New J. Phys. 15, 033022 (2013).

[49] G. Manzano, J. M. Horowitz, and J. M. R. Parrondo, Phys. Rev. X 8, 031037 (2018).

[50] D'enes Petz, Quantum Information Theory and Quantum Statistics, Theoretical and Mathematical Physics (Springer Berlin Heidelberg, Berlin, Heidelberg, 2008).

[51] T. Sagawa, in Lectures on Quantum Computing, Thermodynamics and Statistical Physics (2012) pp. 125–190.

[52] R. Balian, From Microphysics to Macrophysics (Springer Berlin Heidelberg, Berlin, Heidelberg, 1991).

[53] A. E. Allahverdyan, K. V. Hovhannisyan, D. Janzing, and G. Mahler, Phys. Rev. E 84, 041109 (2011).

[54] L.-A. Wu, D. Segal, and P. Brumer, Sci. Rep. 3, 1824 (2013).

[55] D. Reeb and M. M. Wolf, New J. Phys. 16, 103011 (2014).

[56] L. Masanes and J. Oppenheim, Nat. Commun. 8, 14538 (2017).

[57] A. Wehrl, Rev. Mod. Phys. 50, 221 (1978).

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[16] Alessio Belenchia, Mauro Paternostro, and Gabriel T. Landi, "Informational steady states and conditional entropy production in continuously monitored systems: The case of Gaussian systems", Physical Review A 105 2, 022213 (2022).

[17] M. Hamed Mohammady and Alessandro Romito, "Symmetry constrained decoherence of conditional expectation values", arXiv:1901.01460, (2019).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-18 12:38:57) and SAO/NASA ADS (last updated successfully 2024-06-18 12:38:58). The list may be incomplete as not all publishers provide suitable and complete citation data.