arXiv subjects
Publications and source records attributed to S. Parker.
It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an arbitrary mixed state is sufficient to implement Shor's factorization algorithm efficiently.
This report summarizes a study of the physics potential of the CLIC e+e- linear collider operating at centre-of-mass energies from 1 TeV to 5 TeV with luminosity of the order of 10^35 cm^-2 s^-1. First, the CLIC collider complex is surveyed, with emphasis on aspects related to its physics capabilities, particularly the luminosity and energy, and also possible polarization, γγand e-e- collisions. The next CLIC Test facility, CTF3, and its R&D programme are also reviewed. We then discuss aspects of experimentation at CLIC, including backgrounds and experimental conditions, and present a conceptual detector design used in the physics analyses, most of which use the nominal CLIC centre-of-mass energy of 3 TeV. CLIC contributions to Higgs physics could include completing the profile of a light Higgs boson by measuring rare decays and reconstructing the Higgs potential, or discovering one or more heavy Higgs bosons, or probing CP violation in the Higgs sector. Turning to physics beyond the Standard Model, CLIC might be able to complete the supersymmetric spectrum and make more precise measurements of sparticles detected previously at the LHC or a lower-energy linear e+e- collider: γγcollisions and polarization would be particularly useful for these tasks. CLIC would also have unique capabilities for probing other possible extensions of the Standard Model, such as theories with extra dimensions or new vector resonances, new contact interactions and models with strong WW scattering at high energies. In all the scenarios we have studied, CLIC would provide significant fundamental physics information beyond that available from the LHC and a lower-energy linear e+e- collider, as a result of its unique combination of high energy and experimental precision.
We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initally maximally mixed qubits (S. Parker and M. B. Plenio, Phys. Rev. Lett. 85, 3049 (2000)) . This leads us to ask how this affects the entanglement in the algorithm. We thus investigate the behaviour of entanglement in Shor's algorithm for small numbers of qubits by classical computer simulation of the quantum computer at different stages of the algorithm. We find that entanglement is an intrinsic part of the algorithm and that the entanglement through the algorithm appears to be closely related to the amount of mixing. Furthermore, if the computer is in a highly mixed state any attempt to remove entanglement by further mixing of the algorithm results in a significant decrease in its efficiency.
We develop theoretical and numerical tools for the quantification of entanglement in systems with continuous degrees of freedom. Continuous variable entanglement swapping is introduced and based on this idea we develop methods of entanglement purification for continuous variable systems. The success of these entanglement purification methods is then assessed using these tools.