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Quantum measurement precision approaches Heisenberg
limit
February 26, 2010 By Lisa Zyga

Enlarge

This illustration shows an adaptive feedback scheme being used to
measure an unknown phase difference between the two red arms in the
interferometer. A photon (qubit) is sent through the interferometer, and
detected by either c1 or c0, depending on which arm it traveled through.
Feedback is sent to the processing unit, which controls the phase shifter in one
arm so that, when the next photon is sent, the device can more precisely measure
the unknown phase in the other arm, and calculate a precise phase difference.
Image credit: Hentschel and Sanders.

(PhysOrg.com) -- In the classical world, scientists
can make measurements with a degree of accuracy that is restricted only by
technical limitations. At the fundamental level, however, measurement precision
is limited by Heisenberg’s uncertainty principle. But even reaching a precision
close to the Heisenberg limit is far beyond existing technology due to source
and detector limitations.

Now, using techniques from machine learning, physicists Alexander Hentschel
and Barry Sanders from the University of Calgary have recently shown how to
generate measurement procedures that can outperform the best previous strategy
in achieving highly precise quantum measurements. The new level of precision
approaches the Heisenberg limit, which is an important goal of quantum
measurement. Such quantum-enhanced measurements are useful in several areas,
such as atomic clocks, gravitational wave detection, and measuring the optical
properties of materials.

“The precision that any measurement can possibly achieve is limited by the
so-called Heisenberg limit, which results from Heisenberg's uncertainty
principle,” Hentschel told PhysOrg.com. “However, classical measurements
cannot achieve a precision close to the Heisenberg limit. Only quantum
measurements that use quantum
correlations can approach the Heisenberg limit. Yet, devising quantum
measurement procedures is highly challenging.”

Heisenberg's uncertainty principle ultimately limits the achievable precision
depending on how many quantum resources are used for the measurement. For
example, gravitational waves are detected with laser interferometers, whose
precision is limited by the number of photons available to the interferometer
within the duration of the gravitational wave pulse.

In their study, Hentschel and Sanders used a computer simulation of a
two-channel interferometer with a random phase difference between the two arms.
Their goal was to estimate the relative phase difference between the two
channels. In the simulated system, photons were sent into the interferometer one
at a time. Which input port the photon entered was unknown, so that the photon
(serving as a qubit) was in a superposition of two states, corresponding to the
two channels. When exiting the interferometer, the photon was detected as
leaving one of the two output ports, or not detected at all if it was lost.
Since photons were fed into the interferometer one at a time, no more than one
bit of information could be extracted at once. In this scenario, the achievable
precision is limited by the number of photons used for the measurement.

As previous research has shown, the most effective quantum measurement
schemes are those that incorporate adaptive feedback. These schemes accumulate
information from measurements and then exploit it to maximize the information
gain in subsequent measurements. In an interferometer with feedback, a sequence
of photons is successively sent through the interferometer in order to measure
the unknown phase difference. Detectors at the two output ports measure which
way each of the photons exits, and then transmit this information to a
processing unit. The processing unit adapts the value of a controllable phase
shifter after each photon according to a given policy.

However, devising an optimal policy is difficult, and usually requires
guesswork. In their study, Hentschel and Sanders adapted a technique from the
field of artificial intelligence. Their algorithm autonomously learns an optimal
policy based on trial and error - replacing guesswork by a logical, fully
automatic, and programmable procedure.

Specifically, the new method uses a machine learning algorithm called
particle swarm optimization (PSO). PSO is a “collective intelligence”
optimization strategy inspired by the social behavior of birds flocking or fish
schooling to locate feeding sites. In this case, the physicists show that a PSO
algorithm can also autonomously learn a policy for adjusting the controllable
phase shift.

As Hentschel and Sanders show, after a sequence of input qubits have been
sent through the interferometer, the measurement procedure learned by the PSO
algorithm delivers a measurement of the unknown phase shift that scales closely
to the Heisenberg limit, setting a new precedent for quantum measurement
precision. The new high level of precision could have important implications for
the gravitational wave detection.

“Einstein’s theory of General Relativity predicts gravitational waves,”
Hentschel said. “However, a direct detection of gravitational
waves has not been achieved. Gravitational wave detection will open up a new
field of astronomy that augments electromagnetic wave and neutrino observations.
For example, gravitational wave detectors can spot merging black holes or binary
star systems composed of two neutron stars, which are mostly hidden to
conventional telescopes.”

More information: Alexander Hentschel and Barry C. Sanders. “Machine
Learning for Precise Quantum Measurement.” Physical Review Letters 104,
063603 (2010). DOI:10.1103/PhysRevLett.104.063603

Copyright 2010 PhysOrg.com.
All rights reserved. This material may not
be published, broadcast, rewritten or redistributed in whole or part without the
express written permission of PhysOrg.com.

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broglia - Feb 26,
2010

Rank: 1.8 / 5 (5)

If gravitational waves are forming longitudinal waves of
vacuum environment, then they cannot be detected just because of uncertainty
principle - they would form just the longitudinal portion of CMB noise, which
prohibits us to observe objects more exactly.

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axemaster - Feb 26,
2010

Rank: 5 / 5 (7)

Broglia, I'm taking quantum in college right now, and I have
no idea what are you talking about...

CMB noise is microwaves, emitted
quite a while after the Big Bang, when the first stars ionized the
interstellar hydrogen and made the universe transparent to EM radiation.
Gravitational waves and the CMB shouldn't be related at all.

Moreover,
any gravity waves generated around that time would have stretched to very long
wavelengths by now, making them pretty much impossible to detect.

The
gravitational waves they are hoping to detect are those emitted by black
holes, particularly when they coalesce (they make a big pulse). The CMB is
irrelevant.

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seneca - Feb 26,
2010

Rank: 2 / 5 (4)

..gravitational waves and the CMB shouldn't be related at all.

You can use the water surface model to understand the relation
between light and gravitational waves. Water surface corresponds the
space-time, formed by vacuum foam: it's so large, just because energy spreads
so slowly around in in transversal waves, which are corresponding light waves
in vacuum. After then the gravitational waves are density (scalar) waves of
sound, spreading through underwater. They're so weak just because they're
spreading so fast. But waves faster then the surface waves cannot behave like
true waves at the water surface, instead of it, they would appear like noise.
This model doesn't exclude existence of harmonic waves though, in analogy to
sound spreading through SOFAR channel.

This model is supported by
holographic model of Universe, too. In this model Universe cannot behave like
holographic projection, until speed of gravitational waves wouldn't highly
superluminal.

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seneca - Feb 26,
2010

Rank: 2.3 / 5 (3)

..any gravity waves generated around that time would have
stretched to very long wavelengths by now..
This stance can be
objected again by using of surface water wave model of space-time, where speed
of transversal waves decreases with increasing frequency, while speed of
longitudinal waves (which are forming analogy of GW here) behaves in the
opposite way.

Again, this model is supported for example by prof.
Turok/Steinhardt's cyclic cosmology, in which gravitational waves are
blue-shifted due to the propagation of gravity through the dimensional
manifold.

http://arxiv.org/PS_cache/hep-th/pdf/0611/0611259v2.pdf
http://arxiv.org/PS_cache/hep-th/pdf/0702/0702153v1.pdf

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seneca - Feb 26,
2010

Rank: 2.3 / 5 (3)

Although this model of gravitational waves has a robust
meaning in dense aether theory, there is only subtle experimental evidence of
it. The passage of gravity waves would appear like less or more temporal
change in CMB intensity, as some events from GEO600 interferometer
indicate:

http://startswithabang.com/wp-content/uploads/2009/02/img35.gif

We
can compare it to our experience from underwater nuclear explosions, where
passage of sound wave from underwater appears like wave of noise at water
surface.

http://www.youtube.com/watch?v=SHoXJuv8tDM

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baudrunner - Feb 26,
2010

Rank: 5 / 5 (1)

The problem with detecting gravitational waves is that no
wave, as such, is actually produced. Rather, a shift in the gravitational
field equilibrium, which is not reflected (very important), will occur when
massive bodies interact in space. The process preserves that equilibrium. It's
like an ongoing, web-like action. You pull the web in a number of directions,
but no oscillating function is produced, ergo - no wave.

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seneca - Feb 26,
2010

Rank: 5 / 5 (1)

..shift in the gravitational field equilibrium, which is not
reflected, will occur when massive bodies interact in space..

Maybe you're right, maybe not - but I don't see any logic in this
sentence. What the "gravitational field equilibrium" is supposed to be, for
example?

In general you should explain/predict unknown phenomena by
using of known phenomena, not by introduction of new unknown concepts -
because it just introduces tautology into such explanation.

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seneca - Feb 26,
2010

Rank: 5 / 5 (1)

Why not - the derivation of the number of Kaluza spheres in
our Universe by using of well known constants is nice - but I don't see any
way, how such result could be tested.

This approach is somewhat
analogous to previous post of baudrunner: you're deriving untestable numbers
by using of well testable physical constants, thus increasing entropy of human
understanding. After all, this is the reason, why string theory is considered
a fring theory: it predicts lotta numbers, but these numbers cannot be tested
so easily, being quite abstract. It lacks robust predictions at logical
level.

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Question - Feb 27,
2010

Rank: 1 / 5 (3)

It would appear they are using a computer simulation and the
photon (pulse) may or may not be detected. What this tells me is that they
would be using such a small quantity of light that when it enters the splitter
and is reduced by 1/2 it may register at either detector or NO detector at
all. It is such a small pulse it would not be detected by both detectors
because if it were they would automatically assume two or more photons were
used and the pulse would be reduced in strength.

The experiment is
flawed from start to finish.

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Thrasymachus - Feb
27, 2010

Rank: not rated yet

Seneca, in an earlier post, you write "You can use the water
surface model to understand the relation between light and gravitational
waves. Water surface corresponds the space-time, formed by vacuum foam: it's
so large, just because energy spreads so slowly around in in transversal
waves, which are corresponding light waves in vacuum."

Later, you
write, " ...where speed of transversal waves decreases with increasing
frequency, while speed of longitudinal waves (which are forming analogy of GW
here) behaves in the opposite way."

However, light waves travel at the
same speed c, regardless of their frequency or wavelength. This has been
measured to be true to an arbitrary degree of precision. Please explain.
(dance crazy monkey, dance!)

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seneca - Feb 27,
2010

Rank: 2.3 / 5 (3)

The relativity model in light speed understanding was forced
in 1983 by introduction of SI meter unit based on the wavelength of krypton-86
light. While time unit is defined by frequency of light, it effectively means,
the light speed is invariant by its very definition (in fact isn't, because
second unit is based on radiation of cesium 133 atoms, so that dispersion of
vacuum foam still could apply here - but the differences will be really
small).

But at the moment, when we use for example iridium prototype,
then the changes in light speed in vacuum emerge, because the space-time
inside of matter expands faster, then the rest of Universe (space-time inside
of matter is condensed). This behavior manifests itself by dilatation and
evaporation of iridium kilogram and meter prototypes, for example.

http://www.physorg.com/news64.html
http://www.physorg.com/news108836759.html

These
subtle phenomena render our Universe as a much more dynamic environment, then
it appears at the first sight.

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seneca - Feb 28,
2010

Rank: 3 / 5 (4)

..This has been measured to be true to an arbitrary degree of
precision..
Well, only locally: light speed measured locally is
really invariant. But the observation of gravitational lensing means, the
light propagates in different speed through lens. The relativist would say,
it's because, the space-time is deformed there. But strictly speaking, such
claim is just a conjecture, because the measurement of space-time deform would
require to place clock into this gravitational lens. In another words, we are
assuming measurement, which was never done.

Gravitational lensing and
time dilatation can never occur at the same moment: when we would visit
galactic cluster with clock to prove space-time deform, we would observe, the
relativistic aberration would disappear, because space-time is homogeneous at
the center of cluster.

This principal inconsistency in measurements
brings a conceptual problem into relativity. The quite similar, just dual
problem exists with quantum mechanics.

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KBK - Mar 01, 2010

Rank: 1 / 5 (1)

The problem with detecting gravitational waves is that no wave,
as such, is actually produced. Rather, a shift in the gravitational field
equilibrium, which is not reflected (very important),..........an ongoing,
web-like action. You pull the web in a number of directions, but no
oscillating function is produced, ergo - no
wave.

Massive bodies in space are a secondary
function, not primary. Which leads to situation where the effects of the
interactions are a minimum of a full logarithmically (and
spherical-progressive from all individual wave interactives) calculated
magnitude less.

Makes for interesting results, but the Newtonian gross
calcs that Einstein used are known, even by him, to have been incorrect.
(Corrected by him in 1927 via his proper inclusion of Maxwell's full works not
the edited ones) to achieve a proper and working Unified Field theory, which
since 1927, has slowly been buried/removed, due to it's extreme
ramifications.

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KBK - Mar 01, 2010

Rank: 1 / 5 (1)

As far as i can tell, tho, this article is not about precise
measurement, but rather is about enforced determination from the superposition
dual wave state..to a historical point of the past.

Time is linear, it
moves, according to our observation, in one direction only. The past is locked
and permanent, but the future has a minimum of two indeterminate states, which
are fused to the single, upon observation.., thus, in the moment, CREATING the
flow of time and the past, from the 'prior' moments of
'indeterminacy'.

The Hitachi experiment in the 1980's proved this. So
to utilize a system of measurement that attempts to do a loopback and remove
the open possibility of the future and fuse it into the locked character of
the past results in nothing but some bizarre form of attempting to force
potentiality to a permanent state that reflects the past. ie, to erase
possibility and/or potential--- from the future.

And THAT, is very
seriously messed up.

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broglia - Mar 01,
2010

Rank: 1 / 5 (1)

All these seemingly miraculous phenomena have their very
trivial analogy at water surface, where transversal waves are always affected
by Brownian noise. We can arrange 2D analogy of observation by using of pair
of surface wave detectors - the precision in detection of location and speed
of objects observed would be affected by this background noise in similar way,
like during observation in vacuum by CMB noise.

Such model enables to
think about quantum phenomena from perspective, which is unachievable for us,
because in vacuum we can use only transversal waves for observation - the
gravitational waves are too weak and low distance ones for being available for
more objective observations.

http://www.physorg.com/news78650511.html

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VerGreeneyes - Mar
01, 2010

Rank: not rated yet

Particle Swarm Optimization, eh? Milkyway@Home also uses that
- they're also trying Differential Evolution, and have tried a Genetic search
in the past. I wonder if these scientists have considered those alternatives
as well?

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