1.
Beating the classical diffraction limit
We demonstrate the
generation of four-photon entangled states and their
subsequent utilization in pure four-particle interferometry. The
observed interference fringes confirm the theoretical expectation that
the de-Broglie wavelength of a four-photon state is one fourth of a
single photon. This overcomes state-of-the-art two-particle
interferometry and opens new possibilities in quantum metrology and in
quantum imaging applications.
2.
Realization of a photonic Controlled-NOT (CNOT) gate
We
report the first experimental
demonstration of a quantum controlled-NOT gate based on linear optics.
In the experiments, using an entangled ancillary pair of photons and
post-selection. we were able to sucessfully
3.
Quantum state tomography of photonic GHZ states
We
completely characterized the
polarization state of three
photons in a Greenberger-Horne-Zeilinger
entangled
state using quantum state tomography. The
description, called the density matrix, allows
one to predict the
results of any polarization measurements made on these photons.
The real
(left) and imaginary (right) parts of the density matrices. The diagonal runs from the far corner to the
near corner.
K.J. Resch, P.
Walther, and A. Zeilinger, Physical Review Letters 94, 070402 (2005)
4.
Local conversion of Greenberger-Horne-Zeilinger states to approximate W
states
Genuine 3-qubit entanglement comes in two different inconvertible types
represented by the GHZ state and the W state. We describe a specific
method based on local positive operator value measures (POVMs) and
classical communication that can convert the ideal N-qubit GHZ state to
a state arbitrarily close to the ideal N-qubit W state. We then
experimentally implement this scheme in the 3-qubit case and
characterize the input and the final state using 3-photon quantum state
tomography.
The left figure represents the density matrix (real part only) of an
ideal (a) and experimentally measured 3-photon GHZ state The
state is displayed in the D/A-basis, where D=(1/(√2))(|H>+|V>)
and A=(1/(√2))(|H>-|V>).
The right figure shows the density matrix (real part only) of an
approximate W output state after the POVM procedure. For comparison, we
show (a) the action of the POVM operation on the ideal GHZ state and
(b) our experimentally obtained GHZ state after the three local POVM
operations. The application of the POVMs have suppressed several of the
matrix components such that the final state contains only 9 major
elements. These are the same 9 elements for the ideal W
state. The operation has increased the fidelity of our state with
a W state from 61% to 68% while at the same time reducing the fidelity
of our state with a GHZ state from 79% to 60%.
P. Walther, K.J. Resch, and A.
Zeilinger, Physical Review Letters 94, 240501 (2005)
5.
Quantum nonlocality obtained from local states by
entanglement purification
The real (left-hand side)
and imaginary (right-hand side) parts
of the density matrices of a) the first initial pair , b) the second
initial pair, and c) the purified pair, with dramatically improved
entanglement and purity.
P. Walther, K.J. Resch, Č. Brukner,
A.Steinberg, J.-W. Pan, and A. Zeilinger, Physical Review Letters 94, 040504 (2005)6.
Quantum teleportation across the Danube
Long Distance Quantum teleportation
of individual qubits has been demonstrated by using
glass fiber optics in a channel underneath the river Danube in Vienna
( right picture) . There we have the
stations of Alice and Bob and above
the river there will be a direct connection for the classical channel
(left picture). A most interesting feature of that experiment will
exploit the fact that the speed of light in glass fibers is only 2/3 of
the speed in free space.
Therefore, using very fast electronics, it can be expected that the
classical signal propagating in free space can actually be transmitted
from Alice's station at a time after the photon has been launched but
still arrive at Bob's station significantly early enough to set unitary
transformation at Bob's side in time such that the arriving photon will
be subject to the appropriate unitary transformation, in order to
become an exact replica of the original.
R.
Ursin, T. Jennewein, M. Aspelmeyer,
R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, Nature 430, 849 (2004).
This
experiment was chosen by the British PhysicsWeb
to be one of the Highlights
of the year 2004.
Some of the media coverage (mostly in german)
is shown in our Press
Review (4 MB).
7.
Free-space quantum communication I
We used
direct line-of-sight optical
links to send entangled photons over 500m in an outdoor experiment and
violate a Bell inequality. The longer of the two links passed over the
main branch of the Danube River
in Vienna.
Layout
of the experiment (left). The entangled
photon source and the sending
telescopes (right).
M.
Aspelmeyer, H. Boehm, T. Jennewein, T. Gyatso,
R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M.
Taraba, R. Ursin, P. Walther, and A. Zeilinger, Science 301, 621 (2003). Also,
John Rarity wrote a news
article on this experiment in the same issue of Science.
This experiment was also presented by the New
Scientist.
8.
Free-space quantum communication II
Our team has sent
entangled photons from the Kuffner Sternwarte (Observatory) to the
Millennium Tower through a 7.8 km path directly over the city of
Vienna. The detection time tags from the photon pairs were shared
over the internet and analyzed using coincidence software. These
coincidence counts were demonstrated to convincingly violate a Bell
inequality. In doing so, we have extended the distance over which
entangled photons can be distributed by over a factor of 10 and
demonstrated entanglement distribution through an atmospheric
equivalent.
A schematic drawing of
the setup and a picture of the link between
Alice and Bob can be seen on the left picture, while the right picture
shows some of us when building the table at Kuffner Sternwarte.
K.
Resch, M. Lindenthal,
B. Blauensteiner, H.Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T.
Schmitt-Manderbach, M. Taraba, R.Ursin, P.Walther, H. Weier, H.
Weinfurter, and A. Zeilinger, Optics
Express 13, 202 (2005)
9.
Experimental realization of a one-way quantum computer
The one-way quantum
computer proposed by Raussendorf and Briegel ( PRL
86, 910),
( PRL 86,
5188) is an
entirely new concept for quantum computation: starting from a su fficiently large cluster state (at least
four qubits), any gate necessary for quantum computation can be
implemented by making measurements on individual qubits and feeding the
results forward to adapt the subsequent measurements accordingly.
Cluster state quantum computation is universal in that any quantum
circuit can be implemented. To be more explicit, universal cluster
state quantum computing simply requires measuring its
particles individually in a certain order and in certain bases. Di fferent algorithms only require a di fferent "pattern" of single qubit
operations on a su fficiently
large cluster state.
We have experimentally
realized a cluster state made of four entangeld photons (picture
above), which allowed us to demonstrate generel one- and two-qubit gate
operations (picture below) as requried for quantum computation.
Once a clsuter state is
generated, the gates or software for the computation is defined by the
order of the single-qubit measurments. While a one-dimensional cluster
states gives access to singel-qubit operations, a two-dimensional
cluster allows to perfom two-qubit gate operations.
We further demonstrated
the strength of clsuter state computation by implementing Grover's
fast quantum search algorthm (picture above). A blackbox labels one of
four different input states (red arrow). Grover's search algorithm uses
quanutm interference to get the right result out of the four by asking
only once, which is called inversion about the mean value.
P. Walther, K. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A.
Zeilinger, Nature 434, 169 (2005).
In an additional
experiment we experimentally demonstrated that correlations in a
four-qubit linear cluster state cannot be described by local realism.
This exploration is based on a recently derived Bell-type inequality by
Scarani et al. (PRA 71, 042325 ) which is tailored, by using a
combination of three- and four-particle correlations, to be maximally
violated by cluster states but not violated at all by GHZ states. We
observed a cluster state Bell parameter of about 2.59 which is
significantly larger than the threshold of 2 imposed by local realism.
The figure above represents the experimentally extracted polarization
correlations. The cluster-state Bell inequality requires four different
polarization correlations, which were extracted from a complete set of
48 four-fold coincidence measurements.
P. Walther, M.
Aspelmeyer, K.J. Resch, and A.
Zeilinger, Physical Review Letters 95, 020403 (2005)
In the most recent experiments we were able to implement active
feed-forward to achieve a determinsistic quantum computation once a
cluster state is given. This was realized b y
employing
up to three active-switching Electro-Optical Modulators (EOM) in a
four-qubit
cluster state. Using these switches we
demonstrate
detrministic one- and two-qubit gate operations as well as Grover’s
quantum
search algorithm. A major advantage of optical quantum computation
is the very short time for one computational step achievable by using
these
ultra-fast switches. Impressingly, with present technology this
feed-forward step can be performed
in less than 150 nanoseconds, which is about three orders of magnitude
faster
than in other physical realizations of quantum computers.
The figure above shows
how active-feed fowarding is implemented. The deterministic
cluster-state computation proceeds by consecutive polarization
measurements on photons 1-4. Dependent on the outcomes of photons
1-3, three fast electro-optical modulators (EOMs) are employed to
implement the active feed-forward. One EOM adapts the measurement
basis of photon 3, while two EOMs, aligned for X and Z operation, apply
the error-correction on output photon 4. Two single-mode fibres, 30m
and 60m long, serve to locally delay the photons during the detection
stage, logics operation and switching/charging process of the EOMs.
R. Prevedel, P.Walther,
F.Tiefenbacher, P. Böhi, R.Kaltenbaek, T. Jennewein, A. Zeilinger, Nature
445, 65 (2007)
10.
Experimental Entangled Entanglement
Entanglement according to Schroedinger - the essential property of
quantum mechanics - teaches us that the properties of individual
quantum systems cannot be considered to be (local) elements of physical
reality before and independent of observation. Yet it is a widespread
belief that the way the observations on, say, two particles are
correlated, i.e. the specific type of their entanglement, can still be
considered as a property of the physical world. We present experimental
evidence to the contrary. We have measured the correlations between a
single-particle property, the polarization state of a photon, and a
joint property of two particles, the entangled state of a photon pair,
in a three-photon entangled state. The measured correlations between
these properties are too strong for any local-realistic explanation and
demonstrate a convincing violation of the Clauser-Horne-Shimony-Holt
Bell inequality.
The left figure represents a schematic cartoon for the Bell experiment
based on the entangled entangled state. One photon is received by Alice
and two other photons by Bob. Alice controls an anylzer that makes
measurments of the polarization of her photon. When the photon’s
polarization is measured to be parallel (perpendicular) to the
orientation, θ1, of the analyzer, the measurement outcome is +1 (-1).
In
contrast, Bob makes projective measurements onto a two-particle
entangled state, where the orientation of his analyzer is defined by
the angle, θ2. Bob’s outcomes are defined as +1 or -1. b)
When Alice and Bob measure with the local settings θ1 and θ2 such that
θ1+θ2=0, π, 2π, etc. they observe perfect correlations, i.e., the
product of their local measurement outcomes yields +1. c) Perfect
anti-correlations will be obtained when θ1+θ2= π/2, 3π/2, etc., given
by product -1 of the local results, while correlated and
anti-correlated events will occur at angles away from these specific
settings. These correlation measurements with different measurement
settings form the basis of a test of local realism using entangled
entanglement.
The right figure represents the experimentally measured coincidence
counting rates used to test the CHSH Bell inequality. This Bell
inequality contains 4 correlations between Alice’s polarization
measurement outcomes and Bob’s entangled state projective measurement
outcomes. Each of these correlations in turn can be extracted from 4
coincidence counting rates. The requisite coincidence measurements for
the 16 different measurement settings are shown. Each measurement
was performed for 1800 seconds. For measurement settings, {θ1, θ2}, the
axis labels ++, +-, -+, and -- refer to the actual settings of {θ1,
θ2}, {θ1, θ2+π/2}, {θ1+π/2, θ2}, and {θ1+π/2, θ2+π/2} respectively.
These data can be combined to give the Bell parameter
S=2.48±0.09.
P. Walther, K.J.
Resch, C. Brukner, and A.
Zeilinger, Physical Review Letters 97,
020501 (2006)
11.
Heralded generation of multi-photon entanglement
Despite many different
sources for entangled pairs, spontaneous parametric down-conversion is
the
state of the art method for many experiments dealing with entanglement.
However,
due to the intrinsic probabilistic generation of entangled photon-pairs
through
down-conversion existing sources rely on post-selection on specific
multiparticle-entangled states. We present
a simple scheme consisting of linear optics and nonlinear
down-conversion
crystals for the generation of heralded polarization-entangled
multi-photon
states. Specifically, this proposal allows the generation of heralded Bell states or
GHZ
states. By measuring ¾ of the N
photons involved in the experiment as ancilla photons, the remaining
photons are in the desired entangled state. This proposal allows the
usage of
state-of-the art photo-detectors and optical devices and does not need,
as
always claimed, photo-detectors with single photon resolution. This is
an important
step toward deterministically working quantum computers and
communication protocols. Furthermore this scheme gives
access to optical lithography beyond the diffraction limit by using
path-entangles states, so called N00N-states.
 
The pictures above show a
schematic
setup for the heralded preparation multi-photon maximally entangled
states. A conditional generation of two-photon Bell-states can be seen
on the left drawing while the conditional generation of multi-photon
states of the GHZ-type on the right drawing.
P.Walther,
M. Aspelmeyer, and A. Zeilinger, Physical Review A 75, 012313 (2007)
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