Quantum measurements and

Landauer’s principle

Vladimir Shevchenko

NRC «Kurchatov Institute», Moscow

Quarks-2014Suzdal, Russia07 June 2014

• Information is physical

J.von Neumann, ‘27L.Szilard, ‘29C.Shannon, ‘48L.N.Brillouin, ‘53

i) Information processing systems («hardware») are to obey the laws of physics

ii) An algorithm of computation («software») might have intrinsic energy or entropy cost

E.T.Jaynes, ‘57R.Landauer, ‘61C.H.Bennett, ‘73J.D.Bekenstein, ‘73

J.C.Maxwell, ‘1871 L.Boltzmann, ‘1886

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• Maxwell’s demon

Information can be transferred to energy

(picture from http://deskarati.com/)

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• Landauer principle

M.B.Plenio, V.Vitelli, The physics of forgetting: Landauer’s erasure principle and information theory, Contemporary Physics, 42 (2001)25

For introduction see review

R. Landauer, Irreversibility and Heat Generation in theComputing 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

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Erasure«hard» «soft»

{0, 1} → {0}

erasure by thermalization

E.Lubkin, ‘87

{0, 1}↓

{(1-p) •0 + p•1}5/27

«Even if you're not burning books, destroying information generates heat»

(picture from P.Ball, Nature News, Mar 7, 2012)6/27

• Exorcising the Maxwell demon

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(picture from M.Plenio and V.Vitelli, ‘01)

«Brain» of the demon is a physical system: information(negentropy) can be converted to energy

• 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 thermodynamicsNature 483 (2012) 187

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J.England, Statistical physics of self-replication,Journal of Chemical Physics 139 (2013)121923 (2013);

Interesting attempt to apply Landauer’s principle to dynamics of self-replication of biological systems is

«A New Physics Theory of Life»– Quanta Magazine, ‘14

Erasure protocol used by E.Lutz’s group

Probability distribution for dissipated heat

Dissipated heat as a function of erasure time

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Comment on T-noninvariance versus irreversibility

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Any measurement usually implicitly implies irreversibility

Arrow of time? CP-violation?

Example – neutral meson oscillations and CP-violation

Neglecting decay widths the evolution is described by

Oscillation of the phase of for

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• More refined formulation of Landauer’s principleD.Reeb and M.M.Wolf, (Im-)Proving Landauer’s Principle arXiv: 1306.4352 [quant-ph]

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Cristallization

Perpetuum mobile of the second kind

Explosion

Melting

LP: trivialOriginal LP. Erasure dissipates energy

LP: using thermal energy increases entropy

LP: forbidden. Cannot make system more ordered using thermal energy

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Defining quantum field theory means to define action and integration measure.

UV-regularization:

Dynamics can be shifted from action to measure and back.

Casimir boundaryconditions:

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.

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(picture from http://www.linearcollider.org )

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 partand «ugly» detector part...

But is it correlated or not is a quantitative physical question. Example: (V.Sh.,’13) strong magnetic fields in CME exist for about 0.2 Fm/c. Quark Fermi energies become uncertain, Dirac sea is wavy, and there is effective µ5 even if bare axial chemical potential is absent.

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• Time-dependent measurements

Transition amplitude for Unruh-DeWitt detector:

Transition probability:

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Infinite measurement time:

Transition probability in unit time:

Problems and ambiguities in (almost) any non-trivial case..

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

Much less is known for finite time measurement

L. Sriramkumar and T. Padmanabhan ‘94; see also L.C.Barbado, M.Visser, ‘12

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Transition probability using mixed representation for the window functions:

where

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Transition rates

with the operator

read

Infinite measurement time case:

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Quasi-stationary limit: leading finite time correction

where

Gaussian shape

All information about time profile of the measurement procedure is encoded in just one number in this limit

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High-temperature limit:

Thermal character of the spectrum kept, temperature gets renormalized:

We get entropic uncertainty relation:

Taking into account that

Intrinsic quantum limits on recognition speed?21/27

these processes are classical but should have quantum limitsA system with average energy E can perform a maximumof 4E/h logical operations per second. Ultimate 1 kg laptop cannot do more than 5.4×1050 op/sec. N.Margolis, L.Levitin, ’98

(photos from http://cdnec1.fiverrcdn.com and http://lhcb-trig.web.cern.ch)

Fast but coarse

Typical trigger system (LHCb @ LHC):

Slow but fine

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

The above formalism can easily be generalized for any Green’s function of the form:

where

with the same operator

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Two level system:

Entropy:

After interaction:

Energy conservation:

Landauer’s principle:

? 25/27

Stationary measurement:

LP – OK

Non-stationary measurement:

LP – limit on work done by external force:

Resume: fast erasure requires larger energy26/27

Instead of conclusion:

Happy Birthday,

Yuri Antonovich!

Yu.A.Simonov – 80

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