November 28, 2022

August 22-23, 2009
Canadian Quantum Information Student Conference



Optical implementation of a POVM measurement for photonic cluster-state quantum computing
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.


Zero discord
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)


A Quantum Algorithm for Approximating Partition Functions
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.


The Geometry of Anticoherent Spin States
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.


Measurement-induced entanglement localization on a three-photon system
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)


The Multiplicative Domain in Quantum Error Correction
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.


Remote state preparation: Quantum vs. Classical
Nathan Killoran
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.


Decoherence Supression via environment preparation
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.


Quantum walks with anyons
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.


Characterizing the Quantum Gate Fidelity
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.


Quantum Key Distribution at 810 nm Through Installed Fibre Optics
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.


Testing contextuality on quantum ensembles with one clean qubit.
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.


The Geometry of The Higher-Rank Numerical Range and its Implications in Quantum Data Error Correction
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.


The geometry of Schur maps and their application to the description of random unitary channels
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.


Approximating the Jones polynomial: an NMR experiment
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).


Optimal Protocols for Non-locality Distillation
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.


Atomic phase estimation using a composite method of adaptive feedback and multiple phase shifts
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).


Predicative Quantum Programming
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.


Frameness of Formation for Single Qubits
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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