| 1. |
- Johansson, Niklas, 1987-
(författare)
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A Resource for Quantum Computation
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we address the question, what is the resource, or property, that enables the advantage of quantum computers? The theory of quantum computers dates back to the eighties, so one would think there already is an answer to this question. There are several proposed solutions, but to this date, there is no consensus on an answer. Primarily, the advantage of quantum computers is characterized by a speedup for certain computational problems. This speedup is measured by comparing quantum algorithms with the best-known classical algorithms. For some algorithms we assume access to an object called oracle. The oracle computes a function, and the complexity of the oracle is of no concern. Instead, we count the number of queries to the oracle needed to solve the problem. Informally, the question we ask using an oracle is: if we can compute this function efficiently, what else could we then compute. However, using oracles while measuring a quantum speedup, we assume access to vastly different oracles residing in different models of computation.For our investigation of the speedup, we introduce a classical simulation framework that imitates quantum algorithms. The simulation suggests that the property enabling the potential quantum speedup is the ability to store, process, and retrieve information in an additional degree of freedom. We then theoretically verified that this is true for all problems that can be efficiently solved with a quantum computer.In parallel to this, we also see that quantum oracles sharply specify the information we can retrieve from the additional degree of freedom, while regular oracles do not. A regular oracle does not even allow for an extra degree of freedom. We conclude that comparing quantum with classical oracle query complexity bounds does not provide conclusive evidence for a quantum advantage.
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| 2. |
- Alarcón Cuevas, Alvaro, 1991-
(författare)
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A Few-Mode-Fiber Platform for Quantum Communication Applications
- 2022
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Society as we know it today would not have been possible without the explosive and astonishing development of telecommunications systems, and optical fibers have been one of the pillars of these technologies.Despite the enormous amount of data being transmitted over optical networks today, the trend is that the demand for higher bandwidths will also increase. Given this context, a central element in the design of telecommunications networks will be data security, since information can often be confidential or private.Quantum information emerges as a solution to encrypt data by quantum key distribution (QKD) between two users. This technique uses the properties of nature as the fundamentals of operation rather than relying on mathematical constructs to provide data protection. A popular alternative to performing QKD is to use the relative phase between two individual photon paths for information encoding. However, this method was not practical over long distances. The time-bin- based scheme was a solution to the previous problem given its practical nature, however, it introduces intrinsic losses due to its design, which increases with the dimension of the encoded quantum system.In this thesis we have designed and tested a fiber-optic platform using spatial-division- multiplexing techniques. The use of few-mode fibers and photonic lanterns are the cornerstone of our proposal, which also allow us to support orbital angular momentum (OAM) modes. The platform builds on the core ideas of the phase-coded quantum communication system and also takes advantage of the benefits proposed by the time-bin scheme. We have experimentally tested our proposal by successfully transmitting phase-coded single-photon states over 500 m few-mode fiber, demonstrating the feasibility of our scheme. We demonstrated the successful creation of OAM states, their propagation and their successful detection in an all in-fiber scheme. Our platform eliminates the post-selection losses of time-bin quantum communication systems and ensures compatibility with next-generation optical networks and opens up new possibilities for quantum communication.
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| 3. |
- Johansson, Niklas, 1987-
(författare)
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On the Power of Quantum Computation: Oracles
- 2018
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Quantum computation solve some computational problems faster than the best-known alternative in classical computation. The evidence for this consists of examples where a quantum algorithm outperforms the best-known classical algorithm. A large body of these examples relies on oracle query complexity, where the performance (complexity) of the algorithms is measured by the number of times they need to access an oracle. Here, an oracle is usually considered to be a black box that computes a specific function at unit cost.However, the quantum algorithm is given access to an oracle with more structure than the classical algorithm. This thesis argues that the two oracles are so vastly different that comparing quantum and classical query complexity should not be considered evidence, but merely hints for a quantum advantage.The approach used is based on a model that can be seen as an approximation of quantum theory, but can be efficiently simulated on a classical computer. This model solves several oracular problems with the same performance as their quantum counterparts, showing that there is no genuine quantum advantage for these problems. This approach also clarifies the assumptions made in quantum computation, and which properties that can be seen as resources in these algorithms.
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| 4. |
- Larsson, Jan-Åke, 1969-
(författare)
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Quantum paradoxes, probability theory, and change of ensemble
- 2000
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, the question "What kind of models can be used to describe microcosmos?" will be discussed. Being difficult and very large in scope, the question has here been restricted to whether or not Local Realistic models can be used to describe Quantum-Mechanical processes, one of a collection of questions often referred to as Quantum Paradoxes. Two such paradoxes will be investigated using techniques from probability theory: the Bell inequality and the Greenberger-Horne-Zeilinger (GHZ) paradox.A problem with the two mentioned paradoxes is that they are only valid when the detectors are 100% efficient, whereas present experimental efficiency is much lower than that. Here, an approach is presented which enables a generalization of both the Bell inequality and the GHZ paradox to the inefficient case. This is done by introducing the concept of change of ensemble, which provides both qualitative and quantitative information on the nature of the "loophole" in the 100% efficiency prerequisite, and is more fundamental in this regard than the efficiency concept. Efficiency estimates are presented which are easy to obtain from experimental coincidence data, and a connection is established between these estimates and the concept of change of ensemble.The concept is also studied in the context of Franson interferometry, where the Bell inequality cannot immediately be used. Unexpected subtleties occur when trying to establish whether or not a Local Realistic model of the data is possible even in the ideal case. A Local Realistic model of the experiment is presented, but nevertheless, by introducing an additional requirement on the experimental setup it is possible to refute the mentioned model and show that no other Local Realistic model exists.
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