Construction of an instrument for the measurement of educational philosophy

Thesis (M.Ed.)--Boston Universit

Strategies for enhancing quantum entanglement by local photon subtraction

Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyse different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimised set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximise the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.Comment: 13 pages, 11 figures. Updated version for publicatio

Quantum and Classical in Adiabatic Computation

Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialised state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose groundstate encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimisation algorithms and quantum adiabatic optimisation. This new perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing - though inconclusive - results

A constructive theory of the numerically accessible many-body localized to thermal crossover

The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $\nu=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$, resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [\v{S}untajs et al, 2019] and [Sels & Polkovnikov, 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.Comment: 27 pages, 12 figure

Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices

We study ground states and elementary excitations of a system of bosonic atoms and diatomic Feshbach molecules trapped in a one-dimensional optical lattice using exact diagonalization and variational Monte Carlo methods. We primarily study the case of an average filling of one boson per site. In agreement with bosonization theory, we show that the ground state of the system in the thermodynamic limit corresponds to the Pfaffian-like state when the system is tuned towards the superfluid-to-Mott insulator quantum phase transition. Our study clarifies the possibility of the creation of exotic Pfaffian-like states in realistic one-dimensional systems. We also present preliminary evidence that such states support non-Abelian anyonic excitations that have potential application for fault-tolerant topological quantum computation.Comment: 10 pages, 10 figures. Matching the version published Phys.Rev.

Advanced modulation technology development for earth station demodulator applications

The purpose of this contract was to develop a high rate (200 Mbps), bandwidth efficient, modulation format using low cost hardware, in 1990's technology. The modulation format chosen is 16-ary continuous phase frequency shift keying (CPFSK). The implementation of the modulation format uses a unique combination of a limiter/discriminator followed by an accumulator to determine transmitted phase. An important feature of the modulation scheme is the way coding is applied to efficiently gain back the performance lost by the close spacing of the phase points