Abstracts
Optical implementation of a POVM measurement
for photonic cluster-state quantum computing
by
Devon N. Biggerstaff
Institute for Quantum Computing
Coauthors: Terry Rudolph, Nathan Killoran, Rainer Kaltenbaek, Deny
Hamel, and Kevin J. Resch
The one-way or cluster-state model has shown promise as an alternative
to the quantum circuit model for quantum computing with photons.
However, experimental implementations are currently limited by the
difficulty of generating many entangled photons. Recent theory has
shown that 'virtual qubits' may be added to a given graph by replacing
one or more projective measurements on the cluster with a POVM.
We experimentally demonstrate the ability to perform a three-qubit
cluster computation using only two entangled photons and a linear-optical
POVM. A three-qubit cluster is sufficient to prepare arbitrary qubit
states; by spatially separating the two photons we achieve the first
deterministic Remote State Preparation (RSP) of arbitrary polarization
qubits. Our results feature an an achieved mean RSP fidelity of
0.9832 +/- 0.0002 for several hundred pure states spread over the
Bloch sphere, as well as the ability to remotely prepare mixed states,
and the clear violation of thresholds limiting the RSP fidelity
achievable without entanglement.
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Zero discord
by
Aharon Brodutch
Macquarie University
Coauthors: Daniel Terno
The non local nature of quantum mechanics allows for stronger correlations
between two distant parties then those of the classical world. Entanglement
is the strongest manifestation of these quantum correlations but
it seems that non locality can exist without any entanglement. A
possible measure for the "quantumness of correlations"
is the discord [1,2]. Zero discord which implies no quantum correlations
is a rare property of mixed quantum states. Those states which exhibit
zero discord are important in measurement theory and in evolution
of the subsystems. We will look at some of the properties of zero
discord states and show that in most cases there is an efficient
way to verify zero discord.
[1] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of
the Quantumness of Correla-tions, Physical Review Letters 88 (2002),
[2] L. Henderson and V. Vedral, Classical, quantum and total correlations,
Journal of Physics A Mathematical General 34 (2001)
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A Quantum Algorithm for Approximating Partition
Functions
by
Chen-Fu Chiang
University of Central Florida
Coauthors: Pawel Wocjan (University of Central Florida) Daniel Nagaj
(Slovak Academy of Sciences) Anura Abeyesinghe
We present a quantum algorithm based on classical fully polynomial
randomized approximation schemes (FPRAS) for estimating partition
functions that combine simulated annealing with the Monte-Carlo
Markov Chain method and use non-adaptive cooling schedules. We achieve
a twofold polynomial improvement in time complexity: a quadratic
reduction with respect to the spectral gap of the underlying Markov
chains and a quadratic reduction with respect to the parameter characterizing
the desired accuracy of the estimate output by the FPRAS. Both reductions
are intimately related and cannot be achieved separately.
First, we use Grover's xed point search, quantum walks and phase
estimation to efficiently prepare approximate coherent encodings
of stationary distributions of the Markov chains. The speed-up we
obtain in this way is due to the quadratic relation between the
spectral and phase gaps of classical and quantum walks. The second
speed-up with respect to accuracy comes from generalized quantum
counting, used instead of classical sampling to estimate expected
values of quantum observables.
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The Geometry of Anticoherent Spin States
by
Jason Crann
University of Guelph
Coauthors: Rajesh Pereira
Coherent states have been of interest since their discovery by
Schrödinger in the 1920’s, being the most “classical”
of all quantum states. In quantum information theory, one is often
interested in states that display purely quantum phenomena, such
as entanglement. To this end we discuss “anticoherent”
spin states, those which do not mimic any classical behaviour. Using
the Majorana representation we associate spin states with collections
of points on the unit sphere. This beautifully illustrates the geometry
of anticoherent states, which appear in very symmetrical configurations.
These symmetries not only give an intriguing look into the most
“quantum” spin states, they warrant the application to
quantum information theory. We provide a wealth of new examples
by relating anticoherence to spherical designs. Specifically, we
show that spherical designs which are orbits of finite subgroups
of O(3) correspond to anticoherent states. We also conjecture that
anticoherent states maximize the well known geometric measure of
entanglement, further illustrating their potential application.
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Measurement-induced entanglement localization
on a three-photon system
by
Miroslav Gavenda
Palacky University Olomouc
Coauthors: Fabio Sciarrino (Sapienza University of Rome) Eleonora
Nagali (Sapienza University of Rome) Francesco De Martini (Sapienza
University of Rome) Radim Filip (Palacky University Olomouc)
Quantum entanglement a key resource in quantum information tasks
willingly interacts with surrounding systems. Due to this interaction
the entangled system under interest couples to surrounding systems
and the amount of entanglement is reduced or even lost and cannot
serve to its application purpose. If the entanglement is completely
destroyed by the coupling, distillation protocol does not work and
other correcting protocols were suggested such as unlocking of hidden
entanglement or entanglement localization [1]. Entanglement localization
can concentrate back redistributed entanglement at least partially
from the surroundings just by measurement on the surrounding system
and proper feed-forward quantum correction. We deal with the situation
when the input state is maximally entangled state of two qubits
and another qubit serves as a surrounding system. Because the surrounding
qubit is inaccessible before the coupling it is in an unknown state.
The qubits in our case are represented by polarization states of
single photons. In this presentation we extensively study the influence
of coherence between the surrounding photon and one photon from
the entangled pair on the localization pro- tocol which is parametrized
by the probability p that the surrounding photon is indistinguishable.
After the coupling between photons, represented by transmissivity
T of the beamsplitter, the entanglement of the input state is reduced
and for some T entanglement is completely redirected to the surrounding
photon. We theoretically prove that for any linear coupling it is
possible to localize non-zero entanglement back to the pair just
by proper polarization sensitive detection of photon in surrounding
photon (after coupling the surrounding photon is accessible). After
measurement on the surrounding photon we may use additional single-copy
filtration on both photons from the pair to further raise up the
concurrence. Single-copy filtration probabilistically attenuates
one polarization relatively to an orthogonal one. Qualitatively
this localization is independent on the level of coherence between
coupling photons. The theoretical results were experimentally tested
using polarization entangled photons created in SPDC process [2].
An extension of the localization procedure was calculated for multiple
consecutive couplings to the independent surrounding photons. [1]
F. Verstraete, M. Popp and J.I. Cirac, Phys. Rev. Lett. 92, 027901
(2004) [2] Fabio Sciarrino, Eleonora Nagali, Francesco De Martini,
Miroslav Gavenda, and Radim Filip, Phys. Rev. A 79, 060304 (2009)
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The Multiplicative Domain in Quantum
Error Correction
by
Nathaniel Johnston
University of Guelph
Coauthors: Man-Duen Choi and David Kribs
Quantum error correction deals with correcting errors introduced
via quantum channels, modelled by trace-preserving completely positive
maps. Correctable codes are subsystems of the overlying Hilbert
space on which the channel has a left inverse. Given a unital completely
positive map, the multiplicative domain of that map is the largest
subalgebra on which the map acts as a *-homomorphism. We show that
for a unital quantum channel, the codes that are correctable via
conjugation by a unitary (called unitarily correctable subsystems)
are exactly that map's multiplicative domain. We also show that
if we remove the requirement that the map be unital, a weaker relationship
between the two notions still holds. Furthermore, a generalization
of the multiplicative domain can be defined that captures all correctable
codes for arbitrary channels.
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Remote state preparation: Quantum vs.
Classical
by
Nathan Killoran
IQC
Coauthors: Devon N. Biggerstaff, Rainer Kaltenbaek, Deny Hamel,
Kevin J. Resch, and Norbert Lütkenhaus
Remote state preparation is the act of preparing at one location
a state chosen at a different location, without actually transmitting
the state itself. Using a teleportation-based scheme, one can theoretically
prepare any qubit state remotely using at most two classical bits
and one entangled bit. However, since any experiment is imperfect,
the average fidelity between input and output states will not be
perfect. But how good does it have to be? In order for a remote
state preparation experiment to demonstrate genuinely quantum behaviour,
it must beat the optimal threshold of a comparable classical situation.
We examine remote state preparation protocols where only classical
bits may be used, and determine the optimal fidelity value in several
different cases, providing benchmarks for genuinely quantum behaviour.
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Decoherence Supression via environment
preparation
by
Olivier Landon-Cardinal
Universite de Montreal
Coauthors: Richard MacKenzie
Decoherence provides an elegant framework to explain why an open
quantum system coupled to its environment will exhibit a set of
preferred states, usually ruling out a coherent superposition of
arbitrary states. This framework relies essentially on the interaction
between the system and its environment. In the simplest model of
decoherence, it was readily realized that there exist initial state
of the environment that allow for decoherence-free unitary evolution
of the quantum system.
We investigate the conditions under which such special initial states
do exist in a framework where the quantum system interacts with
its environment and the environment also evolves by itself. The
results obtained underline the crucial role of the environment's
self-evolution. The ability to identify those special initial states
and to prepare them might be used in order to store quantum states.
Indeed, even if the environment cannot be controlled, it might be
possible to prepare it in a specific initial state. However, our
results restrict what can be expected from such a technique. More
precisely, we obtain a mathematical characterization for the existence
of an initial state allowing decoherence-free evolution in presence
of an interaction hamiltonian and a self-evolution of the environment.
This result is stated in terms of the structure of the two hamiltonians.
We also present topological evidences that indicate that pairs of
hamiltonians allowing for decoherence-free evolution are rare among
pairs of hamiltonians.
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Quantum walks with anyons
by
Lauri Lehman
QISS, Macquarie University, Australia
Coauthors: Gavin Brennen
Quantum walks are coherent adaptations of Markovian random walks
to quantum mechanical dynamics and they exhibit dynamics not found
in classical walks (e.g. quadratic vs. linear dispersion). In this
talk, the quantum walk scheme with anyons is introduced. Anyons
are point like particles in two dimensions which can have an arbitrary
phase under exchange in the Abelian case or a matrix valued action
on the Hilbert space of fusion outcomes in the non-Abelian case.
The non-trivial action under exchange acts as source of non-local
decoherence on the anyonic walker. Simulations and analytical results
for the walk on a disk and on an annulus are presented and the properties
of anyon walks are compared to those of Markov walks and discrete
quantum walks.
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Characterizing the Quantum Gate Fidelity
by
Easwar Magesan
University of Waterloo
Coauthors: Joseph Emerson, Robin Blume-Kohout
I will introduce the quantum gate fidelity and discuss some of
its basic properties. Much of the focus regarding the gate fidelity
has been on finding its average and minimum over the set of input
states. I will further characterize the gate fidelity by giving
some different expressions for its variance. I will also discuss
what features of the noise can be learned from this information.
A procedure for finding the variance in the case of time-dependent
noise will also be discussed.
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Quantum Key Distribution at 810 nm Through
Installed Fibre Optics
by
Meyer-Scott, Evan
University of Waterloo
Coauthors: Hannes Huebel Chris Erven Thomas Jennewein
This poster demonstrates how currently installed fibre optic cables
can be used as a medium for Quantum Key Distribution, using photons
of wavelength 810 nm. Though telecommunication fibres use photons
near 1550 nm for minimal attenuation, single photon detectors at
this wavelength are bulky and inefficient. We will show that telecom
fibre can be used for 810 nm photons, where good sources and detectors
exist. An existing free-space link at the University of Waterloo
will be transformed to operate on a 2.2 km fibre optic connection
between the University of Waterloo and the Perimeter Institute.
The system will operate a full Quantum Key Distribution protocol,
including time stamping and analysis to compensate for the dispersion
of different modes in the fibre: using coincidence analysis software,
one of the modes will be selected and used for Key Distribution.
Thus it will be shown that any existing fibre optic network is a
potential candidate for Quantum Key Distribution.
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Testing contextuality on quantum ensembles
with one clean qubit.
by
Osama Moussa
Institute for Quantum Computing
Coauthors: C. A. Ryan, D. G. Cory, R. Laflamme
We present a protocol to estimate the expectation value of the
correlations of measurement outcomes for ensembles of quantum systems,
and use it to experimentally demonstrate-under an assumption of
fair sampling-the violation of an inequality that is satisfied by
any non-contextual hidden-variables theory. The experiment is performed
on an ensemble of molecular nuclear spins in the solid state, using
established Nuclear Magnetic Resonance (NMR) techniques for quantum
information processing.
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The Geometry of The Higher-Rank Numerical
Range and its Implications in Quantum Data Error Correction
by
Nishan Mudalige
Department of Mathematics and Statistics, University of Guelph
Coauthors: Professor R. Pereira, Department of Mathematics and Statistics,
University of Guelph
For many years, the classical numerical range of an operator has
been studied extensively by mathematicians interested in the areas
of functional analysis and matrix analysis. In this talk, we will
discuss the recent discovery of the higher-rank numerical range
introduced by Choi, Kribs and Zyczkowski and we shall explore its
properties from an algebraic and geometric point of view. We will
also present ways in which it has been used to develop techniques
for quantum data error correcting codes. Emphasis will be given
to the geometry of the higher-rank numerical range.
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The geometry of Schur maps and their application
to the description of random unitary channels
by
Corey O'Meara
University of Guelph
Coauthors: Rajesh Pereira
The relationship between characteristics of quantum channels and
the geometry of their respective sets can provide a useful insight
to some of their underlying properties. The aim of this talk is
twofold; one, to introduce the notion of random unitary channels,
and two, to describe the relevance of a particular class of unital
completely positive trace preserving maps, namely the Schur maps.
Schur maps have several properties which are useful in the geometric
descriptions of the convex sets of random unitary channels and correlation
matrices. Some preliminary results concerning these areas will be
presented and future work will be discussed.
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Approximating the Jones polynomial: an
NMR experiment
by
Gina Passante
Institute for Quantum Computing
Coauthors: O. Moussa, C.A. Ryan, R. Laflamme
The class of problems efficiently solvable on quantum computers
with one bit of quantum information is known as DQC1 [1]. This model
is believed to be strictly weaker than standard quantum computers,
but still more powerful than their classical counterparts. Recently,
Shor and Jordan [2] proved that the problem of approximating the
Jones polynomial at the fifth root of unity completely encapsulates
the power of DQC1. The Jones polynomial is a knot invariant that
is not only important to knot theory, but also to statistical mechanics
and quantum field theory. We present an adaptation of the algorithm
developed by Shor and Jordan suitable for implementation on a liquid
state NMR quantum information processor, and report on the experimental
implementation of the algorithm to evaluate the Jones polynomial
for all knots whose braid representation has four strands and three
crossings.
References: [1] E. Knill and R. Laflamme. Phys. Rev. Lett., 81,
5672 (1998).
[2] P. Shor and S. Jordan. Quant. Inf. and Comm., 8, 681-714, (2008).
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Optimal Protocols for Non-locality Distillation
by
Jibran Rashid
University of Calgary
Coauthors: Peter Hoyer
We know that quantum mechanics is not optimally non-local in general.
In fact, an optimal non-local source yields a 1-bit communication
protocol. It is not known whether this is true for all stronger
than quantum non-local sources. Combining n copies of a weak non-local
source to obtain a stronger non-local source is known as "distilling"
non-locality.
I will sketch a proof that for non-adaptive n-copy distillation
protocols parity is optimal. I will also discuss several possible
approaches to generalize the proof for adaptive distillation protocols.
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Atomic phase estimation using a composite
method of adaptive feedback and multiple phase shifts
by
Ressa S. Said
Research Centre for Quantum Science & Technology (QSciTech)
and Department of Physics & Electronic Engineering, Faculty
of Science, Macquarie University
Coauthors: Dominic W. Berry and Jason Twamley
In this work we present a new method to estimate, with near Heisenberg
limited precision, an unknown dynamical phase which is acquired
by a two-level atomic spin system over a known time period. We utilise
Ramsey interferometry and combine this with adaptive feedback measurements
[1], and multiple applications of the unknown phase shift [2]. These
methods have been previously used in linear optics to estimate the
phase acquired when a photon passes through a phase-shifter. The
resulting estimation protocol proposed in this work [2], achieved
a precision close to the Heisenberg limit. In our work we adapt
this protocol to estimate the phase (rotation about the Z-axis),
experienced by a spin within a fixed, known, time duration. Since
such a phase may be generated through the spin's interaction with
a magnetic field or a local strain field, our phase estimation protocol
can be regarded as a high sensitive sensing method. We focus our
discussions on estimating the phase associated with an external
unknown, temporally constant, magnetic field and one hence could
consider our protocol as Heisenberg-limited magnetometry.
Heisenberg-limited phase estimation, which can provide the phase
estimate with the uncertainty below standard quantum limit, leads
to a better estimation precision than that of standard procedures
for a given amount of available resources. Our protocol requires
no pre-existing knowledge about the system phase, (or magnetic field
in the case of magnetometry), since the final phase estimate is
independent to the initial random guess of the phase.
In principle, the proposal can be implemented in any two-level
physical system, e.g. atomic vapours [3], or nitrogen-vacancy (NV)
centres [4]. The latter are remarkably interesting because they
can be individually addressed, optically polarised and measured,
and maintain their coherences at room temperature [5]. It has been
reported recently that electronic spins associated with NV centres
could be used for high-spatial-resolution magnetic field detection
and are predicted to possess sensitivities exceeding that of other
magnetometry methods (SQUIDs and Hall bar), by an order of magnitude
[4]. The realisation of Heisenberg-limited magnetometry in an NV-magnetometry
protocol may be feasible in the near future using our protocol and
we perform numerical simulations of this to explore the boundaries
of the ultimate precision possible using our protocol.
[1] D. W. Berry and H. M. Wiseman, Phys. Rev. A, 63, 013813 (2000).
[2] B. L. Higgins, et. al., Nature, 450, 393 (2007). [3] I. M. Savukov,
et. al., Phys. Rev. Lett., 95, 063004 (2005). [4] J. M. Taylor et.
al., Nat. Phys., 4, 810 (2008). [5] F. Jelezko and J. Wrachtrup,
J. Phys. Condens. Matter, R1089 (2004).
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Predicative Quantum Programming
by
Anya Tafliovich
University of Toronto
We will present Quantum Predicative Programming - a theory of developing
programs intended for execution on a quantum computer. It is the
most general theory of quantum programming proposed today. Our formal
framework provides a methodology to rigorously specify, implement,
and analyse quantum algorithms, the paradigm of quantum non-locality,
quantum pseudo-telepathy games, computing with mixed states, quantum
communication protocols, and quantum cryptographic protocols. Our
work takes a step beyond what formal verification traditionally
addresses, namely proofs of correctness. The framework provides
tools to formally express and verify such properties of quantum
systems, quantum algorithms and quantum protocols, as time, space,
and communication complexity.
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Frameness of Formation for Single Qubits
by
Borzumehr Toloui
Institute for Quantum Information Science at the University of Calgary
Coauthors: Dr. Gilad Gour, Dr. Barry C. Sanders
Almost all states and operations in the lab involve some degree
of mixedness, so it is necessary to extend the results of the newly
developed reference frame resource theories to include mixed states.
We produce, for the first time, explicit results for a qubit's frameness
of formation. The frameness of formation denotes the average resource
cost of generating a mixed state. This cost is measured in terms
of standard resource states, called refbits, that are chosen as
units of frameness. In order to determine the exact value of this
frameness measure, we develop a novel technique that generalizes
Wootter's idea for entanglement of formation to a wide class of
reference frame resource theories. We introduce the "concurrence
of frameness" as a generalization of the concurrence measure
to the case of reference frames. The concurrence of a resource state
is explicitly determined, and the cost of preparing a resource is
expressed as a simple function of this concurrence. This approach
is applicable to resource measures of any given group of transformations
associated with a superselection rule, as long as the related resource
cost can be written as an explicit function of the concurrence of
frameness. Finally, we demonstrate the application of our result
to the resource theories of the groups Z_2 and U(1) that are associated
with chiral and phase reference frames respectively.
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