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Quantum measurements and Landauer’s principle

Quantum measurements and Landauer’s principle. Vladimir Shevchenko NRC « Kurchatov Institute », Moscow. Quarks-2014 Suzdal , Russia 07 June 2014. Information is physical. J.C.Maxwell , ‘1871 L.Boltzmann , ‘ 1886. E.T.Jaynes , ‘57 R.Landauer , ‘61 C.H.Bennett , ‘73

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Quantum measurements and Landauer’s principle

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  1. Quantum measurements and Landauer’s principle Vladimir Shevchenko NRC «Kurchatov Institute», Moscow Quarks-2014 Suzdal, Russia 07 June 2014

  2. Information is physical J.C.Maxwell, ‘1871 L.Boltzmann, ‘1886 E.T.Jaynes, ‘57 R.Landauer, ‘61 C.H.Bennett, ‘73 J.D.Bekenstein, ‘73 J.von Neumann, ‘27 L.Szilard, ‘29 C.Shannon, ‘48 L.N.Brillouin, ‘53 Information processing systems («hardware») are to obey the laws of physics An algorithm of computation («software») might have intrinsic energy or entropy cost 2/27

  3. Maxwell’s demon (picture from http://deskarati.com/) Information can be transferred to energy 3/27

  4. Landauer principle R. Landauer, Irreversibility and Heat Generation in the Computing Process, IBM Journal of Research and Development, 5 (1961) 83 Erasure of one bit of information leads to dissipation of at least kBT log 2 of energy by «erasure» (almost) any operation that does not have single-valued inverse is understood Forgetting is costly For introduction see review M.B.Plenio, V.Vitelli, The physics of forgetting: Landauer’s erasure principle and information theory, Contemporary Physics, 42 (2001)25 4/27

  5. Erasure «hard» «soft» erasure by thermalization E.Lubkin, ‘87 {0, 1} ↓ {(1-p) •0 + p•1} {0, 1} → {0} 5/27

  6. «Even if you're not burning books, destroying information generates heat» (picture from P.Ball, Nature News, Mar 7, 2012) 6/27

  7. Exorcising the Maxwell demon (picture from M.Plenio and V.Vitelli, ‘01) «Brain» of the demon is a physical system: information (negentropy) can be converted to energy 7/27

  8. Recent progress S.Toyabe, T.Sagawa, M.Ueda, E.Muneyuki and M.Sano, Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality, Nature Phys. 6 (2010) 988 A.Berut, A.Arakelyan, A.Petrosyan, S.Ciliberto, R.Dillenschneider, E.Lutz, Experimental verification of Landauer’s principle linking information and thermodynamics Nature 483 (2012) 187 Interesting attempt to apply Landauer’s principle to dynamics of self-replication of biological systems is J.England, Statistical physics of self-replication, Journal of ChemicalPhysics139 (2013)121923 (2013); «A New Physics Theory of Life» – Quanta Magazine, ‘14 8/27

  9. Probability distribution for dissipated heat Erasure protocol used by E.Lutz’s group Dissipated heat as a function of erasure time 9/27

  10. Comment on T-noninvarianceversus irreversibility Any measurement usually implicitly implies irreversibility Arrow of time? CP-violation? 10/27

  11. Example – neutral meson oscillations and CP-violation Neglecting decay widths the evolution is described by Oscillation of the phase of for 11/27

  12. More refined formulation of Landauer’s principle D.Reeb and M.M.Wolf, (Im-)Proving Landauer’s Principle arXiv: 1306.4352 [quant-ph] 12/27

  13. Cristallization Explosion Original LP. Erasure dissipates energy LP: trivial Perpetuum mobile of the second kind Melting LP: using thermal energy increases entropy LP: forbidden. Cannot make system more ordered using thermal energy 13/27

  14. Defining quantum field theory means to define action and integration measure. Dynamics can be shifted from action to measure and back. UV-regularization: Casimir boundary conditions: Measure encodes some a priopri known (or assumed) results of measurements. What information about our theory at we need to know to be able to work at low energy? Just a few numbers – coefficients of marginal operators, like 1/137. 14/27

  15. In most cases in particle physics we assume that physics here («action») is uncorrelated with physics here («measure»). Asymptotic states, plane waves basis etc. «Beautiful» field theoretic part and «ugly» detector part... (picture from http://www.linearcollider.org ) But is it correlated or not is a quantitative physical question. Example:(V.Sh.,’13) strong magnetic fields in CME exist for about 0.2Fm/c. Quark Fermi energies become uncertain, Dirac sea is wavy, and there is effective µ5 even if bare axial chemical potential is absent. 15/27

  16. Time-dependent measurements Transition amplitude for Unruh-DeWitt detector: Transition probability: 16/27

  17. Infinite measurement time: Transition probability in unit time: Problems and ambiguities in (almost) any non-trivial case.. Much less is known for finite time measurement L. Sriramkumar and T. Padmanabhan‘94; see also L.C.Barbado, M.Visser, ‘12 We are based on computing relative rates (V.Sh.’14) +finite, well defined, determine population numbers in quasi-stationary case – independence on the coupling strength is fictitious 17/27

  18. Transition probability using mixed representation for the window functions: where 18/27

  19. Transition rates with the operator read Infinite measurement time case: 19/27

  20. Quasi-stationary limit: leading finite time correction where All information about time profile of the measurement procedure is encoded in just one number in this limit Gaussian shape 20/27

  21. High-temperature limit: Thermal character of the spectrum kept, temperature gets renormalized: Taking into account that We get entropic uncertainty relation: Intrinsic quantum limits on recognition speed? 21/27

  22. Fast but coarse Slow but fine (photos from http://cdnec1.fiverrcdn.com and http://lhcb-trig.web.cern.ch) Typical trigger system (LHCb @ LHC): these processes are classical but should have quantum limits A system with average energy E can perform a maximum of 4E/h logical operations per second. Ultimate 1 kg laptop cannot do more than 5.4×1050 op/sec. N.Margolis, L.Levitin, ’98

  23. Also resembles pattern recognition by human brain– when human sees something looking similar to a snake: 1: crude but fast analysis by limbic system – dangerous or not, run away or no, etc – life preserving mechanism 2: more precise analysis by neocortex needs more time – is it a snake at all, if yes, what snake it is etc – world exploring system instincts first, curiosity second 23/27

  24. The above formalism can easily be generalized for any Green’s function of the form: where with the same operator 24/27

  25. Two level system: Entropy: After interaction: Energy conservation: Landauer’s principle: ? 25/27

  26. Stationary measurement: LP – OK Non-stationary measurement: LP – limit on work done by external force: Resume: fast erasure requires larger energy 26/27

  27. Instead of conclusion: Yu.A.Simonov – 80 Happy Birthday, Yuri Antonovich! 27/27

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