## Contributed Talks

## Abstracts

**Charlene Ahn**, Caltech

Coauthors: H. M. Wiseman, G. J. Milburn, Kurt Jacobs

*Quantum error correction for continuously detected errors*

We show that quantum feedback control can be used as a quantum error
correction process for errors induced by weak continuous measurement.
In particular, when the error model is restricted to one, perfectly
measured, error channel per physical qubit, quantum feedback can act
to perfectly protect a stabilizer codespace. Using the stabilizer formalism
we derive an explicit scheme, involving feedback and an additional constant
Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical
qubits. This works for both Poisson (jump) and white-noise (diffusion)
measurement processes. In addition, universal quantum computation is
possible in this scheme. As an example, we show that detected-spontaneous
emission error correction with a driving Hamiltonian can greatly reduce
the amount of redundancy required to protect a state from that which
has been previously postulated. The multiple-channel case is also considered,
and it is shown that for arbitrary numbers of channels n physical qubits
can protect n-2 logical qubits.

**Sergey Babichev, **University of Konstanz

with Juergen Appel, Alexander Lvovsky

*Continuous-variable experiments with a nonlocal single photon *

A two-mode optical qubit is generated when a single photon from a parametric
down conversion source entangles itself with a vacuum on a beam splitter.
We have characterized this dual-rail state by means of homodyne tomography.
From the quadrature statistics, applying the maximum likelihood method,
density matrix is calculated which extends over the entire Hilbert space
and thus reveals, for the first time, complete information about the
qubit as a state of the electromagnetic field. A nonlocal nature of
the reconstructed state is shown by a violation of the Bell inequality
for the experimental data converted to a dichotomic format. This experiment
can be interpreted as remote preparation of an arbitrary single-mode
optical qubit. By measuring a quadrature on one of the spatial modes
of the entangled state, we project the other mode onto a coherent superposition
of the single-photon and vacuum states. Surprisingly, the state obtained
in this manner can be of higher purity than the single-photon resource
we started with.

**Robert Badzey**, Boston University

Coauthors: Doru Cuturella, Pritiraj Mohanty

*Quantum Coherent Effects in the Presence of External Control Fields*

Electron coherence effects, such as the Aharonov-Bohm effect, have
been the focus of much interest in condensed matter physics over the
past few decades. At low temperatures, low-dimensional conductors demonstrate
electron coherence even in the presence of a disordered potential. Here
we present results from our initial investigations into applying quantum
control methods to coherent electron systems. We examine the effects
external control fields, both broadband and pulsed, have on an Aharonov-Bohm
ring sample. We discuss the potential for quantum control of electron
coherence through the use of both passive control and bang-bang pulses
with learning control.

**Victor S. Batista**, Yale Universisty, Chemistry
Department

Coauthors: Luis G.C. Rego

*Creating molecular entanglement in functionalized semiconductor
nanostructures*

The feasibility of creating molecular entanglement in functionalized
semiconductor nanostructures is computationally demonstrated. Entangled
holes, localized deep in the semiconductor band gap, are generated by
electron-hole pair separation after photoexcitation of surface complexes.
The approach is illustrated for small arrays of catechol molecules anchored
to TiO2-anatase nanowires under vacuum conditions. It is shown that
molecular entanglement can persist for hundreds of picoseconds at cryogenic
temperature. Moreover, it is shown that the relaxation dynamics of entangled
states can be coherently controlled by a sequence of ultrashort 2-pi
pulses.

**Somshubhro Bandyopadhyay **University
of Toronto

with Daniel Lidar

*Entangling capacities of noisy non-local Hamiltonians *

We show that intrinsic Gaussian fluctuations in system control parameters
impose limits on the ability of non-local (exchange) Hamiltonians to
generate entanglement in the presence of mixed initial states. We find
three equivalence classes. For the Ising and XYZ models there are qualitatively
distinct sharp entanglement-generation transitions, while the class
of Heisenberg, XY, and XXZ Hamiltonians is capable of generating entanglement
for any finite noise level. Our findings imply that exchange Hamiltonians
are surprisingly robust in their ability to generate entanglement in
the presence of noise, thus potentially reducing the need for quantum
error correction.

**Jean Christian Boileau, **University of Waterloo

**
**
with Daniel Gottesman, Raymond Laflamme, Martin Laforest, Casey Myers,
David Poulin, Rob Spekkens

*Polarization-Based Quantum Key Distribution Without Shared Reference
Frame *

Experimentalists attempting to perform QKD over long distances must
deal with inherent noise from optical fibers. If we neglect attenuation
and assume that the coherence time of the photon is large enough, the
noise in the fiber can be represented as a time-dependent rotation of
the polarization states. To overcome this problem, some techniques have
been explored: using an operational system to systematically compensate
the error, encoding the qubits in the phase of the photons or sending
the photon back and forth through the fiber with the help of a Faraday
mirror. I will talk about some new alternate solutions based on decoherence-free
subspace. I will relate them to the problem of implementing quantum
cryptography without a shared reference frame.

**Dan Browne**, Imperial College

with Dan Browne and Terry Rudolph

*Efficient linear optics quantum computation with Bell States *

We present a novel optical quantum computation scheme [1] which utilises,
as its basic resource, maximally polarisation entangled photon pairs
(Bell states). The scheme operates in the “cluster state”
approach to quantum computation [2]. Cluster states are a class of entangled
multi-qubit states with many interesting properties [3]. In particular,
by measuring the individual qubits of a cluster state of sufficient
size in particular eigenbases and in a particular order, any quantum
network can be efficiently simulated and thus universal quantum computation
can be achieved [2]. We will describe how cluster states can be generated
from Bell states non deterministically with linear optical elements
and photo-detection. The quantum computation is then implemented, in
a deterministic step, by polarisation measurements on individual photons.
The resources required to generate the cluster state in our scheme scale
linearly with its size. The scheme which we describe has several attractive
features. Firstly, it avoids the need for the concatenation of large
numbers of beam-splitters, which is necessary in standard linear optics
quantum computation proposals [4] and which places extremely high demands
on the degrees of mode-matching required in their experimental implementation.
Additionally, its resource requirements are much more favourable than
the original linear optics quantum computation proposal [4], and also
improve on more recent schemes such as [5] and the cluster-state based
approach in [6]. References [1] D.E. Browne and T. Rudolph, quant-ph/0405157.
[2] R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188-5191
(2001); R. Raussendorf, D.E. Browne and H.J. Briegel, Phys. Rev. A 68,
022312 (2003). [3] H.J. Briegel and R. Raussendorf, Phys. Rev. Lett.
86, 910-913 (2001). [4] E. Knill, R. Laflamme, and G. Milburn, Nature
409, 46 (2001). [5] N. Yoran and B. Reznik, Phys. Rev. Lett. 91, 037903
(2003). [6] M.A. Nielsen, quant-ph/0402005.

**Tommaso Calarco, **University of Innsbruck

** **
with U. Dorner, P. Julienne, C. Williams, and P. Zoller

*Exploiting quantum control for quantum computation in optical lattices:
marker atoms and molecular interactions *

We develop a scheme for quantum computation with neutral atoms, based
on the concept of "marker" atoms, i.e., auxiliary atoms that
can be efficiently transported in state-independent periodic external
traps to operate quantum gates between physically distant qubits. Quantum
control theory (Krotov's method) is used to optimize the fidelity of
both atom transport and quantum gate operations. This allows for relaxing
a number of experimental constraints for quantum computation with neutral
atoms in microscopic potential, including single-atom laser addressability.
We discuss the advantages of this approach in a concrete physical scenario
involving molecular interactions.

**Hilary Carteret, **Université de Montréal

with M.S. Anwar, D. Blazina, S.B. Duckett, T.K. Halstead, J.A. Jones,
C.M. Kozac and R.J.K. Taylor

*Preparing high purity entangled states for NMR quantum computing
*

A number of objections have been raised against the liquid-phase nuclear
magnetic resonance (NMR) implementation of a quantum computer. In 1997
Warren argued that efficient NMR quantum computation required temperatures
far below 1K. In 1998, Braunstein et al. claimed that liquid-phase NMR
is incapable of universal quantum computation because it cannot produce
entanglement, and thus the computer could be described by local hidden
variable models. This presentation will give an introduction to para-hydrogen
induced polarization (PHIP) and show how this can be used to prepare
a two-qubit system in an almost pure, entangled state. To achieve polarizations
comparable to our observed value of 0.916 +/- 0.019 (out of a maximum
possible value of 1) by thermal means would require cooling the system
to 6.4mK in the 9.6 T field used, or a magnetic field of 0.45 MT at
room temperature. Our states had an entanglement of formation of 0.822.
This method clearly outperforms other liquid-phase initialization methods
for producing both polarization and entanglement, regardless of the
arguments over whether or not entanglement is really necessary for universal
quantum computation.

*Conference key-agreement and secret sharing through
noisy GHZ states*
by

Kai Chen, Dept. of Physics, University of Toronto

Coauthors: Hoi-Kwong Lo

Various protocols (BB84, Ekert91, B92) and security proofs for two-party
common key-agreement have been proposed. We consider here two quantum
communication protocols involving 3 parties in the noisy channel setting.
The first cryptographic task is for Alice, Bob and Charlie to establish
a secure conference key from noisy tripartite Greenberger-Horne-Zeilinger
(GHZ) states in the presence of an eavesdropper. The second cryptographic
task is for Alice to share a secret with Bob and Charlie by using noisy
GHZ states. We use prepare-and-measure protocols where a preparer prepares
an ensemble of GHZ states and distribute them to the three parties through
some noisy channels. The three parties only need to perform quantum
measurements and, subsequently, classical computations and classical
communications. In other words, the three users do not need to perform
quantum computation or long-term storage of quantum signals. Therefore,
our protocol may be feasible with near-future technology.

Paper reference: arXiv:quant-ph/0404133

**Yossi Elran**, University of Toronto

*Decoherence in an Anharmonic Oscillator Coupled to a Thermal Bath*

The decoherence of an anharmonic oscillator in a thermal harmonic bath
is examined via a semiclassical approach. A new computational strategy
is presented and exploited to calculate the time dependence of the purity
and the decay of individual matrix elements in the energy representation
for a variety of initial states. The time dependence of the decoherence
is found to depend on the temperature of the bath, the coupling strength,
the initial state of the oscillator, and the choice of quantity measuring
the decoherence. Recurrences in the purity and in the off-diagonal matrix
elements are observed, as well as the collapse of these matrix elements
to the diagonal, providing evidence for the retention of quantum coherence
for time scales longer than that indicated by the purity. The results
are used to analyze the utility of the Caldeira-Leggett and Redfield
models of decoherence and to assess the dependence of dephasing rates
on the degree of structure in phase space. In several cases we find
that the dephasing dynamics can be described as an initial Zeno-effect
regime, followed by a Caldeira-Leggett region, followed by recurrences.

**Antonio Di Lisi**, Dept of Physics, University
of Camerino, Italy

Coauthors: David Vitali

*Closed loop techniques for decoherence control and entanglement
manipulation*

We give a general description of how closed loop techniques can be
used in quantum optical systems for decoherence control [1] and for
the generation and manipulation of maximally entangled states of small
atomic samples [2]. The schemes consider state of art experimental apparata
(cavity QED systems or spin-polarized samples) and employ closed loops
based on single photon detections. [1] S. Zippilli, D. Vitali, P. Tombesi,
J. M. Raimond, Phys. Rev. A 67, 052101 (2003). [2] A. di Lisi, D. Vitali,
S. de Siena, F. Illuminati, in preparation

**Jose M. Fernandez,** Ecole Polytechnique
de Montreal

with Experiment: Gilles Brassard (U of Montreal), Raymond Laflamme (Waterloo/IQC/PI),
Tal Mor (Technion), Yossi Weinstein (Technion). Theory: Seth Lloyd (MIT),
Tal Mor (Technion), Vwani Roychowdhury (UCLA).

*Theoretical Methods and Experimental Implementation of Heat-Bath
Algorithmic Cooling *

Algorithmic Cooling is a generic term for techniques leading to the
purification of qubit registers whose initial state is not pure. This
term encompasses polarisation transfer techniques of NMR (pre-dating
both QC and NMR-based QC) and also in-place quantum compression schemes
such as those of Schulman and Vazirani. The entropy conservation law
imposes, however, severe restrictions on the efficiency of such techniques,
often referred to as the Shannon Bound. In addition, the necessity that
all transformations applied be unitary (i.e. inner-product preserving),
imposes an even tighter bound, referred to as the Sørensen Bound.
A new kind of algorithmic cooling which bypasses these bounds by pumping
out excess entropy into the environment (i.e. heat bath) has been proposed
in 1999 by Boykin, Mor, Roychowdhury, Vatan, and Vrijen and has been
referred to as "non-adiabatic" or "heat-bath" algorithmic
cooling. This talk presents an improved non-adiabatic cooling algorithm,
more efficient in terms of the number of required qubits, which achieves
an exponential increase in polarisation with a linear number of qubits.
Furthermore, we report on the first proof-of-concept non-adiabatic cooling
experiment ever, performed in April 2002 at the Université de
Montréal on a 3-spin molecule.

**Ignacio Franco**, University of Toronto

Coauthors: Paul Brumer

*Coherent Control of Charge Transport in Photoexcited trans-Polyacetylene*

Conjugated polymers are of interest both for their broad technological
applications and also because they are model systems to gain fundamental
understanding of the properties of soft organic and biological matter.
The photoexcited dynamics of these systems is characterized by a strong
coupling between, and mutual influence of, nuclear and electronic degrees
of freedom. This, in turn, gives rise to a very rich photophysics of
solitons, polarons and excitons (self-localized nonlinear excitations
associated with a lattice distortion) and constitutes an important distinction
between "soft" materials and rigid solids based on semiconductor
or crystalline metal materials.

In this talk we present numerical simulations of the highly nonlinear
electron-vibrational dynamics of trans-polyacetylene under the influence
of a symmetry breaking coherent control scenario. We show how the interference
between a one-photon and a two-photon route can be used to induce directed
electronic transport along the backbone of the conjugated polymer and
assess the effect of the electron-phonon interactions on the applicability
of the scenario.

**J.D. Franson, **Johns Hopkins University

with B.C. Jacobs and T.B. Pittman

*Quantum Computing Using Single Photons and the Zeno Effect *

We show that the quantum Zeno effect can be used to suppress the errors
that would otherwise occur in a linear optics approach to quantum computing.
This allows quantum logic gates to be implemented without the need for
ancilla or measurements, including a logic operation that is similar
to the square-root of SWAP. The operation of these devices depends on
the fact that the Zeno effect can force photons to behave like non-interacting
fermions instead of bosons. In applications of this kind, the Zeno effect
can be viewed as a form of quantum control.

**Shohini Ghose**, University of Calgary

with Xiaoguang Wang (Macquarie University), Ivan Deutsch (University
of New Mexico), Barry Sanders (University of Calgary)

*Entanglement Dynamics in a Chaotic System *

We analyze quantum signatures of chaos in the entanglement dynamics
of cold atoms trapped in a magneto-optical lattice. The system has two
coupled degrees of freedom (atomic position and spin), allowing the
dynamics of entanglement to be studied both theoretically and experimentally.
The entanglement between spin and motional degrees of freedom exhibits
quasi-periodic behavior for states localized in a regular region of
phase space. For states localized in a chaotic region, the growth of
entanglement is faster and no quasi-periodic behavior is evident. We
explain the main features of the entanglement dynamics by examining
the support of the initial state on the system eigenstates. Our analysis
is general and applicable to other quantum chaotic systems with unitary
evolution.

* Entanglement-assisted Coherent Control in Bimolecular
Scattering*
by

**Jiangbin Gong**, Department of Chemistry and The James Franck Institute,
University of Chicago

Coauthors: Paul Brumer

Intriguing quantum phase control effects that result from entangled
molecular rovibrational states are considered in identical diatom-diatom
scattering. Computational results on elastic and inelastic scattering
of para H2 and para H2 are presented. The results are also relevant
to our understanding of quantum entanglement between indistinguishable
molecules.

** Timothy F. Havel**, MIT

Coauthors: David G. Cory, Chandrasekhar Ramanathan, Joseph Emerson, Yaakov
Weinstein, Suddhasattwa Sinha

*Quantum Control of Spin Systems by NMR*

NMR spectroscopy is an established testbed for quantum control methods
in the liquid state, and in the solid state offers a promising approach
towards large-scale QIP. I will provide an overview of the current state-of-the-art
in these these methods, including quantum process tomography, methods
of refocussing inhomogeneous field effects, and a dressed-states approach
to the interaction of dipole coupled spin systems with a radiation field.

**Kaveh Khodjasteh**, University of Toronto,
Dept. of Physics

Coauthors: Daniel Lidar

*Concatenated Dynamical Decoupling Pulse Sequences*

The origins of noise and decoherence in the evolution of open quantum
system are the uncontrollable interactions of the parts of the system
with an environment that normally challenges production or manipulation
of quantum states in experimental realizations of quantum information
processing. Dynamical decoupling (DD) pulse sequences are feedback free
and conceptually simple means of eliminating the unwanted terms of the
interaction Hamiltonian in a system (possibly) coupled to an environment
or the bath, by applying fast, strong pulses to the system in regularly
paced intervals.

DD pulses, has by far been limited to simple models in which the pulses
are applied in series and the removal of the undesired interactions
depends on the following: (a) the width of the pulses must be small
enough so that the evolution of the system during the pulse can be ignored
and (b) the time between consecutive pulses has to be much smaller than
the time scales of the bath. These conditions restrict the applicability
of simple DD pulses, usually known as parity kicks.

In this work we use an analogy with quantum error correction codes
and investigate the idea of concatenating dynamical decoupling pulses
to obtain further cancellations of the error terms in the Hamiltonian.
To this end we develop a series of renormalized Hamiltonians that are
used to estimate the strength of the undesired interactions, after applying
each layer of dynamical decoupling. The sources of these Hamiltonians
will be the errors due to the pulse imperfections (including the effects
of the pulse width) and the errors due to the evolution of the bath
between the application of pulses. We further present a criteria in
terms of the system-bath interaction Hamiltonian strength HSB, bath's
internal Hamiltonian strength HB, the time between consecutive pulses
\tau, and the pulse width t, for the overall usefulness of concatenating
dynamical decoupling pulses against decoherence. We also compare these
results with the threshold calculations in quantum error correction
literature.

**Robert Kosut**, SC Solutions, CA

Coauthors: Ian Walmsley (Oxford University, Oxford, UK walmsley@physics.ox.ac.uk)
and Herschel Rabitz (Princeton University, Princeton, NJ hrabitz@princeton.edu)

*Quantum Tomography and Detection: Design via Convex Optimization*

In this paper we show that a number of problems in quantum state estimation
(state tomography), quantum system identification (process tomography)
and quantum state and system detection can be cast as convex optimization
problems. The great advantage of convex optimization is a globally optimal
solution can be found efficiently and reliably, and perhaps most importantly,
can be computed to within any desired accuracy using an interior-point
method.

Some of the problems addressed in this paper are already known to be
convex but have not fully exploited the available convex solvers or
duality theory. For example, it is known that Maximum likelihood Estimation
(MLE) of the quantum state (density) is a convex optimization. What
we also show is that a number of other MLE problems are convex, e.g.,
estimating the distribution of known states and quantum process tomography
in the Kraus operator sum representation (OSR) in a fixed basis. One
important problem which is not convex is MLE of Hamiltonian parameters.
We show, however, how duality theory can help establish bounds on the
parameter estimates for this problem.

Another problem which can be solved via convex optimization is experiment
design. (Experiment design here means choosing the number of experiments
to be performed in a particular system configuration; a configuration
being any number of combinations of sample times, hardware settings,
etc. For example, in quantum state photonic tomography, we can determine
the optimum number of wave plate setting to achieve a desired estimation
accuracy.) In this paper we will apply the experiment design procedure
invoked by the Cramer-Rao Inequality to all the MLE problems mentioned
above, including MLE of Hamiltonian parameters. We will show that in
all these cases the optimum experiment design problem, although integer-combinatoric,
can be relaxed to a convex optimization problem whose solution provides
upper and lower bounds on the unknown optimal integer solution. The
MLE of the state or process can be combined with the optimal experiment
design in a ``bootstrapping'' iteration to make the estimation more
efficient.

Finally, we also address the problem of designing a detector which
is maximally sensitive to specific quantum states. We show that the
design problem can be formulated as a convex optimization problem in
the matrices of the POVM (positive operator valued measure) which characterize
the measurement apparatus, or with a given POVM, the matrices which
characterize the OSR in a fixed basis. We specifically address maximizing
the posterior probability of detection and show that this is a quasiconvex
optimization problem in either the POVM or OSR matrices. Previous work
in this area has only considered the joint probability of detection
over POVM matrices,

In all the cases described above we show how duality theory can be
used in various special cases to give insight into the nature (and possible
physical implementation) of the optimal solutions. In addition we will
briefly comment on the numerical properties of the convex programming
methods required. At present we have some experimental results for some
of the above cases.

**Debbie Leung ***, *Institute of Quantum
Information

with Panos Aliferis, Andrew Childs, Michael Nielsen

*A systematic derivation of measurement-based schemes for quantum
computation *

We present a systematic derivation of simplified one-way quantum computation
schemes (initially introduced by Raussendorf and Briegel [PRL 86, 5188
(2001)]) based on the simple underlying principle of teleportation.
The presentation is based on quant-ph/0404082, quant-ph/0404132.

**Masoud Mohseni**, Department of Physics, University
of Toronto

Coauthors: Daniel. A. Lidar

*Universal Fault-Tolerant Quantum Computation with the Exchange Interaction*

The ability of a quantum system to perform arbitrary or "universal"
computation is restricted to its naturally available/controllable interactions.
It has been shown that quantum systems with controllable exchange interactions
can be made computationally universal by encoding the information within
a subspace of the full Hilbert space: "encoded universality".
However, there has not been any success on development of a general
theory to make this encoded universal computation also resilient against
decoherence. In this work, we introduce a class of hybrid encoded-universality
stabilizer quantum error correcting codes, and demonstrate that quantum
error-correction can be performed in systems with controllable exchange
interactions. Specifically, we present an analytical method for leakage-correction
using only unitary operations generated by exchange interactions. Furthermore,
we demonstrate that any arbitrary quantum operation can be performed
on these codes without accumulation or propagation of logical or leakage
errors. In other words, universal fault-tolerant quantum computation
is possible from the exchange interaction.

**Ashwin Nayak, University of Waterloo**
with Leonard Schulman (Caltech) and Umesh Vazirani (UC Berkeley)

*A quantum algorithm for the Ising model *

The Ising model has been widely studied as a model for magnetisation
in the area of statistical physics. Computational solutions to problems
centred around the Ising model are based on sampling from the Gibbs
distribution for the model. We demonstrate how one can sample from this
distribution efficiently on a quantum computer. Our algorithm follows
an approach that is radically different from an efficient classical
solution that was discovered subsequently. In particular, our algorithm
illustrates how a seemingly hard-to-sample-from distribution (for instance,
using standard Markov chain techniques) can be transformed to an efficiently
sampleable distribution via a quantum Fourier transform. The algorithm
is polynomially more efficient than the best known classical algorithm
in certain regimes, and may generalise to the Potts model as well.

**Robert Raussendorf**, IQI, Caltech

Coauthors: Simon Anders, Hans Briegel (University of Innsbruck, Austria)

*Fault-tolerant quantum computation using graph states*

Graph states are highly entangled multi-qubit quantum states which
can be created from a product state via an Ising-type (i.e. z-z-) interaction.
The neighborhood relation, i.e. which qubit interacts with whom, is
specified by a graph.

Graph states form algorithmic resources for quantum computation: for
every quantum algorithm there exists (at least) one graph state such
that this algorithm can be realized by measuring the graph state qubits
in one-qubit measurements [1]. There arises the question of whether
the graph state picture of quantum computation is useful for fault-
tolerance, too. In particular, can graph state constructions improve
the error threshold?

As a simple illustrative example, an efficient circuit for fault- tolerant
data storage (i.e. a stabilizer tester circuit) using purified bicolorable
graph states [2] in a gate teleportation scheme [3] is shown. The more
general problem of fault-tolerant universal quantum computation is reduced
to fault-tolerantly creating two types of encoded quantum states: -
+>:=X - +> and - T>:= (X+Y)/sqrt(2) - T>. Procedures to
manufacture these states making use of redundant syndrome information
are displayed.

[1] R. Raussendorf, D.E. Browne and H.J. Briegel, PRA 68, 022312 (2003).

[2] W. Dür, H. Aschauer and H.J. Briegel, PRL 91, 107903 (2003).

[3] D. Gottesman and I.L. Chuang, Nature 402, 390 (1999).

**Barry C. Sanders, **University of Calgary

with Rolf Horn and Karl-Peter Marzlin

*Optical quantum fingerprinting *

Fingerprinting is used to compare bit strings via transmission of much
shorter strings, which reduces storage and communication resources dramatically
below that required for direct bit-wise comparison, and quantum fingerprinting
(which has not yet been performed experimentally) can yield an exponenential
improvement over its classical counterpart. We explain how linear optics
quantum fingerprinting can be performed for short strings, and show
that our scheme performs close to the optimal case without the linear
optics restriction.

**Anatoly Yu. Smirnov** , D-Wave Systems Inc.

*Decoherence and noise control in strongly driven superconducting
quantum bits *

We have examined fluctuations and dissipation in a quantum bit interacting
with a heat bath and driven by a strong resonant field. This model is
of immediate relevance for three Josephson junctions (3JJ) flux qubits,
which have been experimentally studied by Chiorescu et al. [1] and by
Il'ichev et al. [2]. The setup of the experiment [2] consists of a qubit
loop inductively coupled to a high-quality LC-circuit (tank) having
a resonant frequency, that is much lower than the frequency of quantum
beating in the qubit. Measurements of the average and spectral characteristics
of the tank voltage give information about low-frequency parts of a
qubit's magnetic susceptibility and a spectrum of fluctuations. The
resonant driving force induces Rabi oscillations, which modify the damping
rates and noise characteristics of the quantum bit. With non-Markovian
stochastic equations [3,4] we have calculated effects of the Rabi oscillations
on the dissipative evolution of the 3JJ qubits and have shown that experimental
results [1] are indicative of significant decoherence suppression by
the strong resonant field. Besides that, the nonequilibrium spectrum
of current fluctuations in the qubit loop has been obtained analytically.
The low-frequency component of this spectrum has a peak at the Rabi
frequency with a linewidth, which determines a decay of the Rabi oscillations.
Changing the amplitude of the driving force allows to control the decoherence
rate and the noise level in the qubit. This control has been demonstrated
in the experiment [2]. A comparison with theoretical predictions [4]
lets us to extract a long enough decoherence time, near 2.5 microsec,
for a decay of Rabi oscilations in the 3JJ quantum bit coupled to a
linear detector (the tank). We have analyzed a back-action of the detector
on the quantum system and have found a signal-to-noise ratio. It has
been shown that the noise spectroscopy performed in Ref.[2] can be considered
as an example of quantum weak continuous measurements. [1] I. Chiorescu,
Y. Nakamura, C.J.P.M. Harmans, and J.E. Mooij, Science, v.299, 1869
(2003). [2] E. Il'ichev, N. Oukhanski, A. Izmalkov, Th. Wagner, M. Grajcar,
H.-G. Meyer, A.Yu. Smirnov, A. Maassen van den Brink, M.H.S. Amin, and
A.M. Zagoskin, Phys.Rev.Lett., v.91, 097906 (2003). [3] A.Yu. Smirnov,
Phys.Rev.B, v.67, 155104 (2003). [4] A.Yu. Smirnov, Phys.Rev.B, v.68,
134514 (2003).

*Quantum control of entanglement by phase manipulation*
by

**Vladimir S. Malinovsky**
Michigan Center for Theoretical Physics & FOCUS Center, Department
of Physics, University of Michigan,

Coauthors: Ignacio R. Sola, Departamento de Quimica Fisica I, Universidad
Complutense, 28040 Madrid, Spain

A new method of entangled states preparation of two-qubit systems is
proposed. The method combines the techniques of coherent control by
manipulation of the relative phase between pulses, and adiabatic control
using time-delayed pulse sequences. A two-qubits system with couplings
forming a closed-loop configuration allows full preparation of entangled
states by controlling the relative phase of the fields. We have shown
that time-delayed sequences provide very stable mechanisms to control
the dynamics in the adiabatic regime. The relative phase between the
pulses is essential in preparing entanglement with specific phase relationships.
We have obtained the exact relationship between the control phase and
the phase of the prepared entangled state. Both counterintuitive and
intuitive pulse sequences are needed to prepare entanglement with all
possible phases. In the resonant scheme we have shown that the relative
phase between the pulses is the most sensitive parameter that governs
the entanglement in the counterintuitive sequence, while the pulse area
is the most sensitive parameter that controls entanglement in the intuitive
sequence. The off-resonant scheme provides the most stable mechanism
to prepare specific entangled states. We believe that the present scheme
provides additional flexibility for quantum control of entanglement
and could facilitate experimental implementation of quantum logic gates
in a few qubits systems.

All-optical processing in coherent nonlinear spectroscopy

by

**Dan Oron**, Weizmann Institute of Science

Coauthors: Nirit Dudovich (Weizmann Institute), Thomas Polack (Weizmann
Institute), Yaron Silberberg (Weizmann Institute)

The use of shaped ultrashort pulses has enabled achievement of coherent
nonlinear vibrational spectroscopy, where both the vibrational excitation
and its probing are done by the same laser pulse. Here we show that
shaped pulses can not only excite and probe coherent molecular vibration
but can also perform simple coherent processing and analysis of the
observed spectra. This is done by inducing intereference between contributions
to the total signal by quantum paths passing through different intermediate
states. Due to its coherent nature, this type of optical processing
results in significantly improved background rejection and in signal
enhancement. Schemes allowing for single-pulse coherent multidimensional
spectroscopy will also be discussed.

*Unconditional Security of the Bennett 1992 quantum
key-distribution protocol over a lossy and noisy channel*
by

**Kiyoshi Tamaki, **Perimeter Institute for Theoretical Physics

Coauthors: Masato Koashi, Norbert Luetkenhaus, Nobuyuki Imoto

We study the unconditional security of the Bennett 1992 quantum key-distribution
protocol (B92) over a lossy and noisy channel. For the simplicity of
the analysis, we assume that Alice encodes bit values into the single
photon polarization state, and Bob's detectors discriminate between
single photon states on one hand and vacuum state or multi-photon states
on the other hand. To prove the security, we first propose an unconditionally
secure protocol that employs the entanglement distillation protocol
(EDP) based on a filtering operation and the Calderbank-Shor-Steane
(CSS) quantum error correcting codes. The bit errors and the phase errors,
which have to be estimated for the EDP based protocol, are correlated
after the filtering operation, and we can bound the phase error rate
from the observed bit error rate by an estimation method involving nonorthogonal
measurements. By showing the equivalence between this EDP based protocol
and the B92, we have proven the unconditional security of the B92.

*Quantum Coherent Control of Current and Chiral
Cat States*
by

**Ioannis Thanopulos**, Weizmann Institute of Science

Coauthors: Petr Kral, Moshe Shapiro

We develop a robust methodology for preparation of novel quantum entangled
states, by combining phase-sensitive coherent control techniques with
the use of nonclassical light states. The idea is that population components
of different ``semiclassical phases" in such light states guide
the system to different components of the entangled states. Thus, a
system of the |A> and |B> material states, driven by light in
the |alpha> +|-alpha> cat state, can get in the |A>|alpha>
+ |B>|-alpha> entangled state. In this way, we can prepare ``current"
or ``chiral" cat states, if |A> and |B> are momentum states
of opposite directionality or chiral states of left-handed and right-handed
symmetries, respectively.

*Secure quantum protocols for voting*

by

**J.A. Vaccaro**, University of Hertfordshire

Coauthors: A. Chefles (University of Hertfordshire), J. Spring (University
of Hertfordshire)

We introduce quantum protocols for ensuring the secrecy of the individual
votes of a number of voters. The votes are recorded in a distributed
system using local operations yet the tally of the votes exists nonlocally.
At every stage the tally remains hidden to local observers which ensures
the secrecy of individual votes. The exact value of the tally during
the voting can only be determined if all parties share a maximally entangled
state and they cooperate. If one party, say a scrutineer, refuses to
cheat in this manner, the absolute secrecy of the tally is guaranteed.
At the end of the voting process the tallyman and scrutineers are given
access the whole system, which allows them to determine the value the
tally.

*Quantum Logics using Four-Photon Entanglement*

by

**Philip Walther**, Institute for Experimental Physics, University
of Vienna

The availability of four-photon entanglement allows demonstrating probabilistic
quantum logic gates, such as the controlled-not (cnot) and sign-shift
gate, as well as path-entanglement of up to four photons. A cnot gate
[1] was achieved by using polarization entangled qubits and polarizing
beamsplitters. A similar configuration of the setup for the cnot-experiment
leads to a sophisticated interferometer [2], which was required for
the first experimental observation of the reduced deBroglie wavelength
of a nonlocal four-photon state. One of the central elements in linear
optics quantum computing is a conditional phase shift such that if one
photon is present, no phase shift arises, but if two photons are present,
the state achieves the phase shift of . Most recently such a gate [3]
was realized in our group using only one beamsplitter.

[1] S.Gasparoni, J.-W.Pan, P.Walther, T.Rudolph, A.Zeilinger, Realization
of a Photonic CNOT Gate sufficient for Quantum Computation, accepted
for publication in Phys. Rev. Lett.

[2] P.Walther, J.-W.Pan, M.Aspelmeyer, R.Ursin, S.Gasparoni, A.Zeilinger,
De Broglie Wavelength of a Nonlocal Four-Photon state, Nature (in press)

[3] K.Sanaka, T.Jennewein, J.-W.Pan, K.Resch, A.Zeilinger, Experimental
Nonlinear Sign Shift for Linear Optics Quantum Computation, Phys. Rev.
Lett. 92, 017902 (2004)

*Highly efficient frequency conversion in double lambda systems without
maximal atomic coherence*

by

**Arlene D. Wilson-Gordon**, Bar-Ilan
University, Israel

Coauthors: Hagay Shpaisman (Bar-Ilan University), Harry Friedmann (Bar-Ilan
University)

The irrelevance of phase matching in obtaining efficient four-wave
mixing (FWM) in various systems has recently been stressed. For example,
it has been demonstrated that efficient frequency conversion can be
achieved in a double lambda system within the coherence length, by establishing
electromagnetically induced transparency (EIT), via maximal Raman coherence.
We have re-examined this claim and found that the propagation distance
for efficient conversion can also be shortened by increasing the intensity
of the generating beams. We have therefore implemented an alternative
scheme, based on the transverse intensity profile control of the parametrically
interacting fields by means of ordinary (one-photon) or Raman self-focusing
and cross-focusing. We find that in the presence of such focusing, the
on-axis intensity of the generated field is much higher than in the
absence of focusing, provided the two-photon coherence is not maximal.
Our results clearly indicate that saturation can replace EIT for avoiding
losses by absorption, and that the implementation of sufficiently intense
applied fields is a sufficient condition for making phase matching irrelevant
and for obtaining efficient frequency conversion within the coherence
length.

* Feedback Control of Open Quantum Systems with
Linear Dynamics: Recent Results*
by

**Howard Wiseman**, Griffith University

Coauthors: Andrew Doherty

Quantum feedback control is the control of the dynamics of a quantum
system by feeding back (in real time) the results of monitoring that
system. For systems with linear dynamics, the control problem is amenable
to exact analysis. In these cases, the quantum system is equivalent
to a stochastic system of classical phase-space variables with linear
drift and constant diffusion, and with a measured current (e.g. a homodyne
photocurrent) linear in the system variables. However, the classical
evolution is constrained in order to represent valid quantum evolution.
We quantify this in terms of a linear matrix inequality (LMI) relating
the drift and diffusion (a sort of zero temperature fluctuation-dissipation
theorem), and another LMI for the covariance matrix of the possible
conditioned states (i.e. under all possible monitoring schemes consistent
with the master equation). For manipulable systems (i.e. where the experimenter
has arbitrary control over the parameters in a Hamiltonian linear in
the system variables) the covariance of the conditioned state is all
that is needed to calculate the effectiveness of the feedback. In this
case the double optimization problem reduces to a semidefinite program,
which can be solved efficiently in general. We illustrate this with
an example drawn from quantum optics.

*Non-Markovian Effect and Control of Quantum
Information*

by

**Chikako Uchiyama**, University of Yamanashi

Coauthors: Masaki Aihara (Nara Institute of Science and Technology)

It is known that the "bang-bang" method is effective to suppress
the decoherence caused by the interaction between qubit and environment.
Conventionally, the degree of suppression is discussed in the limit
of extremely short pulse interval. Since this condition is difficult
to execute in experimental settings, we will propose a strategy where
the condition for the pulse interval can be released by paying attention
to the dynamical behavior of the environment. We find that the coherence
can be periodically recovered by synchronizing pulse interval with the
dynamical motion of the reservoir. This is because that the non-Markovian
property of the system (memory effect of environment) is the physical
background of the suppression of decoherence by synchronized multipulse
application. We will show that we can extend this strategy to control
disentanglement.