### Abstracts

Monday August 10

**Robin Blume-Kohout**

Perimeter Institute

*"Tomography: What is it good for?"*

State tomography is a basic primitive in experimental quantum information
processing. You prepare a bunch of systems in the same way, measure
them, and estimate a state (density matrix) from the results. There
is an ongoing debate about the "best" way to infer a density
matrix from data. The only way to resolve this confusion is to figure
out exactly what task[s] we are trying to accomplish -- which in
turn determines an operational metric of success, which we can use
to conclusively rank different state estimation procedures. In this
talk, I'll show why several common tasks don't actually require
state estimation, then argue that data compression is a suitable
paradigmatic task. I'll conclude by exploring the consequences of
this choice, and showing that it implies (among other things) a
radically new conception of state estimation.

A.M. Steinberg, R.B.A. Adamson, and L.K. Shalm

Centre for Quantum Information & Quantum Control and Institute
for Optical Sciences

Department of Physics, University of Toronto

Measuring Quantum States in the Presence of Fundamental Symmetries

Quantum State Tomography is the science (and sometimes art) of
measuring a quantum state. In this talk, I will discuss some of
our recent work on characterizing the state of 2- and 3-photon systems,
and the broader implications for tomography of multi-dimensional
quantum systems.

Typical approaches to quantum tomography are all, to a greater
or lesser extent, brute force attempts to measure enough data to
be able to extract a density matrix from or fit one to observations.
I will argue that these approaches neglect the underlying symmetries
of the state space, in ways that come at a cost.

In particular, I will present our theoretical and experimental
work on the characterization of states of "partially distinguishable"
photons, and Wigner-function tomography of multi-photon states on
the Poincaré sphere.matrix. I will present our experimental
results on squeezing and oversqueezing of the triphoton, and tomographical
reconstructions of the resulting Wigner function.

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**Peter Turner**

University of Tokyo

*Comparison of maximum-likelihood and linear reconstruction
schemes in*

quantum measurement tomography

The effects on quantum states caused by measurement apparatuses
can be described in general by sets of completely positive maps
called instruments. There exists a linear reconstruction scheme
for the instrument describing a given measurement apparatus from
experimental data, but the scheme has the disadvantage that it can
give unphysical reconstructions. In this poster we propose a maximum-likelihood
reconstruction scheme that addresses this disadvantage. We show
that our scheme always gives a physical reconstruction, and that
it does so more efficiently than the linear scheme.

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**Colm Ryan**

Institute for Quantum Computing

*Randomized benchmarking in liquid-state NMR.*

Being able to quantify the level of coherent control in a proposed
device implementing a quantum information processor (QIP) is an
important task for both comparing different devices and assessing
a device's prospects with regards to achieving fault-tolerant quantum
control. I will review the motivation behind randomized benchmarking
as a solution to this problem. I will show results from our experiments
in a liquid-state nuclear magnetic resonance QIP using the randomized
benchmarking protocol presented by Knill et al (PRA 77: 012307 (2008)).
We report an error per randomized p/2 pulse of (1.3±0.1)10-4
with a single qubit QIP and with a generalization to multiple qubits
an average error rate for one and two qubit gates of (4.7±0.3)10-3.
We estimate that these error rates are still not decoherence limited
and thus can be improved with modifications to the control hardware
and software. I will show where this fits with other recent results
from other implementations where randomized benchmarking error rates
have also been measured.

----------------------------------------------------------------------

**David Cory**

MIT

*Efficient and Robust Decoupling*

I will outline the challenges of using decoupling to remove interactions
with an environment, show a variety of approaches from magnetic
resonance and introduce a new approach that is robust to the expected
experimental errors.

###

Tuesday August 11

**John Holbrook**

University of Guelph

*Introduction to Numerical Ranges*

We survey some of the properties and applications of the classical
numerical range of a matrix. We make connections with the higher-rank
numerical ranges recently studied in the context of quantum error
correction.

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**Marcus Silva**

Université de Sherbrooke

*Numeric ranges and minimal fidelity guarantees in the physical
realization of unitaries *

In some physical realizations of quantum information devices it
is highly advantageous to consider the implementation of more complex
unitaries through continuously varying Hamiltonians, instead of
decomposition such unitaries in terms of a discrete gate set. The
control parameters of such Hamiltonians are determined by numerical
search, where a particular evolution is compared against the desired
unitary by considering the fidelity of their outputs, averaged over
a uniform distrubution of all input states. In principle this can
be improved upon by looking at the minimal fidelity between the
outputs of the two unitaries. Casting this problem in terms of numeric
ranges, we demonstrate that the minimum fidelity between two unitaries
has a simple geometric interpretation, and that it can be readily
computed. We conclude by discussing some of the obstacles in generalizing
this approach to the comparison between general quantum maps and
unitaries.

[Work done in collaboration with C. Ryan (U.Waterloo), M. Laforest
(T. U. Delft) and D. W. Kribs (U. Guelph)]

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**Yiu Tung Poon**

Iowa State University

*Generalized numerical ranges and quantum error correction*

In this talk, geometric properties of the joint higher rank numerical
ranges are obtained and their implications to quantum computing
are discussed. It is shown that if the dimension of the underlying
Hilbert space of the quantum states is sufficiently large, the joint
higher rank numerical range of operators is always star-shaped and
contains a non empty convex subset. In case the operators are infinite
dimensional, the joint infinite rank numerical range of the operators
is a convex set lying in the core of all joint higher rank numerical
ranges, and is closely related to the joint essential numerical
ranges of the operators. In addition, equivalent formulations of
the join infinite rank numerical range are obtained. As by products,
previous results on essential numerical range of operators are extended.

------------------------------------------------------------------------

**Cedric Beny**

National University of Singapore

*Inverting a channel with near-optimal worst-case entanglement
fidelity*

Avoiding decoherence is the major challenge of any quantum information
experiment. Here we consider the possibility of reversing the effect
of the noise on a subspace (code) after it happened. Exactly correctable
codes are characterized by the Knill-Laflamme conditions. It was
shown however that good codes exist which cannot be found under
the assumption of exact correctability. Here we give necessary and
sufficient conditions for a code, or a subsystem code, to be approximately
correctable in terms of the worst-case entanglement fidelity of
the noise channel. We also show how to build a family of near-optimal
recovery channels.

Wednesday August 12

**Man-Duen Choi**

University of Toronto

*Hard results of the soft mathematics in quantum information*

The beautiful setting of completely positive linear maps serves
the most vivid description of quantum information. Here, we look
into some profound natures of the simple structure of completely
positive linear maps on matrix algebras.

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**Chi-Kwong Li**

College of William and Mary

*Completely positive linear maps, unitary orbits, and quantum
operations*

We will some recent results on completely positive linear maps
and unitary orbits in connection to the study of quantum operations.

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**Claudio Altafini**

SISSA-ISAS International School for Advanced Studies

*Feedback schemes for radiation damping suppression in NMR:
a control-theoretical perspective*

In NMR spectroscopy, the collective measurement is weakly invasive
and its back-action is called radiation damping. The aim of this
study is to provide a control-theoretical analysis of the problem
of suppressing this radiation damping. It is shown that two of the
feedback schemes commonly used in the NMR practice correspond one
to a high gain oputput feedback and the other to a 2-degree of freedom
control design with a prefeedback that exactly cancels the radiation
damping field. A general high gain feedback stabilization design
not requiring the knowledge of the radiation damping time constant
is also investigated.

### Thursday August 13

**Thomas Schulte-Herbruggen**

Technical University of Munich, Germany

*Matching Lie and Markov properties in open quantum systems*

On a general scale, Markovian quantum channels can be defined by
their Lie-semigroup properties [1] with the GKS-Lindblad generators
as Lie wedge or tangent cone. These differential properties provide
powerful tools not only when addressing reachability and controllability,
but also for deciding whether effective Liouvillians are physical
or whether time-dependent Markovian channels simplify to time-independent
ones [1].

Applications of optimal control of Markovian and non-Markovian
open quantum systems are shown for realistic examples: they typically
cut errors by one order of magnitude [2,3]. These dramatic improvements
come at the cost of algorithms that in open systems [1,2,3] are
far more intricate than in closed ones [4]. -- Implications in view
of quantum CISC-compilation [5] for large systems (with say 100
qubits) are given.

Finally we sketch new controllability criteria based on absence
of dynamic symmetries [6].

This work contains collaborations mainly with Gunther Dirr, Indra
Kurniawan, and Uwe Helmke from the Institute of Mathematics, University
of Wuerzburg, Germany.

References:

[1] Dirr, Helmke, Kurniawan, Schulte-Herbrueggen, arXiv:0811.3906,
to appear in Rep. Math. Phys. (2009)

[2] Schulte-Herbrueggen, Spoerl, Khaneja, Glaser, quant-ph/0609037

[3] Rebentrost, Serban, Schulte-Herbrueggen, Wilhelm, Phys. Rev.
Lett. 102, 090401 (2009)

[4] Schulte-Herbrueggen, Glaser, Dirr, Helmke, arXiv:0802.4195

[5] Schulte-Herbrueggen, Spoerl, Glaser, arXiv:0712.3227

[6] Sander, Schulte-Herbrueggen, arXiv:0904.4654

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**Masoud Mohseni**

MIT

*Environment-Assisted Quantum Processes*

In this talk, we discuss how decoherence can be helpful in guiding
an open system to a particular target quantum operation/process.
We first develop a general approach for monitoring and controlling
evolution of open quantum systems by introducing a dynamical equation
for the evolution of the process matrix operating on the system.
This equation is applicable to non-Markovian and/or strong coupling
regimes. We show how one can identify quantum Hamiltonian systems
via partial tomography/estimation, and discuss its efficiency and
limitations for certain classes of sparse Hamiltonians. Additionally,
we introduce a novel optimal control setting in order to drive quantum
dynamics of Hamiltonian systems to a desired target process matrix,
specifically to suppress or manipulate decoherence.

In the second part of this talk, we present certain examples of
how environmental-induced dynamics can in fact enhance quantum transport
(e.g., energy transfer) in biological and nano-scale systems via
an effective interplay of free Hamiltonian and dynamical decoherence.
Finally, we discuss how one may develop similar techniques for performing
quantum information processing with experimentally available open
quantum systems.

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**Bei-Lok Hu**

University of Maryland

*Entanglement Dynamics between Two Qubits in a Quantum Field:
Birth, Death and Revivals*

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