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- Johansson, Niklas, 1987-
(author)
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A Resource for Quantum Computation
- 2021
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Doctoral thesis (other academic/artistic)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-
(author)
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A Few-Mode-Fiber Platform for Quantum Communication Applications
- 2022
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Licentiate thesis (other academic/artistic)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-, et al.
(author)
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Conjugate Logic
- 2023
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In: The Quantum-Like Revolution. - Cham : Springer. - 9783031129858 - 9783031129865 ; , s. 157-180
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Book chapter (peer-reviewed)abstract
- We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about outcomes of future observations on some systems. For a quantum system, these predictions are statements about future outcomes of measurements performed on specific degrees of freedom of the system. The proposed logic will include propositions and their relations, including connectives, but importantly also transformations between propositions on conjugate degrees of freedom of the systems. A key point is the addition of a transformation that allows to convert propositions about single systems into propositions about correlations between systems. We will see that subtle choices of the properties of the transformations lead to drastically different underlying mathematical models; one choice gives stabilizer quantum mechanics, while another choice gives Spekkens’ toy theory. This points to a crucial basic property of quantum and quantum-like systems that can be handled within the present conjugate logic by adjusting the mentioned choice. It also enables a discussion on what behaviors are properly quantum or only quantum-like, relating to that choice and how it manifests in the system under scrutiny.
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