Download Quantum measurements and Landauer principle

Quantum measurements
and
Landauer’s principle
Vladimir Shevchenko
NRC «Kurchatov Institute», Moscow
Quarks-2014
Suzdal, Russia
07 June 2014
• Information is physical
i)
J.C.Maxwell, ‘1871
L.Boltzmann, ‘1886
J.von Neumann, ‘27
L.Szilard, ‘29
C.Shannon, ‘48
L.N.Brillouin, ‘53
E.T.Jaynes, ‘57
R.Landauer, ‘61
C.H.Bennett, ‘73
J.D.Bekenstein, ‘73
Information processing systems («hardware»)
are to obey the laws of physics
ii) An algorithm of computation («software»)
might have intrinsic energy or entropy cost
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• Maxwell’s demon
(picture from http://deskarati.com/)
Information can be transferred to energy
3/27
• 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
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Erasure
«hard»
«soft»
erasure by
thermalization
E.Lubkin, ‘87
{0, 1} → {0}
{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)
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• 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
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• 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 Chemical Physics 139 (2013)121923 (2013);
«A New Physics Theory of Life»
– Quanta Magazine, ‘14
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Probability distribution
for dissipated heat
Erasure protocol used
by E.Lutz’s group
Dissipated heat as a
function of erasure time
9/27
Comment on T-noninvariance versus irreversibility
Any measurement usually implicitly implies irreversibility
Arrow of time?
CP-violation?
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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 principle
D.Reeb and M.M.Wolf, (Im-)Proving Landauer’s Principle
arXiv: 1306.4352 [quant-ph]
12/27
Cristallization
Explosion
Original LP. Erasure
dissipates energy
Perpetuum mobile of
the second kind
LP: forbidden. Cannot
make system more ordered
using thermal energy
LP: trivial
Melting
LP: using thermal energy
increases entropy
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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
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 0.2 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..
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
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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
All information about time profile of the measurement
procedure is encoded in just one number in this limit
Gaussian shape
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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?
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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
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
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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 energy
26/27
Instead of conclusion:
Yu.A.Simonov – 80
Happy Birthday,
Yuri Antonovich!
27/27