Entanglement and Quantum Computing

A very active field of current research is the exploration of possible applications of entangled photons to communication, cryptography and quantum computation. 

Part I Role of entanglement in quantum computing and information processing... 

ROLE OF ENTANGLEMENT IN QUANTUM COMPUTING AND INFORMATION PROCESSING... 

Entanglement is a vital information resource employed in quantum teleportation, dense coding and quantum computation [Nielsen 2000], The fundamental role played by the entanglement in quantum information science was discussed in part I this part of the book is devoted to the generation and characterization of the entanglement of photons and their usage in quantum communication and computation protocols. 

One may envision extensions of the present approach to matter teleportation [Opatrny 2001] and quantum computation based on continuous variables [Braunstein 1998 (a) Lloyd 1998 Lloyd 1999], Such extensions may involve the coupling of entangled atomic ensembles in optical lattices by photons carrying quantum information. 

The general conclusion of the authors is that there is more to quantum information processing than entanglement and that, keeping in mind the limitations of room temperature liquid-state experiments, the NMR of these systems is an excellent test bed for the principles of quantum information and quantum computation. 

A desire to understand quantum entanglement is fueled by the development of quantum computation, which started in the 1980s with the pioneering work of Benioff [26], Bennett [27], Deutsch [28], Feynman [29] and Landauer [30] but gathered momentum and research interest only after Peter Shor s revolutionary... 

Besides quantum computations, entanglement has also been at the core of other active research such as quantum teleportation [32, 33], dense coding [34, 35], quantum communication [36], and quantum cryptography [37]. It is believed that the conceptual puzzles posed by entanglement have now become a physical source of novel ideas that might result in applications. 

In this chapter, we will focus on the entanglement behavior in QPT for the two-dimensional array of quantum dots, which provide a suitable arena for implementation of quantum computation [88, 89, 103]. For this purpose, the real-space renormalization group technique [91] will be utilized and developed for the finite-size analysis of entanglement. The model that we will be using is the Hubbard model [83],... 

Entanglement is the main resource of quantum information processing, without which quantum computation will not be faster than its classical counterpart [8] and quantum communication protocols will not work [113-115]. Moreover, as shown... 

Schrbdinger s verschrdnkung or entanglement is a quantum effect without classical analog and plays a key role in quantum computing [201,... 

But stakes are much higher. If quantum computers are to be one day constructed [27, 29,31,32], a proper understanding of quantum physics, including entangled states [32], is mandatory. Entanglement between objects, be they microscopic or macroscopic, does not make sense objects are classical entities with properties independent of any measurement, and this is so by definition. However, entanglement between quantum states sustained by macroscopic materials is more natural extension to present quantum views. 

Laflamme et al. s three-qubit system [103] is 26. In this molecule the two carbon nuclei are in different chemical environments and therefore represent two qubits, whilst the proton serves as the third. Compound 26 therefore represents the binary numbers 000, 001, 010, 011, 100, 110, and 111. A pulse of radio waves causes the nuclei to be thrown into the entangled superposition state, where they can act as qubits. The NMR machine then initiates the quantum computer program—a series of radiofrequency pulses that act like gates on the qubits and carry out the calculation. The superposition state is then collapsed to give an answer. 

A quantum computer thus has the capability of operating in a massively parallel mode. A 300-qubit quantum computer could theoretically store 2 10 bits of information, more than the estimated number of atoms in the known Universe, and also be capable of doing 2 ° simultaneous calculations. A classical computer can be likened to a solo musical instrument, a quantum computer to a full orchestra. If the music is well played, a symphony is much more profound than the sum of its parts. A major technical problem in constructing quantum computers is to minimize interactions within the machine and with the environment, which would cause decoherence—a breakdown in quantum entanglement. 

In this article I will discuss entanglement and its role in quantum information processing - especially, but not exclusively in the context of quantum computation. 

Quantum coherence is extremely sensitive to environmental interactions. This is a main stumbling block in the attempts to build quantum computers, and in spite of the fact that such devices are planned to be based on very weakly interacting systems (entanglement of photons or atoms well isolated in cavities) it is extremely difficult to preserve coherence over a sufficiently large number of basic operations steps. Coherent states in molecules are still more perturbed, as displayed for instance by the difference between the spectra of NHs and AsHs gases [Omnes 1994], Here, the H-atom in NH3 is delocalized in a quantum superposition, being on both sides of the //.rplane, while the spatial coherence of the heavier As-atom disappears during the time of observation which results in quite different optical properties. 

Here, we rq>ort related trapped-ion research at NIST on (1) the study of the dynamics of a two-level atomic system coupled to harmonic atomic motion, (2) the creation and characterization of nonclassical states of motion such as Schrodinger-cat superposition states, and (3) quantum logic for the generation of highly entangled states and for the investigation of scaling in a quantum computer. 

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