Requirement for quantum computation

We identify "proper quantum computation" with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish "no-go" theorems for classes of quantum optical experiments that cannot yield proper quantum computation, and we identify requirements for optical proper quantum computation that correspond to violations of assumptions underpinning the no-go theorems.Comment: 11 pages, no figure

Plasmon-enhanced quadrupolar transitions with nanostructured graphene

Many important molecules have quadrupolar excitations which occur at much slower rates than the competing dipolar transitions and hence are termed forbidden. In this work, we propose a new approach to enhance quadrupolar transitions using graphene nanostructures. We provide a detailed investigation of the enhanced transition rate in the vicinity of graphene nanoislands and use rigorous computational methods to analyze how this quantity changes with the geometrical and material parameters of the nanoisland. To support these calculations we also provide a semi-analytic approach. Finally, we investigate the performance of arrays of graphene nanoribbons, which constitutes a suitable platform for the experimental verification of our predictions. This work opens new possibilities for the enhancement and control of quadrupolar transitions of molecules and can find application in the detection of relevant chemical species

Quantum Encodings in Spin Systems and Harmonic Oscillators

We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for analyses of quantum vs classical computation, in practice qubits are often realized in higher-dimensional systems by truncating all but two levels, thereby reducing the size of the precious Hilbert space. We develop natural qudit gates for universal quantum computation, and exploit the entire accessible Hilbert space. Mathematically, we give representations of the generalized Pauli group for qudits in coupled spin systems and harmonic oscillators, and include analyses of the qubit and the infinite-dimensional limits.Comment: 4 pages, published versio

Geometric Phase in SU(N) Interferometry

An interferometric scheme to study Abelian geometric phase shift over the manifold SU(N)/SU(N-1) is presented.Comment: 14 pages, 1 figure, presented at the Doppler Institute-CRM meeting, (Prague, Czech Republic, June 18-22 2000

Geometric Phase of Three-level Systems in Interferometry

We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based on U(1)-invariant states, our scheme geodesically evolves U(2)-invariant states in a four-dimensional SU(3)/U(2) space and is physically realized via a three-channel optical interferometer.Comment: 4 pages, 3 figure

On the Determinants of the Value of Call Options on Default-Free Bonds

Models of interest-dependent claims that imply similar term structures and levels of interest rate volatility also produce similar estimates of bond option values. This result is established for simple option forms with known closed-form solutions as well as for more complex options that require numerical methods for evaluation. The finding is confirmed for a wide range of economic conditions, and it is robust with respect to the number and nature of factors that generate interest-rate movements.