FOR RESEARCH IN MATHEMATICAL SCIENCES
Quantum Information Seminars
held at the Fields Institute , 3rd Floor Stewart Library
by Hoda Hossein-Nejad, Yasaman Soudagar
Quantum Information Seminar - QUINF - is held roughly
every two weeks to discuss ongoing work and ideas about
quantum computation, cryptography, teleportation, et cetera.
We hope to bring together interested parties from a variety
of different backgrounds, including math, computer science,
physics, chemistry, and engineering, to share ideas as
well as open questions.
June 29, 2012
Revzen (Technion - Israel Institute of Technology)
Classical and Quantum State Reconstruction
Computer assisted tomography (CAT scan) technique for reconstruction
of material density, \rho(x,y), is compared with reconstruction
scheme for physical state- the phase space density, \rho(q,p)
of our classical system and the Wigner function for the quantum
one. All require the inversion of the Radon transform. A purely
approach based on mutual unbiased bases (MUB) by-passes the
Radon transform is also given.
The talk includes accounts of all concepts: State Reconstruction,
CAT scan tomography, Wigner function, and MUB and should be
palatable to graduate physics students.
Monday June 4, 2012 11:10AM
Room MP 606,
60 St. George Street, Toronto
non-standard date and time
Holger Hofmann (University of Hiroshima)
Weak measurements and quasi-realities: explaining the paradoxical
statistics of quantum systems
I point out that the complex-valued quantum statistics observed
in weak measurements may be understood as the quantum limit
of classical causality. In this limit, the quantum of action
defines a measure of logical tension between different measurement
contexts that might explain what Bohr meant when he claimed
that there is no quantum reality. It is then possible to explain
the strangeness of quantum effects as a new fundamental relation
between alternative measurement contexts.
[References: NJP 13, 103009 (2011) and NJP 14, 043031 (2012)]
May 18, 2012 11:10AM
Dominic Berry (Macquarie University, Australia)
Universality of the Heisenberg limit / Simulation using
This is a talk in two parts. In the first part I discuss recent
work challenging the Heisenberg limit, and present our results
showing that the Heisenberg limit is universal, provided one
takes into account lack of initial knowledge of the phase.
In the second part I present an approach to simulate Hamiltonian
evolution by using a Szegedy quantum walk. This provides an
improvement in efficiency that seems to be impossible using
a standard Trotter-Suzuki approach.
May 3, 2012
John Rarity (University of Bristol)
Can we make solid state quantum networks
The secure exchanging of cryptographic keys over fibre 
or free space  is now approaching a commercial reality
through advanced quantum cryptography systems. One key limitation
to all present quantum key distribution systems is the finite
range of a single quantum link and the inability to amplify
the fading signal by classical means. The quantum repeater
 has been suggested as a possible solution to this exponential
decrease of bit rate with distance. Ideal repeater schemes
extend the distance using "entanglement swapping"
and "teleportation" and by concatenating short entanglement
swapping sub-sections it is in principle possible to generate
entangled (correlated) bits over very long distances with
bit rate only limited by the losses in one short section.
If realised this would extend quantum key distribution out
to distances of thousands of kilometres. Each sub-section
is linked to the next by an optical circuit which performs
a 'Bell' measurement between photons arriving from each direction.
Proof of principle experiments  carried out to date have
been limited to using quantum interference effects at a beamsplitter
to perform a limited Bell measurement with 25% success rate
when photons arrive simultaneously at the beamsplitter. These
quantum 'relays' are extremely inefficient and cannot extend
the range in practical system.
May 4, 2012
Seth Lloyd (MIT)
Optimizing quantum transport
Photosynthetic systems have attained a high degree of efficiency
in transporting energy. This talk shows how this high efficiency
arises from a sophisticated interplay between quantum
coherence and decoherence. Too little quantum coherence or
too much leads to low efficiency, but at just the right level
of quantum coherence, energy transport becomes highly efficient,
a phenomenon called the `quantum Goldilocks effect.' I present
a simple theory of how biological systems optimize quantum
transport, and show how we can emulate photosynthesis to optimize
quantum transport in man- and woman-made systems.
Apr 20, 2012
Patrick Hayden (McGill University)
Towards the fast scrambling conjecture
The theory of quantum error correction has focused attention
on the relationship between the relaxation timescales of black
holes and their information retention time. Motivated by the
consistency of black hole complementarity, Sekino and Susskind
have conjectured that no physical system can delocalize, or
"scramble", its internal degrees of freedom in time
faster than (1/T) log S, where T is temperature and S the
system's entropy. By considering a number of toy examples
and general Lieb-Robinson-type causality bounds, I'll explore
the range of validity of the conjecture. Specific toy examples
suggest that logarithmic-time information scrambling is indeed
possible, while the adaptation of causality arguments to nonlocal
Hamiltonians excludes faster scrambling under quite general
hypotheses. (Joint work with Nima Lashkari, Douglas Stanford,
Matthew Hastings and Tobias Osborne.)
Feb 17, 2012
Mackillo (Mack) Kira (Philipps-University, Germany)
Quantum mechanics inevitably implies that only a wave-function
measurement can provide the ultimate control over matter.
At the same time, the ascent of nanotechnology will eventually
depend on whether or not one can control the wave function
of interacting many-body systems. Yet, it seem nearly impossible
to realize such a "quantum-state tomography" for
interacting many-body systems.
I will overview the latest development in this field and explain
how many-body theory and quantum optics  can be systematically
combined to produce a new level of laser spectroscopy. In
particular, I will show why the light-matter interaction has
an inherent capability to directly excite targeted many-body
states through light source's
quantum-optical fluctuations. This leads to a precise excitation
and characterization of desired many-body states, as the first
steps toward the many-body quantum-state tomography.
To characterize the quantum-optical response experimentally,
one simply needs to collect a massive set of optical responses
 to classical laser excitations. The quantum-optical responses
can be projected from the classical data set by applying the
so-called cluster-expansion transformation  (CET). As a
proof of principle, I will analyze quantum-well measurements
by CET projecting their
quantum-optical absorption to Schr¨odinger's cat-state
sources. The results expose a completely new level of many-body
physics that remains otherwise hidden.
 M. Kira and S.W. Koch, Semiconductor quantum optics, (Cambridge
University Press, 2011).
 M. Kira and S.W. Koch, Phys. Rev. A 73, 013813 (2006);
S.W. Koch, M. Kira, G. Khitrova, and H.M. Gibbs, Nature Mat.
5, 523 (2006); M. Kira and S.W. Koch, Prog. Quantum Electr.
30, 155 (2006).
 R.P. Smith, J.K. Wahlstrand, A.C. Funk, R.P. Mirin, S.T.
Cundiff, J.T. Steiner, M. Schafer, M. Kira, and S.W. Koch,
Extraction of many-body configurations from nonlinear absorption
in semiconductor quantum wells, Phys. Rev. Lett. 104, 247401
 M. Kira and S.W. Koch, Cluster-expansion representation
in quantum optics, Phys. Rev. A 78, 022102 (2008).
 M. Kira, S.W. Koch, R.P. Smith, A.E. Hunter, and S.T.
Cundiff, Quantum spectroscopy with Schr¨odinger-cat states,
Nature Physics 7, 799-804 (2011).
Stefan Trotzky, University of Toronto
Creating, Manipulating and Detecting Entangled Spin Pairs
in Optical Superlattices
Over the past decade, ultracold atoms in optical lattices
have proven to provide versatile grounds for the study of
fundamental condensed matter phenomena. The ever increasing
number of detection and manipulation methods together with
the variety of accessible lattice geometries allows one to
gain deep insight into ground state properties, excitations
and dynamics of interacting many-body systems. On the other
hand, these systems can be seen as arrays of "micro-laboratories"
in which few atoms can be controlled in a highly parallel
February 3, 2012
Keith Lee, University of Pittsburgh
Quantum Algorithms for Quantum Field Theories
Quantum field theory provides the framework for the Standard
Model of particle physics and plays a key role in many areas
of physics. However, calculations are generally computationally
complex and limited to weak interaction strengths. I shall
describe a polynomial-time algorithm for computing, on a quantum
computer, relativistic scattering amplitudes in massive scalar
theories. The quantum algorithm applies at both weak and strong
coupling, achieving exponential speedup over known classical
methods at high precision or strong coupling. The study of
such quantum algorithms may also help us learn more about
the nature and foundations of quantum field theory itself.
Jan 27, 2012
* Please note the non-standard time
T.C. Ralph, Centre for Quantum Computation and Communication
Technology, University of Queensland.
Advances in Optical Quantum Computing
We will discuss some new ideas and new experiments in optical
quantum computing. In particular, we will present a new experiment
in which a small scale quantum computer calculates the eigenvalues
of an unknown matrix for the first time. Such an operation
has direct relevance to Shor's factoring algorithm. We will
also discuss the Boson Sampling problem, a classically hard
problem, that, in principle, can be emulated efficiently by
a simple optical quantum computer. We will examine the effect
of errors on this problem.
David Gosset, Formerly MIT
Quantum Money from Knots
Quantum money is the idea of using quantum states as currency.
The first proposal for a quantum money scheme was developed
by Wiesner and in that scheme the quantum states used as bills
are unforgeable due to the no-cloning theorem. However, Wiesner's
scheme requires communication with the bank each time a bill
In this talk I will discuss a quantum money scheme where
bills can be spent without communicating with the bank (a
public key quantum money scheme). Our scheme uses the mathematical
theory of knots. This talk is based on joint work with Edward
Farhi, Avinatan Hassidim, Andrew Lutomirski, and Peter Shor.
|Dec 02, 2011
Muller Perimeter Institute
Undecidability in quantum measurements
A famous result by Alan Turing dating back to 1936 is that a
general algorithm solving the halting problem on a Turing machine
for all possible inputs and programs cannot exist - the halting
problem is undecidable. Formally, an undecidable problem is
a decision problem for which one cannot construct a single algorithm
that will always provide a correct answer in finite time. In
the talk, I show that the problem to determine whether sequentially
used identical measurement devices have outcomes that never
occur is undecidable. This is already true for Stern-Gerlach-type
measurement devices with 9 outcomes. This result shows that
even very natural, apparently simple problems in quantum measurement
theory can be provably undecidable. In contrast, the corresponding
classical problem is decidable, by a reduction to a finite binary
semi group problem.
This is a joint work with Jens Eisert, Christian Gogolin, and
|Nov 25, 2011
Abasto, University of Southern California
"Fidelity Approach to Quantum Phase Transitions"
Over the last 15 years a fruitful collaboration between techniques
and concepts from Quantum Information and Condensed Matter Physics
gave rise to ideas such as Density Matrix Renormalization Group
(DMRG), Topological Entanglement Entropy, Projected Entangled
Pair States (PEPs) and MERA. My talk will focus on one particular
area of interplay between Condensed Matter and Quantum Information,
which has been called Fidelity Approach to Quantum Phase Transitions
(QPTs). Distinguishing between two quantum states is at the
core of many quantum information processing tasks. The fidelity
quantifies such degree of distinguishability and it provides
a useful information-theoretic framework that encompasses all
In this talk I will focus on its applicability to study QPTs
involving topological phases, and describe its advantages
and limitations. Time permitting I will also mention my joint
work with Masoud Mohseni and Seth Lloyd on Quantum Biology.
*Please note the non-standard date and time
Hari Manoharan Stanford University
Supersymmetric Quantum Nanostructures
Embedded into the topology of our universe lurks a subtle yet
far-reaching spectral ambiguity. There exist drum-like manifolds
of different shape that resonate at identical frequencies, making
it impossible to invert a measured spectrum of excitations into
a unique physical reality. An ongoing mathematical quest has
recently compacted this conundrum from higher dimensions to
planar geometries. Inspired by these isospectral domains, we
introduce a class of quantum nanostructures characterized by
matching electronic structure but divergent physical structure.
We perform quantum measurements (scanning tunneling spectroscopy)
on these quantum drums (degenerate two-dimensional
electrons confined by individually positioned molecules) to
reveal that isospectrality provides an extra topological degree
of freedom enabling the mapping of complete electron wavefunctionsincluding
all internal quantum phase information normally obscured by
direct quantum measurement.
The robustness of the technique stems from its connection
to supersymmetric quantum mechanics, where inequivalent superpartner
Hamiltonians produce equivalent energy spectra. The methods
are general and extensible to other nanostructures and fabrication
techniques, and we have recently used variants of these ideas
to experimentally detect superposition phase and the Berry
In these experiments we utilize the exciting technology of
atomic and molecular manipulation: a custom-built scanning
tunneling microscope, operating at low temperature in ultrahigh
vacuum, is used to assemble nanostructures atom-by-atom to
generate versatile quantum laboratories at the spatial limit
of condensed matter.
|Nov 11, 2011
Robert Spekkens Perimeter Institute
Formulating Quantum Theory as a Causally Neutral Theory
of Bayesian Inference
Quantum theory can be thought of as a noncommutative generalization
of Bayesian probability theory, but for the analogy to be
convincing, it should be possible to describe inferences among
quantum systems in a manner that is independent of the causal
relationship between those systems. In particular, it should
be possible to unify the treatment of two kinds of inferences:
(i) from beliefs about one system to beliefs about another,
for instance, in the Einstein-Podolsky-Rosen or "quantum
steering" phenomenon, and (ii) from beliefs about a system
at one time to beliefs about that same system at another time,
for instance, in predictions or retrodictions about a system
undergoing dynamical evolution. I will present a formalism
that achieves such a unification by making use of "conditional
quantum states", a noncommutative generalization of conditional
probabilities. Elements of the conventional formalism, such
as sets of states, positive operator valued measures, quantum
operations and quantum instruments become special cases of
conditional states, and familiar formulas, such as Born's
rule, the expression for the ensemble average, the rule for
dynamical evolution, and the nonselective measurement-update
rule become special cases of belief propagation. (Joint work
with Matthew Leifer)
Nov 4, 2011
Hector Bombin, Perimeter Institute
By characterizing 2D topological stabilizer codes in terms
of 'lattice groups' on infinite lattices, we show that they
can all be characterized in terms of topological charges and
string operators. This is true either for subspace or subsystem
codes, and it has direct applications for error correction,
for example. Subspace codes are directly connected to topologically
ordered condensed matter systems, and we show that all 2D
topological stabilizer codes are locally equivalent to several
copies of one universal phase: Kitaev's topological code.
|Oct 28, 2011
University of Pittsburgh
Superfluid Phase Transition of Long-Lifetime Polaritons
Polaritons are quasiparticles of electronic excitation in
semiconductor structures with extremely light mass, about four
orders of magnitude less than a free electron. Because of this
very light mass, polaritons show Bose quantum effects even at
moderate densities and temperatures from tens of Kelvin up to
room temperature. In the past five years, multiple experiments
have shown effects of polaritons analogous to Bose condensation
of cold atoms, such as a bimodal momentum distribution, quantized
vortices, Bogoliubov excitation spectrum, and spatial condensation
in a trap. In these experiments, though, the lifetime of the
polaritons has been just a little longer than their thermalization
time, which means that nonequilibrium effects play an important
role; in particular, the transition to superfluidity has been
smeared out rather than a sharp transition. In this talk I report
new results with polaritons that have very long lifetime compared
to their thermalization time. We see a discontinuous jump in
the properties of the polariton gas indicative of a true phase
transition, and we see ballistic transport over hundreds of
Oct 21, 2011
Daniel Gottesman, Perimeter Institute
Improving Telescopes With Quantum Repeaters
Interferometry among telescope arrays has become a standard
technique in astronomy, allowing greater resolving power than
would be available to any plausibly-sized single telescope.
For radio frequencies, interferometry can be performed robustly
even between telescopes spread across the planet. Interferometry
between telescopes operating at infrared or optical frequencies
is also possible, but fewer photons arrive at these high frequencies,
making interferometry much more difficult. In today's IR and
optical interferometric arrays, photons arriving at different
telescopes must be physically brought together for the interference
measurement, limiting baselines to a few hundred meters at
most because of phase fluctuations and photon loss in the
transmission. I will discuss how to apply quantum repeaters
to the task of optical and infrared interferometry to allow
telescope arrays with much longer baselines than existing
|Oct 7, 2011
Daniel Turner, University of Toronto
Measuring Quantum Coherence in Molecules, Semiconductors,
and Proteins using 2D Electronic Spectroscopy
Recent studies using 2D electronic spectroscopy have suggested
that electronic coherence is maintained in light-harvesting
proteins for an exceptionally long time, hundreds of femtoseconds
at physiological temperatures. This leads to speculations
about the presence of quantum-mechanical effects such as entanglement.
However, the experiment can also excite vibrational wavepackets,
whose signatures are almost identical to electronic coherences.
Here we examine how electronic and vibrational coherences
can be distinguished by careful
investigation of the cross peak oscillations in several different
samples. Our conclusion is that both electronic and vibrational
coherences are present in the light-harvesting protein we
|Sept 20, 2011
Man-Duen Choi, University of Toronto
Positive Linear Maps through Quantum Computers
What on earth does it mean as a REAL quantum computer? We
seek the ways to go through the maze of quantum entanglements,
in the light of the very easy structure of positive linear
maps on matrix algebras.
This is an expository talk, in simple language of linear
algebra, to show some deep aspects of the quantum foundation.
|Aug 26, 2011
Peter Turner, University of Tokyo
The generation of indistinguishable multipartite states of
quantum systems is an important topic -- such states are manifest
in all experiments exhibiting quantum interference, and are
the basis for many implementations of quantum information
processors. So far, experiments have been limited to few bosons
-- here we investigate the question of how to test and/or
characterise the indistinguishability of many. We adopt a
particle picture for describing multipartite states of N identical
bosons. A distinction must be drawn between 'practical' indistinguishability
imposed by real detectors that are only sensitive to a subset
of the ostensibly complete set of degrees of freedom attributable
to each particle, and 'complete'
indistinguishability where those inaccessible degrees of freedom
are all in the same state. We show that these pictures are
compatible, in that they give rise to the same number of experimentally
accessible measurement outcomes. We will discuss several implications,
such as that informationally complete tomography in a practically
indistinguishable situation does not require exponentially
many measurements, as would be true in the completely distinguishable
The hope is to generate a stimulating informal discussion
about the topic of multipartite indistinguishability and how
it can be understood.
|Aug 19, 2011
Andrew White, University of Queensland
Quantum biology, chemistry, maths and physics
In principle, we can use quantum mechanics to exactly describe
any system of quantum particles - from simple molecules to
unwieldy proteins (and beyond, see figure) - but in practice
this is impossible as the number of equations grows exponentially
with the number of particles. Recognising this, Richard Feynman
suggested that quantum systems be used to model quantum problems
. For example, the fundamental problem faced in quantum
chemistry is the calculation of molecular properties, which
are of practical importance in fields ranging from materials
science to biochemistry. Within chemical precision, the total
energy of a molecule as well as most other properties, can
be calculated by solving the Schrödinger equation. However,
the computational resources required increase exponentially
with the number of atoms involved [1, 2].
In the late 1990's an efficient algorithm was proposed to
enable a quantum processor to calculate molecular energies
using resources that increase only polynomially in the molecular
size [2-4]. Despite the many different physical architectures
that have been explored experimentally since that time - including
ions, atoms, superconducting circuits, and photons - this
appealing algorithm was not demonstrated until last year.
I will discuss how we have taken advantage of recent advances
in photonic quantum computing  to present an optical implementation
of the smallest quantum chemistry problem: obtaining the energies
of H2, the hydrogen molecule, in a minimal basis . We perform
a key algorithmic step - the iterative phase estimation algorithm
[7-10] - in full, achieving a high level of precision and
robustness to error.
I'll also report on our recent results in simulating quantum
systems in material science - phase transitions in topological
insulators - and in biology - light-harvesting molecules in
photosynthesis. Together this body of work represents early
experimental progress towards the long term goal of exploiting
quantum information to speed up calculations in biology, chemistry
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