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Quantum Theory
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
Quantum information theory seeks to address the usual questions of information theory with the assumption that information is now stored in a device which is quantum—one that harnesses the fundamental quantum principles of superposition, entanglement and measurement. What is astonishing about quantum information theory is not just that a new alphabet is being used, qubits instead of bits. Rather it is that information can be processed on quantum devices in a provably faster and more secure manner than on their non-quantum or ‘classical’ counterparts. In the past, increases in speed or security were due to the addition of faster mechanics and more durable materials. Quantum devices owe their efficiency not to greater horsepower but to the exercise of distinct principles of physics never before employed in information-carrying routines.
Enhancement of fidelity of quantum teleportation in a non-Markovian environment
Published in Gin Jose, Mário Ferreira, Advances in Optoelectronic Technology and Industry Development, 2019
Entanglement is one of the most striking features of quantum mechanics; it is also regarded as an important physical resource in quantum communication, computation, dense coding, and so on. As one of the possible applications of quantum information theory, teleportation is universally acknowledged as the most attractive quantum state transmission protocol, which allows an unknown quantum state to be transmitted between two parties (usually dubbed Alice and Bob) by using the resources of quantum entanglement and classical communication. In the seminal work of teleportation, Bennett and Brassard (1984) proposed a scheme for transporting an unknown single-body quantum state via single copy of the maximally entangled state as quantum channel. Later on, teleportation has been extensively investigated both experimentally and theoretically, ranging not only from two-level states to high-dimensional state regimes, but also from discrete variable to continuous variable domains (Bennett et al., 1993; Barrett et al., 2004; Pan et al., 2001; Wagner & Clemens, 2009; Jin et al., 2005). However, the practical implementation of any quantum information protocol has to face the problem of the unavoidable coupling of the quantum system with its environment. Indeed, real systems can never be perfectly isolated from the surrounding world (Zhang et al., 2010). It is therefore important to understand the impact of the coupling with a noisy environment on the stability of quantum protocols.
Photonics: A Dream of Modern Technology
Published in Tarun Kumar Gangopadhyay, Pathik Kumbhakar, Mrinal Kanti Mandal, Photonics and Fiber Optics, 2019
Sourangshu Mukhopadhyay, Shuvra Dey, Subhendu Saha
Just like classical logic gates, quantum logic gates are the main building block of the quantum computer. The information in a quantum computer is stored in the form of quantum bits, or qubits [14]. A qubit, the quantum analogue of the classical bit, is a unit of quantum information, which can represent both pure 0 and 1 states as well as the superposition states. The two states in which a qubit can be measured are known as basis states (or basis vectors). If Dirac notation is used to represent the quantum states corresponding to 0 and 1 as I0〉 and I1〉 respectively, then the general state of the qubit can be written in the following form: () Iψ〉=c0I0〉+c1I1〉
Quantum algorithm for the computation of the reactant conversion rate in homogeneous turbulence
Published in Combustion Theory and Modelling, 2019
Guanglei Xu, Andrew J. Daley, Peyman Givi, Rolando D. Somma
To describe the algorithm, a brief explanation of quantum computing is necessary. The elementary unit of quantum information in quantum computing is a qubit. Unlike classical computation, a qubit's state can be in a superposition of the 0 and 1 states. In standard notation, these states are described as and . The coefficients in the superposition can be complex and satisfy a normalisation condition [39]. A quantum computer is built upon many qubits (n) and a generic quantum state is then a superposition of all possible basis states. The number of such basis states grows exponentially with the number of qubits as . The allowed operations on the state of the quantum computer are unitary transformations, which are typically described as a sequence of simpler one and two-qubit operations. That sequence forms a quantum circuit whose complexity is mainly determined by the number of such simple operations. Each operation on the quantum state can modify all of its amplitudes, providing the opportunity to manipulate large amounts of data.
Precise positioning of an ion in an integrated Paul trap-cavity system using radiofrequency signals
Published in Journal of Modern Optics, 2018
Ezra Kassa, Hiroki Takahashi, Costas Christoforou, Matthias Keller
The field of atomic physics has advanced greatly since the advent of ion traps which confine ions for unprecedented durations without utilising the internal states of the ions. Because ion traps offer unparalleled levels of control over the ions’ mechanical and internal degrees of freedom, many experiments have sought to combine them with optical cavities for enhanced atom-light interactions. As a result, there have been a number of significant experiments: single photons were generated on demand [1], cavity sideband cooling was performed on single ions [2], super-radiance was observed with the collective coupling of coulomb crystals [3], tunable ion-photon entanglement has been demonstrated [4], multiple ions have been deterministically coupled to a cavity [5]. The combination of ion traps with optical cavities is also considered to be one of the most promising avenues for advances in quantum information processing. Whilst there has been remarkable progress in the preparation, gate operation and readout of qubits [6,7], to date, these implementations have been limited to small scales, with 14 being the largest number of qubits entangled [8]. Presently, challenges in the physical implementations of large quantum systems pose the greatest difficulty in advancing experimental quantum information science. Among the proposed solutions to tackle the scalability problem (e.g. [9–12]), distributed quantum information processing based on photonic links is the most promising. Notably, modular approaches using trapped ions as stationary qubits have attracted significant interest. However, so far, optically heralded entanglement with remote trapped ions has only been demonstrated using high numerical aperture lenses for the collection of photons, a method which suffers from low efficiencies in the entanglement generation[13,14]. Placing the ions in an optical cavity, this efficiency can be greatly enhanced. Further, by reducing the cavity mode volume, one can enhance the ion-cavity coupling and, subsequently, the efficiency of operations. To this end, fiber-based Fabry-Pérot cavities (FFPCs) have been combined with ion traps [15–17]. In such ion trap-cavity systems, the optimal positioning of the ion with respect to the cavity mode is of vital importance. In the previously demonstrated designs of ion traps combining FFPCs [15–17], the FFPCs were mechanically translated to optimise the overlap between the ion and the cavity mode. In addition to the need for a three-dimensional positioning system which tends to be bulky and expensive, the movable cavities affect the trapping field and shift the geometrical center of the trap as they are moved. This adds complexity to the trapping and optimisation of the ion-cavity coupling.