Browsing Mathematics (Faculty of) by Subject "quantum information"
Now showing items 1-20 of 27
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Algebraic and combinatorial aspects of incidence groups and linear system non-local games arising from graphs
(University of Waterloo, 2019-06-06)To every linear binary-constraint system (LinBCS) non-local game, there is an associated algebraic object called the solution group. Cleve, Liu, and Slofstra showed that a LinBCS game has a perfect quantum strategy if and ... -
Analysis of Light-Matter Systems
(University of Waterloo, 2022-01-18)In this thesis we introduce the simplest model of a two–level system coupled to a single mode of an optical cavity, called the Jaynes-Cummings model. This model is then extended to an ensemble of identical two-level systems ... -
Classical Authenticated Key Exchange and Quantum Cryptography
(University of Waterloo, 2009-03-16)Cryptography plays an integral role in secure communication and is usually the strongest link in the chain of security. Yet security problems abound in electronic communication: spyware, phishing, denial of service, and ... -
Concentration Bounds from Parallel Repetition Theorems
(University of Waterloo, 2018-08-22)This thesis contributes to the study of parallel repetition theorems and concentration bounds for nonlocal games and quantum interactive proofs. We make the following contributions: - A lemma that is useful for converting ... -
Correlation and Communication via a Quantum Field
(University of Waterloo, 2019-07-15)We study the ability of qubit detectors to i) extract correlations from, and ii) transmit quantum information through, a quantum field. We start by perturbatively studying the harvesting of correlations from thermal and ... -
Entanglement in single-shot quantum channel discrimination
(University of Waterloo, 2018-08-30)Single-shot quantum channel discrimination is the fundamental task of determining, given only a single use, which of two known quantum channels is acting on a system. In this thesis we investigate the well-known phenomenon ... -
Exploring Practical Methodologies for the Characterization and Control of Small Quantum Systems
(University of Waterloo, 2018-09-04)We explore methodologies for characterizing and controlling small quantum systems. We are interested in starting with a description of a quantum system, designing estimators for parameters of the system, developing robust ... -
Extended Nonlocal Games
(University of Waterloo, 2017-03-31)The notions of entanglement and nonlocality are among the most striking ingredients found in quantum information theory. One tool to better understand these notions is the model of nonlocal games; a mathematical framework ... -
Honest Approximations to Realistic Fault Models and Their Applications to Efficient Simulation of Quantum Error Correction
(University of Waterloo, 2014-04-25)Understanding the performance of realistic noisy encoded circuits is an important task for the development of large-scale practical quantum computers. Specifically, the development of proposals for quantum computation must ... -
Information flow at the quantum-classical boundary
(University of Waterloo, 2008-08-28)The theory of decoherence aims to explain how macroscopic quantum objects become effectively classical. Understanding this process could help in the search for the quantum theory underlying gravity, and suggest new schemes ... -
Information propagation and entanglement generation between two Unruh-DeWitt detectors
(University of Waterloo, 2010-07-23)The setup in which two quantum systems, Alice and Bob, communicate using bosonic field quanta can be viewed as a prototype for wireless quantum communication. In this thesis we focus on the most basic case, where Alice ... -
Measurements of quantum fields and the Unruh effect: a particle detector perspective
(University of Waterloo, 2021-11-19)This thesis is devoted to the study of detector models in quantum field theory. A detector model aims to describe a hypothetical physical situation, realistic or not, in which a measurement is performed on a quantum field ... -
Near-optimal quantum strategies for nonlocal games, approximate representations, and BCS algebras
(University of Waterloo, 2023-05-04)Quantum correlations can be viewed as particular abstract states on the tensor product of operator systems which model quantum measurement scenarios. In the paradigm of nonlocal games, this perspective illustrates a ... -
Non-local Quantum Systems with Infinite Entanglement
(University of Waterloo, 2022-08-18)The study of quantum entanglement under quantum information has mostly been done in the mathematical model of tensor product of Hilbert spaces. In infinite dimensions, this model cannot capture all cases of non-local ... -
On the Hardness of the Quantum Separability Problem and the Global Power of Locally Invariant Unitary Operations
(University of Waterloo, 2008-09-18)Given a bipartite density matrix ρ of a quantum state, the Quantum Separability problem (QUSEP) asks — is ρ entangled, or separable? In this thesis, we first strengthen Gurvits’ 2003 NP-hardness result for QUSEP by showing ... -
Parallel Repetition of Prover-Verifier Quantum Interactions
(University of Waterloo, 2012-01-05)In this thesis, we answer several questions about the behaviour of prover-verifier interactions under parallel repetition when quantum information is allowed, and the verifier acts independently in them. We first ... -
Quantum Indefinite Spacetime: Part II
(University of Waterloo, 2018-09-10)We adopt an operational mode of thinking to study spacetime fluctuations and their impacts on questions of quantum gravity. Particular emphasis is put on studying causal structure fluctuations. The study is guided by the ... -
Quantum information in security protocols
(University of Waterloo, 2022-01-18)Information security deals with the protection of our digital infrastructure. Achieving meaningful real-world security requires powerful cryptographic models that can give strong security guarantees and it requires ... -
Quantum Information Processing with Adversarial Devices
(University of Waterloo, 2010-06-09)We consider several applications in black-box quantum computation in which untrusted physical quantum devices are connected together to produce an experiment. By examining the outcome statistics of such an experiment, and ... -
Quantum State Local Distinguishability via Convex Optimization
(University of Waterloo, 2015-08-24)Entanglement and nonlocality play a fundamental role in quantum computing. To understand the interplay between these phenomena, researchers have considered the model of local operations and classical communication, or LOCC ...